Application of the Rolls-Royce Inverse Model to Trent Aero Engines

Shahid Mahmood

MSc in Control Systems

August 2001

ABSTRACT

Within gas turbine technology, the traditional, classical control is dominant in both the industrial and aerospace sectors. Some military aircrafts, however, use advanced nonlinear control techniques. This project analyses the design and subsequent performance of one such technique called the Rolls-Royce Inverse Model (RRIM) control. It embeds the inverse engine dynamics into the control law in order to calculate the amount of fuel necessary to fulfil the engine acceleration demand.

This nonlinear technique can be closely tailored to the nonlinearities of the engine dynamics and reduces the number of control parameters to be tuned to just a single gain for each loop. The results of the study detailed here indicate that this technique may work adequately for the civil engines as well, proving more robust to plant/model mismatch, and result in a reduction in control design time.

This report introduces the RRIM in detail and explains its application to a Trent series aero engine. A comparison is then made between the response of the engine with the RRIM control and that with the traditional control.

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EXECUTIVE SUMMARY

INTRODUCTION/BACKGROUND

This project is an application of the Rolls-Royce Inverse Model (RRIM) to a Trent series engine. The RRIM is an advanced nonlinear control technique applied in some military aircraft engines. The project is performed to investigate the feasibility of applying the RRIM control to a civil aircraft engine. The engine that is selected from the civil aerospace is a Trent series engine that is a high bypass ratio turbofan.

AIMS AND OBJECTIVES

Rolls-Royce plc. wanted to test the RRIM control for a civil engine application. The application of the nonlinear RRIM controller in the simulation-based Electronic Engine Control (EEC) was the first target. The response of the RRIM controller was also to be compared with that of the traditional controller taken as a standard.

ACHIEVEMENTS

Individual control loops were designed for each of the control parameters of the engine. The control loops were then combined together in the EEC. The performance of the controller was compared with an existing traditional controller’s response in the light of some professional criteria both for slam and slow manoeuvres. Requirements for fuel shape, rise time and overshoot etc. were taken into consideration. Both the logical and structural explanations of the controller were used to analyse the performance theoretically. The stability of the control design was investigated using classical tools applied to the linearized control loop. Estimates on computational burden and vulnerability to sensor noise were also analysed. The sea level design was also tested for a high altitude static condition.

CONCLUSIONS / RECOMMENDATIONS

This project is an introductory application of the advanced nonlinear RRIM control in a civil gas turbine engine. The controller performance is comparable with that of the traditional controller. The traditional control design technique is based upon parameter scheduling, a cumbersome design for the gas turbine engine, while the new technique is easy, simple and saves upon time. The performance of the controller is quite robust in that the sea level design is quite satisfactory for the cruise altitude as well.

The new control scheme can be seen, on the basis of results achieved in this project, as a strong candidate for the nonlinear control of a civil gas turbine engine. More work should be done in all areas including designing the rules for tuning the RRIM controller, investigating robustness both in the linear and nonlinear domains, comparing the response with that of a traditional controller more rigorously and precisely, and application to the engine as a multi-input, multi-output system.

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ACKNOWLEDGEMENTS

I thank God Almighty who gave me health and courage to hard on this project. I am proud of the valuable supervision of Professor P J Fleming and acknowledge his personal interest in the project that was a great source of motivation for me. I thank Dr J A Rossiter for his time and interest as a Second Reader of this project. I acknowledge the thorough help from Dr I Griffin at all stages in the project. I would also thank all of the research team members working in the Real Time Laboratory who always welcomed me to discuss any matter and solve any problem in the project. I would also thank Mr I Durkacz from the programming staff who always helped me in solving computer system problems.

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TABLE OF CONTENTS Abstract ii Executive Summery iii Acknowledgements iv List of Symbols ix 1 INTRODUCTION 1 1.1 The Engine Control Systems 1

1.1.1. The Traditional Control of Engine 2 1.1.2. The New Trend 3

1.2 The Project Focus 3 1.3 The Working Environment 4 1.4 List of Achievements 4 1.5 A Brief Review of the Dissertation 5 2 BACKGROUND 6 2.1 The Aero Engine 6

2.1.1. The Jet Engine 6 2.1.2. Turbofans 8

2.2 Some Aerospace Terms and Definitions 9 2.3 The RRAP Engine Models 10

2.3.1. Access to Engine Model 10 2.3.2. Model Description 11 2.3.3. Basic Modelling Elements 12

2.4 Gas Turbine Engine Control Problem 14 2.4.1. Thrust Control 14

2.4.1.1. Ratings Function 15 2.4.2. Limiters 15 2.4.3. Acceleration and Deceleration Control 15

2.5 The Engine Control Problem 16 2.5.1. Selector Control 16 2.5.2. Selector Control for a Gas Turbine Engine 17 2.5.3. Selector Control Design 17 2.5.4. Actuator 20 2.5.5. Sensors 21

2.6 Performance Requirements of Trent Engine 22 2.6.1. EPR Control 22 2.6.2. Minimum Nl Limit 23 2.6.3. Minimum Nh Limit 23 2.6.4. Minimum T30 Limit 23

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2.6.5. Minimum P30 Limit 24 2.6.6. Maximum Nl Limit 24 2.6.7. Maximum Ni Limit 25 2.6.8. Maximum Nh Limit 25 2.6.9. Maximum P30 Limit 26 2.6.10. ACU Schedule 26 2.6.11. Backup ACU Schedule 26 2.6.12. DCU Schedule 27

2.7 Control Implementation 27 2.7.1. Digital Engine Control 27 2.7.2. FADEC 28 2.7.3. Real Time Control 28 2.7.4. Loop Interference 29

3 GAS TURBINE ENGINE CONTROL 30 3.1 Traditional Control of Trent 30

3.1.1. Control Specifications in Traditional Control 32 3.2 Advanced Control of Gas Turbine Engines 32

3.2.1. Why Nonlinear Control? 32 3.3 Nonlinear Control 33

3.3.1. Nonlinear Control Problem 34 3.3.2. Control Specifications in Nonlinear Control 35 3.3.3. Conventionnel Nonlinear Control Techniques 35

3.4 Inverse Modelling Control 37 3.5 RRIM Control 38

3.5.1. Advantages Expected from RRIM Control 39 3.5.2. The RRIM Control Procedures 39 3.5.3. Why Modelled Speed in RRIM? 40 3.5.4. Source of Nhdot Demand 41 3.5.5. Functional Description of Gain 42

4 RRIM CONTROL DESIGN 43 4.1 RRIM Tables 43

4.1.1. Transient Response 44 4.1.2. Steady State Plot 46 4.1.3. Dynamic Response Curve 46 4.1.4. Traditional Scheme in Fuel Scheduling 49

4.2 From Traditional to RRIM 50 4.2.1. ACU Demand 51 4.2.2. DCU Demand 52 4.2.3. The Control Loop Structure in Rate Control 53

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4.2.4. Backup ACU 54 4.2.5. Two-stage Selector Control 55

4.3 Fuel Feedback to RRIM 58 4.4 Tuning Gains in Frequency Domain 59

4.4.1. Why Frequency Domain Analysis? 59 4.4.2. Linearization Procedures 59

4.5 Gains Tuning in Time Domain 62 4.5.1. Verification of Frequency Domain Analysis 62 4.5.2. Avoiding Linearization 63 4.5.3. Criteria for Tuning a Nonlinear Control System 64

4.6 Summary 66 5 PERFORMANCE OF RRIM CONTROL 67 5.1 The Analysis Procedures 67 5.2 Loop in Control Index 68 5.3 Slam Acceleration 70

5.3.1. Pass-off Test Criteria for Slam Acceleration 70 5.3.2. Comparison in Slam Acceleration 70

5.4 Slam Deceleration 75 5.4.1. Pass-off Test Criteria for Slam Deceleration 75 5.4.2. Comparison in Slam Deceleration 76

5.5 Slow Acceleration 80 5.5.1. Pass-off Test Criteria for Slow Acceleration 80 5.5.2. Comparison in Slow Acceleration 81

5.6 Slow Deceleration 83 5.6.1. Pass-off Test Criteria for Slow Deceleration 83 5.6.2. Comparison in Slow Deceleration 84

5.7 Altitude Test 86 5.8 Noise Test 89 5.9 Response of Mixed Control Design 90 5.10 Computational Burdon 90

5.10.1. Interpolating Tables 91 5.10.2. Computing Control Demand 92

5.11 Conclusions 92 6 CONCLUSIONS AND RECOMMENDATIONS 94 6.1 Using RRAP Models from Xmath 94 6.2 Using SystemBuild 95 6.3 Modelling Errors in RRIM 96 6.4 Linearization of RRIM Control Loop 98

6.4.1. What is a RRIM Controller? 100

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6.4.2. Another Interpretation of RRIM 102 6.4.3. Auto Scheduling in RRIM Control 103 6.4.4. Verification of Linear Model 104 6.4.5. Linearization in MATRIXx 105

6.5 Error Analysis in ACU and DCU 106 6.5.1. Error in Traditional ACU/DCU 107 6.5.2. Error in RRIM ACU/DCU 108 6.5.3. Open Loop ACU/DCU in RRIM Control 108

6.6 Tuning RRIM Gains in Time Domain 110 6.7 Why Splitting Control Action in Selector Control? 112 6.8 Conclusions 113 6.9 Further Work and Recommendations 114

6.9.1. Linearization of the Control Loop 114 6.9.2. Time Domain Tuning 115 6.9.3. Further Tuning 115 6.9.4. Performance Analysis 115 6.9.5. Singularities in Inverse Modelling 115 6.9.6. Linearization of the Control Loop 115 6.9.7. Acceleration Demand in RRIM Controller 116 6.9.8. Different Rate Demands for Different Loops 116 6.9.9. RRIM-type Controllers 116 6.9.10. MIMO RRIM Controllers 117

Appendix A A-1 Appendix B B-2 Appendix C C-7 Appendix D D-10 Appendix E E-15 Appendix F F-21

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LIST OF SYMBOLS

dF Overfueling (fuel increment) (lb/hr) EEC Electronic engine control F Fuel flow (lb/hr) Fdot Rate of change of fuel flow demand (lb/hr/s) FMS Fuel Metering System FN Thrust Fss Steady state fuel flow (lb/hr) GTE Gas turbine engine HB Handling Bleed HP High pressure IP Intermediate pressure LCI Loop-in-Control Index LP Low pressure LSL Loop selection logic MP Minimum phase Nh/N3 HP spool speed Nhdot HP spool acceleration Nhdotm Modelled Nhdot Nhm Modelled Nh Ni/N2 IP spool speed Nl/N1 LP spool speed NMP Nonminimum phase MP Mimnimum phase PLA Pilot’s Liver Angle RRAP Rolls-Royce Aero-thermodynamic Performance RRIM Rolls-Royce Inverse Model SLS Static sea level TRA Throttle Resolver Angle (the same as PLA) VIGV Variable Inlet Guide Vane VSV Variable Stator Vane WFE Same as F

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Chapter 1 Introduction

Gas turbine engines (GTEs) have a wide application in aircrafts, automotives and the industrial sector. Different types of gas turbine engines e.g., turbojet, turboprop and turbofan etc. are used in different applications. A turbofan from the civil aircraft engines is selected in this project to examine the performance of an advanced nonlinear controller. A turbofan combines the advantages of a jet type and a propeller type GTE and trade-off is achieved, in principle, by the size of a bypass duct around the jet core of a turbofan. The bypass ratio of a turbofan is a technical measure of the size of bypass duct.

There are two major classes in GTEs used in aircraft application with respect to the areas of application namely the civil and the military aircraft engines. These are, of course, two entirely different areas of application with different requirements of speed, power, take off and landing conditions, manoeuvrability, and flight altitudes even with a same type of engine, say, turbofan. Turbofans appear with different bypass ratios in the two areas. The civil aircraft engines, e.g., the Trent series, fall in high bypass ratio category where as military aircraft engines, in general, lie close to a turbo-jet with a low bypass ratio. This project takes the idea of an advanced controller from a military class engine and is aimed upon seeking its feasibility for the civil class turbofan.

1.1 The Engine Control Systems The engine control problem is to find the amount of fuel that can fulfil the pilot’s demand on engine power or thrust. If pilot does not send a demand, a power/thrust schedule keeps the engine in normal operating condition. The engine follows this schedule until the pilot wants to raise or lower the power level. The engine control, in this case, regarded as the thrust control of the engine.

The engine control problem is much more complex than just a thrust control problem. Air is processed through the engine at very high pressures. Fuel is burnt in the combustor that generates very high temperatures in combustor and turbine. The engine materials cannot tolerate very high temperature and/or pressure. Besides physical stability of the engine systems, there are functional limits on temperature and pressure that ensure a normal operation of the engine. A flameout, for example, may occur at very low or very high-speed air mass flow around the flame. The compressor cannot maintain a steady laminar flow at pressure above a limit and can exhibit stall and surge giving rise to unacceptable performance of the engine. The compressor should, therefore, work above an idle speed

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and below a maximum limit. The limits on temperature and pressure generate separate limits on each shaft speed. Even if there were no limits on temperature, shaft speeds are a question of wear and tear, engine life and its integrity. The fan, for example, has long blades and will tear apart if rotated above a maximum allowable speed. The engine problem becomes even more complex due to the limits on rate of change of speed along with the speed itself. The speed cannot be increased/decreased too rapidly. The acceleration/deceleration control units are designed to take over the control of the engine in the case of slam acceleration/deceleration produced by thrust request of the pilot.

All of the outputs are sensed continuously along with the pilot’s request for the engine power level. The engine must be operated within safety bounds of temperature and pressure and spool speeds. A slam action performed by the pilot can push the engine to surge or stall conditions and is effectively blocked by the acceleration and deceleration control units. And all this is required mainly from the control of fuel input. The single-input, multi-output engine system, like most of the industrial processes, is traditionally dealt as a single-input, single-output (SISO) system in that only one output is taken into care at any time, the other outputs are supposed to be within their normal bounds.

The overall engine control problem is inevitably large. A controller designed for steady state engine operation is also equipped to cope with the situations when engine parameters like temperature, pressure and spool speeds hit their boundaries. All these limits are handled by fuel injection control and positioning of some guide vanes in the engine that change the local direction of flow at different parts of the engine. The engine can, therefore, be viewed as two-input, multi-output system.

Problem Simplification

The major control function in all of the above cases is fuel flow but there are other control variables such as Variable Stator Vanes (VSVs) control and Handling Bleed (HBs) control. These two components are controlled variables and are activated, mainly, to prevent surge and stall. The discussion on VSV and bleed valve control is beyond the scope of this report. Similarly there are other issues such as light up, starting and acceleration to idle etc. and have their own requirements, other than those for the engine in normal mode. These are also not discussed in this report.

1.1.1. The Traditional Control of Engine The use of classical control techniques, both in civil and many military aircrafts, has been a tradition even in the modern aircrafts of the day. But why a tradition of using a classical linear control for nonlinear systems, such as aircrafts and in general all gas turbine engines, is kept on? The answer is that classical control is simple and it works to a certain level of satisfaction.

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The traditional scheme is based upon ‘parameter scheduling, which is a primitive idea of designing a nonlinear controller using linear control techniques. In parameter scheduling, the nonlinear system is linearized at a number of operating points and a linear controller is designed for the linearized system. At the end, the control designer comes up with a series of controllers for a single system such that control parameters are scheduled against any engine parameter that can be a depictive of the operating point. Controller parameter values for the intermediate points are obtained from its schedule by linear interpolation. The controller as a whole is nonlinear because it has nonlinear parameter schedules.

1.1.2. The New Trend The aero engine is a nonlinear multivariable system because the engine power is not a linear function of fuel input or engine speed. Nonlinear control is becoming a popular area of research these days and a lot of nonlinear control techniques have been introduced such as adaptive control, nonlinear robust control and sliding mode control. The idea behind this new trend of research is that a nonlinear controller is more robust and performs better in face of nonlinearities. Some military aircrafts, for example, use advanced control schemes that fall in the area of nonlinear control.

The advanced control investigated in this report named as Rolls-Royce Inverse Model (RRIM) control is nonlinear. The RRIM controller uses data derived from engine tests to find the amount of fuel necessary to fulfil an acceleration demand. It is actually the inverse of what an engine does when fuel is injected into it. That is why it is called an inverse model based controller and takes its name as Rolls-Royce Inverse Model control.

1.2 The Project Focus The project takes the idea RRIM controller from a military engine and applies it to a three-spool Trent series turbofan. The project focuses upon investigating the performance of the advanced nonlinear controller for a civil Trent series turbofan. From the idea that nonlinear controllers can perform better in face of nonlinearities, it was expected that the RRIM controller used in military aircrafts is also a better choice for the civil aircraft engine. Moreover, the traditional scheme of seeking nonlinear control behaviour out of a combination of linear controllers can be eased, if not completely avoided, by using the RRIM controller. The expected performance of the RRIM controller is investigated in this project.

This project introduces the structure of the RRIM controller, its possible interpretations, implementation to the Trent aero engine (a turbofan) and comparison of it with the traditional controller in terms of performance, ease of design, computational burden and vulnerability to sensor noise etc.

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1.3 The Working Environment This project is carried out at Rolls-Royce University Technology Centre (UTC) in the department of Automatic Control and Systems Engineering in collaboration with Rolls-Royce. The project work was done in technical support from Rolls-Royce.

The controller was applied in a simulation-based Electronic Engine Control (EEC) of the Trent engine. The engine model is written is FORTRAN and belongs to the class of turbofan aero engine models called the Rolls-Royce Aero-thermodynamic Performance (RRAP) models. The RRAP models are used in the design and development of the Trent engine.The EEC is implemented in MATRIXx, a simulation bench designed to access engine models via shared memory/semaphore.

MATRIXx is a combination of Xmath and SystemBuild. The two components are similar to Matlab and Simulink respectively. MATRIXx provides support for design and development of engine control systems. Matlab involved in the project in the classical analysis of the controller using linearization. The use of Matlab, instead of MATRIXx, was adopted because of hands on experience and convenience to produce this report.

1.4 List of Achievements Many simulation problems were faced and solved during the course of

familiarization with the engine-modelling environment of MATRIXx.

Individual control loops were designed for each of the engine control parameters. The controller parameters were tuned in time domain to fulfil the design requirements on rise time, settling time and overshoot.

The nonlinear controller was investigated, through linearization, for the design requirements of bandwidth, gain margin and phase margin that were found satisfactory.

A mixed design approach was found to combine the traditional design of acceleration and deceleration control units (ACU and DCU) with the nonlinear RRIM controller.

The ACU and DCU, as demanded by the new RRIM design approach, were designed to complete the nonlinear design exclusively based upon the RRIM.

Two of, perhaps, many possible structural explanations of the controller were found that may give the reader new ideas of looking at the RRIM controller and derive its possible variants to broaden its application the systems other than GTEs.

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The performance of the RRIM controller was analysed against the original pass-off test criteria for the real engine response and found adequate to slow ramp and slam acceleration commands.

1.5 A Brief Review of the Dissertation Chapter 2 introduces the Gas Turbine Engines (GTEs) and some essential terms and conventions relating to this area. It briefly explains the engine control problem and the conventional selector control approach common to both the traditional and the advanced control of the engine. Design specifications of the nonlinear Trent series engine are also given in this chapter.

Chapter 3 describes the general nonlinear control problem and the inverse dynamics control as a particular case. The traditional control scheme is introduced along with the RRIM control scheme to elaborate the difference between the two. It introduces the RRIM controller and explains its functionality in detail.

Chapter 4 hilights the design changes in the traditional EEC proposed by the application of the RRIM controller. It defines the tuning procedure for the RRIM controller in time. The linearized control loop is also discussed to achieve frequency domain specifications.

Chapter 5 compares the performance of the RRIM controller with that of the traditional controller passing both through test-pass criteria for steady state performance. It also compares the two control techniques for robustness, ease of tuning, vulnaribility to sensor noise and computational burdon etc.

Chapetr 6 reviews all critical issues considered in in this project and recommends future course of action on each. It also provides structural interpretation of the RRIM to recommend future mathematical work. Conclusions are derived through out discussions. It ends up with the concluding remarks and proposed future work in this project.

Since the project is carried on a real and very complex simulation-based system, the use of abbreviations is conventional and unavoidable. The abbreviations used in the design of controller are less standard and more professional due to the practical aspect of the project. A list of abbreviations is given at the start of the thesis.

References to books within the text are given by the authers’s last name. Any reference to Rolls-Royce property data also includes ‘RR’ along with the auther’s name and is not accessible by a person not related to the project.

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Chapter 2 Background

2.1 The Aero Engine The aero engine, which is a gas turbine engine, works on the basic principle known as Newton’s third law of motion which says that reaction is always equal and opposite to the action. In practice, air is accelerated and exhausted at extremely high speed from the rear of the engine to produce the required thrust. The amount of thrust achieved is equal to the mass of the air leaving the engine (lb/hr) multiplied by the difference of exhaust and intake velocities. If mass of the air plays a dominant part in propulsion, the engine is of propeller type otherwise a jet. A big advantage of a jet is that it does not suffer from high tip speed effect, which restricts the design of propeller aircraft for a speed well below the speed of sound. Jets, which are gas turbine engines are designed for high subsonic speeds in the civil and high supersonic speeds in the military areas of application [The Jet Engine (1989)]. Turbofan is a compromise between trade offs set by advantages and disadvantages of a pure turbojet and a pure turboprop.

The engine considered in this project is a Trent series engine. The Trent series engine is a turbofan with a high bypass ratio. The core of a turbofan is a jet engine that serves two purposes:

It produces jet thrust to share a certain fraction of the net thrust which is lesser with higher bypass ratio, and

It derives turbines that rotate the fan and compressor stages. The inlet fan produces airflow through the bypass duct.

It is, therefore, the jet operation that explains the basic principle of an aero engine or, in general, a gas turbine engine (GTE). The rest of an engine, that defines the type of an engine, is how the jet power is exploited.

2.1.1. The Jet Engine The schematic of Figure 2.1 shows major jet engine components. Different stations along the engine are labeled by numbers, 0, 1, 2,., and the engine industry follows, more or less, the same station labeling standard. These station numbers are given in Appendix D. Air enters from free stream into the leading edge. The air accelerates from free stream if the engine is static or diffuses from the free stream (ram conditions) in high Mach flight

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conditions. In both cases, it is accelerated by the compressor. The temperature and pressure of the air increase as a result. A typical compression ratio may lie between 4:1 and 25:1. The compressed air then diffuses into the combustion chamber where it is burnt to increase the temperature and pressure. The temperature in the combustor falls in the range 1100 K to 2000 K [Walsh and Flecher (2000)]. This hot air is passed through the turbine to be expanded into the atmosphere from the rear of the engine in order to produce jet thrust. Turbine absorbs a part of the jet power to operate compressors, leaving the rest to exhaust through the jet nozzle in order to produce jet thrust.

0 1 7 3 4 8

Flight intake Nozzle

Combuter Jet pipe

Engine intake Compressor

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Turbine

Figure 2.1 Conventional turbojet.

In pure jet engine, turbines are designed to absorb minimum power to maximize the jet thrust. In advanced turbofans, the hot jet exhaust produces as low as one quarter of the total engine thrust; the rest is produced by the cold exhaust coming from the bypass duct.

The Ram jet is the special class of jet engines where there is no mechanical compressor and compression is achieved by operating the engine at very high Mach (Mach 3). The term ‘ram’ may also be used in defining engine properties that are not associated with the dynamic components such as ram-ratio, which is defined for the free stream ram conditions of the inlet air volume (labeled station ‘0’ in jet engine schematics).

2.1.1.1. Compressor

The purpose of the compressor is to increase the total pressure of the gas stream to the level required by the engine cycle. A fan is, normally, the first stage of a multi-stage compressor as it is in a Trent engine. Compressor is a component of the engine that can be unstable in certain situations. Stall is one of the undesirable conditions that appears when the airflow separates from the compressor blades. In a multistage compressor, stall may be acceptable at front stages during a normal start up. If the stall is, however, severe or appears suddenly, it may drastically deteriorate the engine performance.

Surge can occur in conditions if the pressure ratio across the compressor reaches the surge line at which the flow of the air reverses. This situation can arise at any power level if the other components operate in a way to push the compressor to surge line. It can be thought

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as worst-case stall where the blades cannot support the adverse pressure conditions. Surge appears as a loud bang when part of the flow reverses to low pressure. Variable inlet guide vanes (VIGVs) are used to change the inlet flow and hence the compressor map.

2.1.1.2. Turbines

Turbines drive the compressors. The hot burnt gases are expanded to the outlet nozzle of the engine through the turbine. Turbines absorb a part of exhausting gases to rotate the spools and fan/compressors in turn. Turbines are one of the stable sub-systems of the engine.

2.1.2. Turbofans A pure turbojet is very noisy and inefficient. Turbofan is one of the variants of a pure turbojet. Both of the civil and military Turbofan engines work on the same construction principle. A large fan at the front of the engine accelerates the incoming air. This air is then distributed between the compressor in the centre and a bypass duct around the compressor. Figure 2.2 shows a schematic of a two-spool turbofan engine having low pressure (LP) and high pressure (HP) compressors and turbines. Trent is a turbofan with three spools, with an additional intermediate pressure (IP) compressor and turbine.

0 1,11 7 3 4 8

Flight intake

Hot Nozzle

Combuter HP Turbine Engine intake

Compressor

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LP Turbine

2,12

Bypass duct

Fan

Hot Nozzle

Cold Nozzle

Figure 2.2 Two-spool turbofan.

The difference between the structures of a military and a civil turbofan lies in the size of engine itself and of its bypass duct, both smaller for the military engine. The bypass ratio which is the mass of the air blowing through the bypass duct to the mass of the air going through the core, is, therefore, significantly small in a military engine, typically 0.4 for EJ200 engine. The bypass ratio in a civil engine can be as high as 9 with the fan providing 80% of the total thrust as in a Trent engine [RR Web Site].

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Another difference between a civil and some of the military engines is ‘reheating’. In an engine with reheat, fuel is re-introduced into the downstream flow of gases to achieve a higher temperature and hence a higher exhaust velocity. This increases thrust by almost 80%, though at more than 100% increase in fuel consumption.

This project implements the control technique used in a low bypass ratio military turbofan engine to a high bypass ratio civil engine. The model of the civil engine used to implement the Rolls-Royce Inverse Model (RRIM) is that of Trent series engine and the idea has been taken from military engine. Following is a brief introduction to a Trent engine in comparison with a military engine.

2.1.2.1. Comparison between Civil and Military Engine

The Trent is a three-shaft Turbofan and is designed to power the new generation of wide-bodied jets. The Trent design has been derived from the reliable RB211 three-shaft family of aircrafts.

A common feature of Rolls-Royce RB211 and the Trent engines is that they have three shafts. Because the fan (LP compressor) generates so much of the thrust, the number of turbine stages to drive it is quite large. This is because the turbine uses a small fraction of the compressed air to drive the fan. Table 2.1 summarizes some typical details of a military and a civil aircraft engine [Rolls-Royce web site]. Table 2.1 Comparison between a civil and a military turbofan.

No of stages in Compressor Turbine Engine

Type LP IP HP LP IP HP

Combustor Type Control

Civil 1 8 6 5 1 1 Tiled Classical Military 2 - 5 1 - 1 Annular RRIM

2.2 Some Aerospace Terms and Definitions The performance of the engine is dependent upon the inlet and outlet conditions, specially, temperature and pressure, which are a function of the ambient temperature and pressure and airspeed. The full range of inlet conditions is included in the operational envelope of the engine. The environmental envelope defines the full range of ambient temperature, pressure and humidity conditions for which the engine should perform satisfactorily. The International Standard Atmosphere (ISA) defines the temperature and pressure up to a level of 30,500 m. These are referred to ISA standard day conditions. US military standard MIL 210 provides variations for cold and hot days. Sea level pressure is 14.696 psi, which falls exponentially to 0.16 psi at 30,500 m (100,066 ft). The ambient pressure in ISA is also used to find the altitude, referred to as pressure or Geopotential altitude. The standard day temperature falls at a rate of approximately 6 Co for each 1000

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m up till 11,000 m and then stays constant up till 25,000 m. The standard day sea-level value is 15 Co. Relative density is another factor that is used to define speed of sound, which is, in turn, used to define the aerodynamic speed from the rotational speed of the engine spools. Relative density is the ambient density divided by the standard sea level air density. Density at 30,500 m is just 1.3% of ISA sea level value. The following quasi-dimensionless parameters are used to refer engine parameters to the respective sea level values:

Delta (δ)=P1/14.696 psi Theta (θ)=T1/288.15 K

where P1 and T1 are the engine entry point pressure and temperature. It would not be strange if they were replaced by LP compressor (fan) entry point values, P2 and T2 or free stream values P0 and T0. All these parameters can be related to each other.

2.3 The RRAP Engine Models The project was carried on a real simulation-based model of the engine that belongs to a class of engine models called Rolls-Royce Aero-thermodynamic Program (RRAP). The RRAP engine model programs are used to model the three-spool Trent engine. One of these models described here is BD3104A1. This program is used as a simulation bench for the Trent engine.

The program models the engine as a nonlinear system in a considerable detail. The program runs in both steady state and transient modes and can be used to generate linear models for a classical control design. The RRIM control uses fairly accurate nonlinear model of the engine in the form of graphical relations. Not a detail, but a synopsis

2.3.1. Access to Engine Model The original model code uses FORTRAN 66. The user interface is provided in MATRIXx that is a systems and control design simulation environment used in the Rolls-Royce University Technology Centre (UTC). The interface to the FORTRAN program is built via shared memory and semaphores. Once the link to the code is established, the user can define inputs and observe outputs in MATRIXx. SystemBuild is graphical interface in MATRIXx and Xmath provides a programming workspace. These two components in MATRIXx are similar to, but less user-friendly than, Simulink and Matlab respectively. The program can be invoked both from Xmath and SystemBuild (like a Simulink model can be executed both from Matlab and Simulink). The output of the program is returned in Xmath where it can be plotted and saved. The program files in Xmath are called mathscript files. Figure 2.3 shows the sequence of calls to and returns from the RRAP program.

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Interface

Xmath mathscript File

FORTRAN Code

Engine Model

MATRIXx

User

SystemBulid

Figure 2.3 Engine model and MATRIXx.

Following is a brief introduction to the detail the engine is modelled in. The actual complexity of the model is even more appreciable. Engine performance is evaluated using an iterative cycle-matching process using component characteristics, and conforms, as far as possible, with the relevant SAE (Society of Automotive Engineers) Aerospace Standards. Appendix B gives some more details on RRAP engine models.

2.3.2. Model Description The Trent engine comprises three spools. The engine under consideration has a single-stage fan that is driven by a five-stage low pressure (LP) turbine, an eight-stage IP compressor that is driven by a single-stage intermediate pressure (IP) turbine and a five-stage high pressure (HP) compressor that is driven by a single-stage HP turbine. The engine has separate ducts for the cold and hot air exhausts and is conventionally called ‘unmixed’ type engine. The combustor can be selected to be of staged or conventional type. Variable Inlet Guide Vanes (VIGVs) are provided at IPC entry. Similarly, Variable Nozzle Guide Vanes (VNGVs) have been modelled at the entry to the IP Turbine. Handling Bleeds (HBs) can be operated at IPC delivery (stage 8) and HPC stage 3.

Figure 2.4 shows the schematic of the engine along with ports showing the states and control inputs.

A total of thirty-eight states define the engine dynamics. Important dynamics are the shaft speeds (NL, NI, NH) and the mass flow, temperature and pressure at different locations of

11

the engine. Gas dynamics can be included in transient solution if a full bandwidth model is required. Low frequency heat-soak dynamics are not modelled.

FAN inner

VSV

I P C

H P C Combustor

HP T

I P T

L P T

21A

24 25 40 30 42 44 455

20 80 21 26 31 41 43 45 50

180

130 125

180 FAN uoter

: Dynamic state variables

IP8 handling bleed HP3 handling bleed

WFE

xx xx : Control inputs

Figure 2.4 The engine model: states and control inputs.

The model is versatile in giving the user many options to run the model in different ways. The model has 100 inputs and 143 outputs. All the inputs and outputs may not be activated in any simulation. A selected list of the inputs and outputs activated in EEC, along with the full state vector is given in Appendix D.

2.3.3. Basic Modelling Elements Gas properties are averaged at any cross section. This simplifies the gas temperature and pressure to be one dimensional, along the axial flow of the engine.

A group of non-dimensional groups for flow, work, rotational speed and isentropic efficiency represents the performance characteristic of rotating components. Nozzles and ducts also have their empirical data for thrust, discharge coefficients and pressure losses in the form of tables.

The air system is modelled in a detail necessary to represent its effect on operating gas temperatures, work done in the turbines and the overall performance of the engine. Air bleeds are modelled to represent the gas system. These bleeds remove gas stream between compressors or inter-stage. Flow and energy balance is used to mix the air from bleeds with the mainstream flow. These bleeds can be operated according to the operational requirements but are usually taken to be a fixed percentage of the main gas stream flow.

12

Compressor and turbine energies and mass flows through the components, mixer static pressures, turbine flow capacities and final nozzle areas are used to exploit the mass flow and energy balance for computing the performance of the engine.

2.3.3.1. Fan or Compressor Performance

Fan and compressor have four characteristics as a performance measure namely speed, air mass flow, enthalpy rise and isentropic efficiency. The rotor speed is modelled as aerodynamic speed. The other parameters are modelled as ratios of their actual values to their design values. These parameters are defined as below:

Rotor speed N/√T

Relativised air mass flow (W√T/P)Inlet / [(W√T/P)Inlet]Design Relativised enthalpy rise (∆H/T)Inlet / [(∆H/T)Inlet]Design

Relativised isentropic efficiency η / [η]Design

The corrected rotor speed, N, can be linked to each of the other three parameters using another parameter called Beta (β). This parameter is a simulation tool to simplify the relations to two-dimensional graphs/tables and has no thermodynamic significance. This parameter can be also be ignored in control system design. Linear interpolation is used to define intermediate values of compressor parameters stored against corrected spool speeds. A set of three graphs/tables is modelled for each of fan outer, fan inner, IP compressor and HP compressor. Bleeds are taken from the HP and IP compressors.

2.3.3.2. Primary Burner Performance

Primary burner performance is measured using HP compressor exit airflow, temperature and pressure, turbine cooling bleeds, primary fuel flow and fuel heating value and temperature.

2.3.3.3. Turbine Performance

Like fan and compressor, relativised values for enthalpy drop and isentropic efficiency are taken to define turbine performance. Pressure ratio across the turbine is an additional performance parameter here. The parameters are:

Rotor speed (N /√T)Inlet Inlet flow parameter (W√T/P)Inlet Pressure ratio Pin / Pout Relativised enthalpy drop (∆H/T)Inlet / [(∆H/T)Inlet]Design Relativised isentropic efficiency η / [η]Design

Relativised enthalpy drop that takes place due to compressor power and parasitic losses is used to construct a table/graph for the relativised efficiency for different values of aerodynamic speeds at the inlet of the turbine. The turbine inlet flow function also has a

13

similar graphical representation across relativised enthalpy drop. Turbine cooling bleed mixing takes place after the expansion process. The turbine pressure-ratio is then calculated to model this cooling process.

2.3.3.4. Exhaust System

Bypass and core exhaust systems pressure losses are modelled as a function of total entry pressure, Pin, i.e.,

∆P = Pin × (W √T/Pin)2 / K

where K is a constant defining the loss.

2.4 Gas Turbine Engine Control Problem The engine control problem is to find the amount of fuel that must be pumped into the engine in order to meet an engine power demand.

The pilot’s request on thrust is the main control loop. Besides pilot’s demand, there are other demands generated by Electronic Engine Control (EEC), which the pilot cannot over rule. If the pilot, for example, puts excessive acceleration demand, that may possibly cause a surge problem, then the ACU takes the control of the engine until the demand coming from PLA is within the specified limits. The DCU plays a similar role in the case of excessive deceleration demand. Each of the HP, IP and LP spool speeds has its own limits. In addition, there are limits on HP compressor delivery pressure, P30 that is a measure of how close to surge line the engine is operating. The loop-selection-logic (LSL) should be able to achieve satisfactory transient and steady state response during start up, normal running and failure conditions. A total of 12 control loops are implemented. The control of the engine can be subdivided into three classes:

Thrust control Limiters Acceleration and deceleration control

Thrust control loop is the main control loop.

2.4.1. Thrust Control There are two sources (inputs) of steady state demand namely the pilot’s request on thrust and the steady state fuel flow demand schedule. The pilot sends his or her thrust request from a variable liver angle position called Pilot’s Lever Angle (PLA). The PLA demand is translated into an equivalent EPR demand through a ratings function. In case there is no request coming from the pilot, a well-designed engine power schedule continues to send thrust request to keep the engine at an appropriate thrust level. This mode may be regarded as thrust control of the engine.

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Thrust cannot be measured directly. In some gas turbine engines it is measured from Engine Pressure Ratio (EPR). This quantity, as evident from the name, is a ratio between the low pressure (LP) turbine exhaust point pressure, P50 and the fan inlet pressure, P20. Mathematically,

P20P50EPR = (2.1)

2.4.1.1. Ratings Function

EPR has a good correlation with thrust and temperature and pressure at other points in the engine. The mapping between PLA and EPR may be updated for different flight conditions, in order to map a full range of PLA to a full range of EPR in an appropriate way and is a subject of defining ratings function. Most of the time, for the Trent engine, the ratings function is a piece-wise linear function between EPR and PLA.

In some applications in the military area, thrust is measured from spool speed.

2.4.2. Limiters The engine parameters can also hit limits during normal flight conditions and control of the engine should be able to keep the engine response within certain bounds. In a condition the engine operates on a limit, a limiter becomes active. Following limits are applied in steady state control of a high bypass ratio turbofan.

Maximum limit on LP spool speed, N1 Minimum limit on N1 Maximum limit on IP spool speed, N2 Maximum limit on HP spool speed, N3 Minimum limit on N3 Maximum limit on HP compressor delivery point pressure, P30 Minimum limit on P30

The minimum speed limits are also called the idle speeds. P30 is a limiter loop to keep the HP compressor exit point pressure within an upper and a lower bound. This helps, for example, maintain flame in the combustor chamber and keep temperature within limits. The engine shaft speeds have effect on temperature and pressure in each compartment of the engine and the limits on them provide guarantee for a safe and sound operation.

2.4.3. Acceleration and Deceleration Control Compressor of a gas turbine can exhibit surge and stall if magnitude of acceleration and deceleration is not kept in bounds. Similarly, cooling systems may not be able to perform adequately if HP spool acceleration is too high. Acceleration and deceleration control in

15

effect limits the rate of change of air mass flow and provide enough time to establish the air mass flow to a new steady state value. The control units responsible to keep the magnitude of acceleration and deceleration below a limit are:

Acceleration control unit (ACU) Deceleration control unit (DCU)

In some cases, as in Trent series engine, a backup to the main ACU is provided by the Backup ACU, which is functionally, the same as ACU and, in some situations, replaces the ACU.

2.5 The Engine Control Problem It is now clear from section 2.4 that the engine parameters to be controlled are many and they should be controlled with just one input that is the fuel flow to the engine. All these are candidates to take hold of the engine control but who will decide for whom to win? The answer is the Loop Selection Logic (LSL). The engine, if input to variable guide vanes settings is ignored, can, therefore, be considered as single-input multiple-output system. The single fuel input affects all of these parameters but cannot be used to implement sharp bounds on different engine parameters at one time. The LSL is an addition to the conventional components of a control loop namely the actuator, the sensor, the controller and the system itself. This type of control is sometimes called Selector Control [Astrom and Hagglund (1995)]. Selector control is a popular option in multivariable control working under limits.

2.5.1. Selector Control Consider the situation where there are many measured variables but a single actuator. One variable may be the principle control parameter while the others may have limits on them. Selector control is a classical approach in these situations that applies as many controllers as the number of control parameters but selects, at any time, only one of them to be controlled, keeping the rest of the controllers in an idle stage. Highest and lowest wins functions (HW and LW respectively) decide for the control loop to be active, based upon the limits on and a level of preference for each engine parameter. Figure 2.5 elaborates the principle of selector control. The figure shows a system G, with two outputs, y and z. The output y is the main control variable. The output z is also affected, in some linear/nonlinear proportion, when the main controller C, is active to control y. The two controllers, to keep z within limits, are Cmin and Cmax.

In the normal conditions, zmin<z<zmax, where zmin is the minimum limit on z and zmax is the maximum limit on z. In this case, the output of the Cmin is lower than that of C, hence loses at the highest wins (HW) function while the output of the Cmax controller is higher

16

than that of C, hence loses at the lowest wins (LW). The controller C, therefore, operates as if there were no Cmin and Cmax. When any of these controllers is active, the highest and lowest wins functions make the main controller C inactive.

y

-

+ Zmin -

+ yref

+ zmax

z L W

HW

Cmax

C

G

Cmin

-

Figure 2.5 Selector control system.

The highest and lowest wins functions in the selector control may be thought as nonlinear but they are very simple to implement. The control loops can be designed independently in the conventional way. There may be some noise problems due to multiple switching if the system operates at a point where switching between two control loops occurs. The integral terms of the loops that are not in control must also be tracked.

2.5.2. Selector Control for a Gas Turbine Engine This section gives some main features of the selector control design in gas turbine engines from the point of view of its implementation in GTEs. The underlying design criteria are that:

The design should be computationally efficient. Loop interference should be minimal.

The first principle gives rise to splitting the control action into two parts, one is common to all loops and is shared by all control loops. The second principle allows the use of trims in the event the two loops work close to each other.

2.5.3. Selector Control Design Following are the two steps involved in the design of selector control for gas turbine engines.

DESIGN STEP 1

At first step, the control action is divided into two parts. In general, the input of the controller is an error signal that is pre-processed by the first stage of controller to generate a demand on the engine, e.g., the rate of change of fuel flow demand in the case of the traditional controller and the acceleration demand in the case of nonlinear RRIM

17

controller. The control demand is further processed by the controller to generate a fuel flow command. The demand is, therefore, an intermediate interpretation of the controller action. The final output of the controller is a fuel flow command.

Control Stage ‘1’

Controller Fuel Command

Control Stage ‘2’

Control Error

Control Demand

Figure 2.6 Split control action in Selector control of GTEs.

In the case of traditional controller, the first stage is a lead controller with a gain and the intermediate control action (control demand) is ‘rate of change of fuel flow demand’.

Fuel Command K 1

s T1s+1 T2s+1

Fdot Demand Control

Error

Classical Controller

Control Stage ‘1’ Control Stage ‘2’

Figure 2.7 Split control action in traditional controller.

In the advanced control strategy based upon Rolls-Royce Inverse Model (RRIM), the first stage is a gain and the second stage is the RRIM itself.

K RRIM

Accel. Demand Fuel

Command Control Error

RRIM Controller

Control Stage ‘1’ Control Stage ‘2’

Figure 2.8 Split control action in RRIM controller.

A convention in engine systems to name a demand is to mention the source of demand along with it. This makes the statement descriptive, e.g., in the case of HP spool speed (N3) on high limit, the demand may be called ‘N3max rate-of-change-of-fuel-flow/acceleration demand’. The first stage of the controller will generate a vector of control demands.

DESIGN STEP 2

The reason why the control action is split into two parts is that the part of controller that does not involve any control parameters should be shared together by all the control loops. The LSL should take its decision on a relatively more dynamical part of the

18

controller involves the control parameters and that really makes the difference in design of different control loops.

The sources of demand are many but only one remains active at any time. A demand that is most urgent or appropriate to be fulfilled is passed on to the fuel metering system whilst all others coming from different sources are rejected. A logical circuit is needed to perform this duty and the one that does is called the LSL and is the core of Selector control. In design step 2, a logic circuit is inserted between the two components of the controller of Figure 2.6.

The loop selection logic for the classical control of a high bypass ratio civil aircraft is shown in Figure 2.9 [Oldfield (RR)]. The rate of change of fuel flow demand is indicated as Fdot in the figure.

Steady State Fdot

Fine trim Fdot

Fmax

Fmin

1 s

Fan stall gain factor

Backup ACU Fdot

Dual failure logic switch

N3min_Fdot

P30min_Fdot

N1min_Fdot

N1max_Fdot

P30max_Fdot

N2max_Fdot

N3max_Fdot

F demand

H

W

H

W

ACU Fdot

N3min Fdot

L

W

Backup ACU Fdot

ACU Fdot

DCU Fdot

+

+

L

W

Figure 2.9 Loop selection logic.

The steady state rate of change of fuel flow demand at the input of first highest wins stage is the thrust control part of selector control. Figure 2.10 shows the source and the logical

19

implementation of steady state rate of change of fuel flow (Fdot) demand in the traditional GTE control.

Figure 2.10 shows that the EPR demand (the pilot’s thrust request) will be ignored if reversion mode is selected or reverse thrust is detected (as in the case of run-way deceleration after landing) and the LP spool speed (N1) schedule will take over the control of engine. In normal flight (the mode considered in this project), the lower of the N1-schedule demand and EPR demand is selected. If there is no PLA demand, the steady state N1 schedule takes the control of the engine.

N1 reversion mode selected

L

W EPR Fdot

N1 Fdot T

F

Reverse thrust detected

Steady State Fdot

Figure 2.10 Steady state rate of change of fuel flow demand.

The output of the highest and lowest wins-functions is the final rate of change of fuel flow demand that is integrated to determine fuel flow command to the fuel metering system. The maximum and minimum fuel flow limits are applied to the integration. All the inputs to the loop selection logic are candidates that stand in queue to get hold of the control loop in case there is no PLA demand or the demand exceeds the limits.

The other rate of change of fuel flow demands appearing at the input ports in Figure 2.9 are the outputs of first stage of the controller (Figure 2.7). It would be an acceleration demand in the case of advanced RRIM controller (Figure 2.6). In general different control parameters are applied to the first stage (before LSL). In the case of lead controller in classical control, for instance, each control loop has a schedule for K, T1 and T2. The second stage (after LSL) is common to all control loops.

The same logic has been maintained for the RRIM control as it defines the operational requirements of the engine that are same for any controller. The structure of control loops will, however, change accordingly.

2.5.4. Actuator In the case ofa single input system, the only actuator in the control loop is the fuel metering system (FMS). The FMS designed could be as simple as that in Figure 2.11.

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Kp Fuel Command

-

+ 1 s

PI Controller Valve

1 s Ki

Fuel Injected

Figure 2.11 A simple Fuel Metering System.

Figure 2.11 is a simple fuel metering system with a closed loop control of a fuel metering valve bases upon PI controller. The valve can be estimated as a simple integrator (with upper and lower limits). The closed loop control assures the positioning of the valve that is accurate in steady state.

Engine combustion has always been an area of research to optimise fuel combustion rate and minimize pollutants. Some present day combustors are complex in design and fuel-metering system for them also adopt complex design shapes. The FMS of Figure 2.11, for example, may not be applied to a staged combustor but is appropriate for control design.

2.5.5. Sensors An essential component of control loop is the output sensor. The main part on sensors in engine systems comprises of different pressure sensors. Following pressure sensors are essentially used in high bypass ratio turbofans:

The LP turbine delivery point pressure, P50, The LP compressor (the fan) input pressure, P20, and HP compressor delivery pressure, P30.

P50 and P20 are used in evaluating the EPR and in turn, the thrust of a turbofan engine. P30 is watched to keep limits on it for a smooth engine operation. Transfer function of the sensor can be given as follows:

1sT1)s(H

ss +

= (2.2)

which has a fast pole at s=(1/Ts), say 100, for example. Dynamics of the sensors are very fast, which is one of the reasons they introduce noise in the control loop.

Figure 2.12 combines all major components of a control system of a gas turbine engine mentioned above. Thick and thin lines differentiate between a vector and a scalar signal for a single-input, multi-output engine system.

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Ref. F M S

Output

-

+ Engine

Control Stage ‘1’

Fdot Demand

Fuel Command

Control Stage ‘2’

L S L

Figure 2.12 Gas Turbine Engine control system.

2.6 Performance Requirements of Trent Engine The major parameter of interest, from the pilot’s perspective, is the thrust or power the engine produces. The control of an engine is a means to find the amount of fuel that is necessary to fulfill the pilots demand on engine, to increase or decrease thrust. The control is also meant for keeping track of temperature and pressure at various points in the engine for a safe and satisfactory performance. Limits on pressure ensure a smooth response of the engine. If pressure goes above certain limits, stall and surge conditions may occur. Stall, that is the separation of the airflow from the compressor blades, deteriorates the performance. Surge, that is reverse flow of the air mass, is highly undesirable and, in worst case, can harm the integrity of the engine components. There are limits on temperature because the metals the components are made of cannot hold temperature above a certain level. All these phenomena are coupled with one another, in the sense that one can trigger the other. This does not mean that all the limits are crossed at the same time; the one that is crossed is viewed to correct pushing the engine state back into its operational envelope.

In the absence of pilot’s demand, the low pressure (LP) spool takes the control of the engine. In addition to these two, there are limits on each spool speed that take over the engine control whenever crossed. The limit, in this case, would replace the reference in the normal operation. There are limits on the amount of acceleration that emerge from avoidance of surge and stall etc., and if crossed, replace the acceleration demand coming from any other source. Separate loops are designed for appropriate control in each case and loop selection logic is used to select one to be effective in any particular condition.

Following sections gives the functional requirements of Trent engine in brief [Oldfield (RR)].

2.6.1. EPR Control The engine is controlled to EPR under normal steady state conditions of forward thrust. This EPR demand is generated from the ratings logic to produce a required thrust. The controller should fulfil the following requirements:

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Steady state error ≤ 0.5 % of the minimum N1 limit

Overshoot ≤ 0.02 EPR

Gain margin ≥ 12 dB

Phase margin ≥ 60 deg.

An equivalent damping factor between 0.6 and 0.8

The execution interval of EPR control loop is 50 ms.

2.6.2. Minimum Nl Limit Nl is related to fan and LP turbine. The minimum Nl limit is applied to keep the fan speed above the condition that may cause fan icing. The minimum limit varies from ground to altitude although the altitude value can replace the ground value in the case of failure of the on-ground indication. The minimum Nl limit is used to generate the minimum Nl rate of change of fuel flow demand. The controller should fulfil the following requirements:

Steady state error ≤ 0.5 % of the minimum Nl limit

Overshoot ≤ 1.0 % of the minimum Nl limit

The execution interval for Nl limit is 50 ms.

2.6.3. Minimum Nh Limit Nh is related to HP compressor and turbine and is an indicative of engine idle speed. The idle speed is given as Nh/√θ schedule and is a function of altitude. Two types of idle settings are used; one is higher than the other. The high Nh idle setting may be selected by the aircraft management system or become active when nacelle anti-acing is selected. Icing-idle demand is used in icing conditions. In all other situations, low Nh idle is selected. A trim is applied to both low and high idle schedules. Integrated Drive Generator (IDG) drop out speed is also looked after by the Nh limiter. Nh limit also prevents flameout but the Nh limit schedule is evaluated from the minimum T30 (HP compressor) limit schedule. The minimum Nl limit is used to generate the minimum Nl rate of change of fuel flow demand. Whatever the source of Nh idle demand is, the controller should fulfil the following requirements:

Steady state error ≤ 0.5 % of the minimum Nh demand

Overshoot ≤ 1.0 % of the minimum Nl limit

Nh idle demand is updated every 100 ms but the control loop is executed every 50 ms.

2.6.4. Minimum T30 Limit T30 signal (HP compressor exit point temperature) indicates water ingestion (in rain or hail) conditions when it falls below a limit. This signal is filtered and processed to compensate for thermocouple time lag. This condition is detected from the difference of

23

T30 and the T30 demand coming from P30 (HP compressor exit point pressure). Flameout may occur at that time which can be avoided by rapidly increasing the fuel into the burners. The igniters are turned on bleeds valves are opened to reduce the risk of flameout.

The control system will maintain the fuel flow by generating an equivalent Nh idle limit and passing it to the Nh idle limit control loop. Since fuel is increased suddenly, the controller would be active on stability issues of the engine. In the case ofunavailability of P30 and T30 due to failure, the control will be disabled. The controller should fulfil the following requirement:

Steady state error ≤ ±5 K

Minimum T30 demand is calculated every 100 ms.

2.6.5. Minimum P30 Limit This limit is related to the bleed valve operations and ensures that minimum bleed port pressure fulfils the requirements for operating the bleed valves for nacelle anti-acing (NAI), wing anti-acing (WAI) or environmental control system. (ECS). The minimum P30 demand for WAI and ECS is a function of altitude and ECS minimum pressure requirement. A separate schedule is calculated for NAI. The demand is a function of altitude and airspeed.

The controller should fulfil the following requirement:

Steady state error ≤ 3% of P30 limit

Overshoot ≤ 2.0 % of the minimum Nl limit

Minimum T30 demand is calculated every 100 ms.

2.6.6. Maximum Nl Limit Maximum limits on speeds are, in an extreme case, related with the integrity of the engine. The maximum Nl limit is applied to keep the LP spool speed below the condition that may cause damage to fan or LP turbine blades or other components due to excessive rotational speed or air mass flows. There are two sources for this limit:

Absolute Nl limit (mechanical speed)

Maximum Nl/√θ (aerodynamic speed) computed as a function of altitude

The first limit source is defined as the Nl redline limit minus the Nl headroom. The final Nl limit is the minimum of the maximum N1 limit and the limit coming from Nl/√θ schedule after a root-theta correction. A trim may also be applied for development purpose. If T20 sensor fails (and √θ cannot be found), an offset is added to this limit. The maximum Nl limit is used to generate the maximum Nl rate of change of fuel flow

24

demand. An independent electronic over speed limiter takes aver the control in the case of any control system failure. The controller should fulfil the following requirements:

Steady state error ≤ 0.12 % of the maximum Nl limit

Overshoot ≤ 1.0 % of the maximum Nl limit

In addition, the bandwidth of the Nl limit control loop should be greater than 1

rad/s for the power setting and flight condition above maximum climb EPR (engine

pressure ratio)

The minimum Nl demand is executed every 50 ms. The maximum Nl/√θ (air flow) limit is calculated every 100 ms.

2.6.7. Maximum Ni Limit The maximum Ni limit is applied to keep the IP spool speed below the condition that may cause a need for maintenance. This limit also prevents an engine shut down that may be caused by an independent over-speed protection unit (OPU) in the event of VSV (variable stator vans) malfunction.

The limit is taken as the difference between Ni redline limit and the Ni headroom. The maximum Ni limit is used to generate the maximum Ni rate of change of fuel flow demand. The independent electronic over speed limiter for Nl serves the duplicate purpose of ultimate security in the case of a loss of signal. When maximum Ni loop is in control under normal conditions, the controller should fulfil following requirement:

Steady state error ≤ 0.12 % of maximum Ni limit

Overshoot ≤ 1% of maximum Ni limit with less than 5s duration and no

subsequent undershoot.

The controller should fulfil the following requirements in during the slam acceleration from any power level with VSVs failed low prior to start:

Steady state error ≤ 1 % Ni

Overshoot ≤ 5s duration.

In addition, the bandwidth of the Ni limit control loop should be greater than 1

rad/s for all power setting and flight condition above maximum climb EPR (engine

pressure ratio)

The maximum Ni demand loop is executed every 50 ms.

2.6.8. Maximum Nh Limit The maximum Nh limit is applied to keep the HP spool speed below the condition that may cause maintenance problems. The limit is defined as the Nh redline limit minus the Nh headroom. In the case ofNh signal failure, a synthesised value of Nh is used and an

25

offset is applied to generate the limit. The controller should fulfil the following requirements:

Steady state error ≤ 0.12 % of maximum Ni limit

Overshoot ≤ 1% of maximum Ni limit with less than 5s duration and no

subsequent undershoot.

In addition, the bandwidth of the Nh limit control loop should be greater than 1

rad/s for the power setting and flight condition above maximum climb EPR (engine

pressure ratio)

The maximum Nh control loop is executed every 50 ms.

2.6.9. Maximum P30 Limit This limit is a protection against overpressure, especially in combustor. This limit is disabled in the case of a pipe fault. The controller should fulfil the following requirement:

Steady state error ≤ 0.5 % of P30 limit

Overshoot ≤ 2.0 % of the Maximum Nl limit

The maximum T30 demand control loop is executed every 50 ms.

2.6.10. ACU Schedule The ACU controls the engine acceleration. This limit is applied to achieve consistent acceleration times. This unit is basically Nhdot closed loop control unit. This control will prevent surge in the event of re-slam. The basic ACU Nhdot schedule is the minimum of ACU Nhdot limit and a schedule that is a function of Nh/√θ, oil temperature and altitude with additional P20 and delta correction factors. The sub-idle portion of ACU Nhdot schedule (during start) is a function of oil temperature. A de-rate factor is applied in the event of re-slam anticipation. Nhdot is calculated from Nh that is filtered by two first order filters (lags) in series. The difference between Nhdot and DCU Nhdot is multiplied by a gain to produce the rate of change of fuel flow demand that would prevent Nhdot cross the DCU Nhdot limit. The controller should fulfil the following requirement:

Steady state error ≤ 0.2 %/s of ACU Nhdot

Settling time for the desired EPR should be within 0.25 s.

The ACU Nhdot demand is calculated every 100 ms. The corresponding control loop is, however, executed every 50 ms.

2.6.11. Backup ACU Schedule The backup ACU schedule serves the purpose of an ACU schedule at the start of acceleration in order to avoid surge. The basic backup ACU schedule is defined as Fdot/F (where F is the fuel flow demand and Fdot is its rate) and is a function of Nh/√θ with a

26

delta (δ) correction. The basic schedule is multiplied by the fuel flow demand to give rate of change of fuel flow demand, which is the ultimate parameter to be looked after by this schedule. This limit (schedule), basically, controls the initial rate of change of fuel flow demand at the start of acceleration. The controller, therefore, should fulfil the following requirement for the initial rate of change of fuel flow:

Over-all error ≤ 5 % of the point fuel flow (including the accuracy of FMS)

The backup ACU fuel flow demand is calculated every 100 ms.

2.6.12. DCU Schedule The DCU controls the engine deceleration. This limit is applied to achieve consistent deceleration times that fall within the flight envelope. As a result, Nhdot is limited by the Nhdot schedule. The difference between Nhdot and DCU Nhdot is multiplied by a gain to produce the rate of change of fuel flow demand that would prevent Nhdot go below DCU Nhdot. Another requirement during deceleration is that the engine be protected from flameout. This is achieved by the minimum fuel flow limit applied during slam deceleration under all conditions. The controller should fulfil the following requirement:

Steady state error ≤ 0.2 %/s of DCU Nhdot

The DCU Nhdot demand is calculated every 100 ms. The corresponding control loop is, however, executed every 50 ms.

2.7 Control Implementation This section gives some features of gas turbine engine control of the modern day from its implementation point of view.

2.7.1. Digital Engine Control Digital engine control has become the state of the art in aircraft engine control. It has reduced the number of the ancillary systems of the engine, replacing a huge number of mechanical and hydro-mechanical components with a single fuel-metering valve controlled electronically. This has reduced construction and maintenance costs and complexity of the control system increasing the opportunity to update the control design in much easier way with much lesser costs. The main areas of control are the spool speeds and turbine exhaust temperature and some electronic controls apply only the limits on these control parameters. Full authority Digital Engine Control (FADEC) is at the front of this advanced control.

27

2.7.2. FADEC FADEC not only controls the amount of fuel required to fulfil any demand on the engine but also the rate at which any engine parameter (temperature, pressure, fuel flow, speed) achieves its final state as a result of fulfilling the demand. If FADEC is optimal in reducing the weight of the engine control systems, then a sub-optimal control is FAFC that is Full Authority Fuel Control. This control system has no intelligent capability for the transient compressor airflow control. Full Authority in electronic control means that each and every control parameter of the engine is controlled electronically.

2.7.3. Real Time Control Real time control deals with a real life implementation of the controller. Control loops for all the parameters in all modes are implemented under safety functions and other ancillary systems. This gives rise to trims and correction factors applied to different parameters. Some development features are also included in the design for flexibility to future modifications proposed by long term experiments. The Electronic Engine Control (EEC), at the end of the day, comes out as a complex system with a huge amount of computational burden that cannot be handled at each sampling time in digital implementation.

As a pragmatic approach in real time control, computational burden is chopped and time-multiplexed to utilize the available computational power in an efficient way. The loop selection logic is implemented every 25 ms but the steady state rate of change of fuel flow demand is implemented every 50 ms. The steady state fuel flow that is executed at the end of first 25 ms is repeated at the end of next 25 ms. The following diagram shows various tasks that a multi-rate EEC performs over a cycle of 100 ms.

Loop selection logic

25 ms 25 ms

Loop in control

Steady state rate of change of fuel flow demand SS Fdot

Loop interference logic Fine trim

25 ms 25 ms

Figure 2.13 EEC Timings diagram.

Since loop selection logic updates every 25 ms, EEC receives an update of the control parameter in the first 25 ms while the control response is computed in the next 25 ms.

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2.7.4. Loop Interference In selector control, no two boundaries should be hit at one time and if such a situation arises, the control signal generated by each active loop should be different from that of the others so that only one can win through the LSL and the others remain in the waiting list.

Situations can arise when two or more control loops operate close to each other, e.g., the N3max-loop may be operating in vicinity of one of any other limiter loop. The differential action inherent in the velocity algorithm may amplify noise generating from multiple switching between the two neighbouring loops. Two interfering signals pass through the selection logic in this case. The control offset caused by this interference will result in an equivalent inaccuracy in control action. An additional fine trim comes into play to compensate for this offset by applying additional integral action.

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Chapter 3 Gas Turbine Engine Control

The gas turbine engine control problem is to find the amount of fuel that must be pumped into the engine in order to meet an engine power/thrust demand. The gas turbine engine under consideration is from Trent series and has been introduced in Chapter 2.

The aircraft engine, in general, is a nonlinear system that is subjected to drastic variations of power levels and flight conditions from take off to landing. The input to the system is the rate (lb/hour) at which fuel is injected and burnt in the combustion chamber. The number of parameters to be controlled is quite large because of a number of dynamic components (compressors, turbines, valves for fuel flow, bleeds for cooling and surge avoidance etc) and limits on operating conditions (temperature, pressure and speeds etc). The atmospheric temperature and pressure (and hence density of the intake air) change from sea level to flight altitude and from hot days to cold days. Different flight schedules are designed and developed during extensive testing of the engine performance at different power levels for different temperature and pressure conditions. The atmospheric and operating temperatures of the gas turbine engine give rise to various corrections in the flight schedules.

There are different modes of engine operation, e.g., engine start up, acceleration to idle, restart in case of flame out, steady state reversion mode control etc. The engine behaviour and requirements change from mode to mode.

A linear controller cannot exhibit adequate global performance for a highly nonlinear system. A nonlinear controller is particularly the only choice for a nonlinear system when large operating point changes are to be handled as in the case of gas turbine engines.

3.1 Traditional Control of Trent The traditional control of Trent engines is based upon parameter scheduling which is a primitive approach to nonlinear control design. The control technique used is in parameter scheduling is a variant of PI controller that has a lead control component. Figure 3.1 shows the block diagram of a typical control loop working on EPR.

30

Fuel System

K EPR Demand

EPR

-

+ Engine 1

s T1s+1 T2s+1

Fdot Demand

Fuel Demand

Figure 3.1 The classical control structure used in modern civil engine control.

The controller structure uses the error in EPR demand to correct the fuel flow into the engine. The lead component of the controller with a lead term “T1 s+1” in the numerator, a lag term “T2 s+1” in the denominator and gain “K” converts the EPR demand into a rate of change of fuel flow (Fdot) demand. The rate of change of fuel flow demand is then integrated to generate fuel flow command. This fuel command goes to the fuel metering system, which operates the fuel valve to set its position to allow the commanded fuel. This fuel metering system is a feedback loop, with a PI controller, that ensures the correct valve position for any fuel command.

The control structure of a PI controller that generates the rate instead of an absolute value. Consider the classical form of a PI controller.

+= ∫ dt)t(e

Ti1)t(eK)t(u p (3.1)

The velocity algorithm for equation (3.1) is,

+= )t(e

Ti1)t(eK)t(u p && (3.2)

In Laplace domain,

)s(ET

1sTK)s(ET1sK)s(U

i

ip

ip

+=

+=& (3.3)

With (Kp/Ti) = K and Ti = T1,

[ ] )s(E1sTK)s(U 1 +=& (3.4)

In a practical situation, the controller of equation (3.4) is modified, to suppress high frequency noise, to the following:

)s(E1sT1sTK)s(U

2

1

++

=& (3.5)

which is the same as the lead term and gain of the lead-lag controller in Figure 3.1.

This control is typically implemented in the Trent series [Rolls-Royce, Oldfield].

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3.1.1. Control Specifications in Traditional Control One of the advantages of parameter scheduling in traditional control is that well-established linear control techniques can still be exploited even if the system is nonlinear. The control specifications in classical control are well defined both in frequency and time domain. In frequency domain, they appear as demands on phase margin, gain margin, band-with and damping factor etc. In time domain, specifications are in the form of rise time, settling time and overshoot etc. A 60-degree phase margin is, for example, a common design criteria. Bandwidth depends upon the dynamics of the system and so does rise time.

Design specifications in traditional control are also given in this classical fashion.

3.2 Advanced Control of Gas Turbine Engines Advanced Control of Gas Turbine Engines is based upon pure nonlinear control techniques in which not only the global performance of the controller is nonlinear but also the structure of the controller appears to be nonlinear. From this point onwards, the traditional nonlinear control design technique based upon parameter scheduling in linear control structures may be thought as linear control. A nonlinear controller is the one that is ‘strictly’ nonlinear, both in performance and as an individual system.

3.2.1. Why Nonlinear Control? Nonlinear control is becoming popular in research for applications in the areas of robotics, process control, biomedical engineering and aerospace. There are numerous reasons that support the idea of nonlinear control for nonlinear systems. There are many points in using a nonlinear controller for nonlinear systems and a few of them are as follows:

The performance of the controller designed on the basis of linear model of the system deteriorates as the range of operation increases giving rise to unstable control in worst case. Coriolis and centripetal forces, for instance, in robot joints can be ignored if the motion of the robot is slow. The performance of the classical controller based upon this assumption rapidly degrades as the speed of the robot increases. This simply puts limits on job speed and, hence, productivity of a robotic system. A popular nonlinear control called computed torque control, on the other hand, shows a very good performance over a wider range of operation.

A nonlinear controller is of more importance in the face of hard nonlinearities like Coulomb friction, dead zone, hysteresis and backlash. These nonlinearities are discontinuous in nature and hence do not allow the assumption that the system is

32

linearizable. Nonlinear techniques should be developed to predict and compensate for such nonlinearities and avoid possible spurious limit cycles in the system.

The nonlinear control is also a better choice for nonlinear systems, which exhibit a variation of their parameters with time. Uncertainties in parameters also fall in the same category. A linear controller, though provides phase and gain margin to ensure stability against parameter uncertainties, will not show good performance in the event they occur.

A nonlinear control, on one side, may be complicated in designing procedure but the end product, on the other hand, could be simpler than the linear control. The Rolls-Royce Inverse Model (RRIM) control is a good example and this is because nonlinear control is more deeply rooted into the dynamics of the system. An astonishing result in this case would be a decrease in development time due to simplicity of the control.

The net cost of the nonlinear control, considering design and running and possible update costs, may be lesser than the linear control in long term in cases when lesser components are involved, development period is short, performance is better and maintenance/update of the control system is less likely.

3.3 Nonlinear Control Almost all physical systems in nature are nonlinear, though most of them can be approximated as linear systems if the range of operation is small. A linear system is one whose dynamics can be expressed by linear differential equations. A common representation of a linear system in state space form is:

x=Ax+Bu& (3.6)

Where x is the state vector and u is the external input. The matrix A and B show the dynamics of the system. The system will be time invariant if the matrices A and B do not change with time. A linear time invariant (LTI) system has a unique equilibrium point if A is non-singular and will always converge to it if all eigen values of A have negative real part. Asymptotic stability (convergence to equilibrium) readily implies bounded-input, bounded-output stability of a linear system. Another property of a linear system is superposition, which implies that the response to a sum of inputs will equal the sum of individual responses of all the inputs.

A system that does not have the above said properties, e.g., does not obey superposition or does not have a unique equilibrium point is a nonlinear system. A general representation of nonlinear system, in state space form, is as follows:

x=f(x,u,t)& (3.7)

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A nonlinearity that is inherent in the dynamics of the system such as Coulomb friction and hysteresis is a natural nonlinearity. Natural nonlinearities, almost always, are undesirable and may cause problems in control. A nonlinear controller is a nonlinear system that introduces intentional or artificial nonlinearity in the control loop in order to make the control of nonlinear system efficient. Two classical nonlinear control problems are: the inverted pendulum control and high-speed robotic arms.

3.3.1. Nonlinear Control Problem A general classification in control problems is to divide them into two types: stabilization problem and tracking problem. In stabilization problem, the controller stabilizes the system around an equilibrium point, e.g., stabilizing aircraft at any altitude, positioning the robotic arm at a particular position and controlling temperature at a set point. The problem may be stated as follows:

Given the nonlinear system

x=f(x,u,t)&

find the control input u such that starting from anywhere in a region Ω, the state x tends to zero as t→∞.

This may also be called a regulation problem. The control design for power level and maximum and minimum limits on the engine parameters is a regulation problem.

In the tracking problem, the system response, y is compelled by the controller to track a reference trajectory, yd. The problem may be stated as:

Given the system

x=f(x,u,t)&

y=h(x)

and a desired output trajectory, yd, find a control input, u, such that starting from anywhere in a region, Ω, the tracking error (yd-y) goes to zero while the state remains bounded. For a non-minimum phase systems, perfect tracking (y(t) = yd(t), ∀t ≥ 0) or asymptotic tracking (y(t) = yd(t), ∀t ≥ t0) is not possible [Slotine and Li (1991)]. This effect emerges from ‘undershooting’ that is an inherent property of non-minimum phase systems. Thus the control design objective for a tracking problem of non-minimum phase system should not be perfect tracking; rather it should be keeping the tracking error within specified limits. The design of the Acceleration Control Unit (ACU) of the engine is a tracking problem in which the controller is intended to keep the engine dynamics on a given acceleration curve.

34

3.3.2. Control Specifications in Nonlinear Control To specify control performance criteria for a linear system is very easy both in time and frequency domain. In time domain, it is specified in terms of overshoot(s), rise time, settling time and steady state error. In frequency domain, it appears as phase margin, gain margin, damping ratio and bandwidth etc. Design specification for a non-linear system is much more difficult due to two reasons: first, because the time response to one input may not reflect any conclusion about the time response to another input (principle of superposition does not apply) and second, because frequency domain description is not possible [Slotine and Li (1991)]. What is left behind are some qualitative specifications. Following are some important of them:

Stability

Stabilty must be guaranteed for the nominal model.

Speed of Response and Accuracy

Response to a reference trajectory should have an error that lies within certain bounds. Speed of response is also a measure of how close to a specified trajectory a system response can be.

Robustness

Certain parameters are usually not considered in control design. Measurement noise, input and output disturbance, parameter variations etc. are some important elements the controller should give adequate performance in the face of.

Note: Question of stability of a nonlinear system always comes with an initial condition. Withstanding a persistent disturbance may not, therefore, be a stability requirement of a nonlinear control (which it is for a linear control) because initial conditions change with time, which imply placing a different stability criteria [Slotine and Li (1991)]. Persistent disturbance effects are addressed from robustness platform and some trade-off may have to be set between the accuracy and robustness.

3.3.3. Conventionnel Nonlinear Control Techniques A number of nonlinear control design techniques are available and one may suit better to a class of nonlinear systems as compared to the others.

3.3.3.1. Trial-and-error

Trial-and-error is a primitive approach that is extensively used in tuning parameters in classical control design. A motive behind this is that strong computer analysis and simulation techniques are available and a controller that can be justified from simulations should be chosen. Experience and engineering intuitions help a lot in this method.

35

Analysis tools like phase plane trajectories, describing functions and Liapunov analysis can also be used. This method loses its adequacy with the increase in the complexity of the system.

3.3.3.2. Feedback Linearization

A classical approach to designing control for nonlinear systems is to obtain system models that are fully or partially linear so that well known powerful linear control design techniques can be used for nominal models. This design technique may not be robust in face of parameter uncertainties.

3.3.3.3. Robust Control

In the design of controller based upon linear nominal models, robustness is not very clear. In robust nonlinear control (such as H-∞ and sliding mode control), the design procedure takes into account a certain description of uncertainties in a solid mathematical form. Robust nonlinear control is a hot issue in robust control and has proven its efficacy in a lot of advanced applications such as automotive and aircraft control.

3.3.3.4. Adaptive Control

Adaptive controllers are inherently nonlinear [Slotine and Li (1991)]. Strong adaptive control techniques are available for linear time varying systems. Some adaptive control techniques can also be applied to a class of nonlinear systems. These techniques are an alternative to robust control.

3.3.3.5. Parameter Scheduling

Feedback linearization is the design of linear controller for a nominal model. The nominal model may not be applicable if the range of operation is very large such as in aircraft control. A single controller is, therefore, not applicable for the whole range. An immediate solution that emerges from the basic idea of feedback linearization is to linearize the model at a series of nominal points on a trajectory and design individual control for each point. The control parameters are scheduled along the trajectory. The control parameters for the intermediate points are obtained by linear interpolation. The overall controller can be viewed as a nonlinear controller with a perfect design at nominal points and slightly degraded design on intermediate points. This technique is easy, logical and successful in many cases but does not have any mathematical explanation. Another disadvantage, associated with this technique, is that it could be computationally cumbersome. A trade-off needs to be set between the cost of the controller (number of computations at each sample time, length of design period etc.) and the accuracy over a global performance range. This control technique is dominant in control of gas turbine engines.

36

RRIM control is a nonlinear control and embeds, as the name shows, the inverse model of the engine into the control law. Following sections gives a general approach to inverse modelling control.

3.4 Inverse Modelling Control Inverse modelling is a classical approach in linear control in order to achieve easy solutions to tracking problems. The primitive idea is to design a controller that will make the overall transfer function between the input and output mimic unity. Such a controller, in open loop, can be obtained by inverting the transfer function of a linear system if no zeros of it lie in the right half plane. The controller is intended to produce the input of the system from the output of the system and thus exhibits inverse dynamics of the system and, when placed in cascade with the system, can cancel out the dynamics of the system. The idea of inverse model appears as inverse dynamics when extended to nonlinear systems. For the non-linear system:

)u(g)x(fx +=& (3.8)

)x(hy = (3.9)

To track the reference signal yd(t), the control problem is to find the initial condition x(0) along with the control law u. To solve this control problem on the basis of inverse dynamics, first assume that perfect tracking is possible, i.e.,

0d tt)t(y)t(y ≥∀≡ (3.10)

Equation (3.10) implies that time derivatives, of all orders, of y(t) and yr(t) are also equal, i.e.,

1r,...,2,1,0k)t(y)t(y )k(r

)k( −=≡ (3.11)

Equation (3.10) can be differentiated as follows:

hLy

hLxx

]hL[y

hLxxhy

kf

)k(

2f

f

f

=

=∂

∂=

=∂∂

=

M

&&&

&&

(3.12)

Equation (3.10) and (3.12) imply that initial condition should obey

(0)y h(x(0))L , (0),y h(x(0))L yr(0), h(x(0)) 1)-(rr

1)-(rfrf === L& (3.13)

Define first r states of the nonlinear system in companion form: T)1r( ])t(y)t(y)t(y[)t( −=ζ L& (3.14)

37

so that following linear subspace Rr in Rn can be used to define a linear system:

ηζ+ηζ

ζζ

=

ζ

ζζ

)t(u),(b),(a

)t()t(

)t(

)t()t(

dtd 3

2

r

2

1

MM (3.15)

where η are the rest (n-r) states that are defined using a set of (n-r) nonlinear differential equations:

),(w)t( ηζ=η& (3.16)

A corresponding set of states ζr(t), over the reference trajectory yr(t) can also be defined in a similar way such that

)0()0(and)t()t( rr ζ=ζζ=ζ (3.17)

and η(0) could be arbitrary.

The control input u(t) must satisfy

)t(u),(b),(a)t(y rr)r( ηζ+ηζ= (3.18)

Equation (3.18) can be used to define the control law:

),(b),(a)t(y)t(u

r

r)r(

ηζηζ−

= (3.19)

Equation (3.19) shows that given a reference trajectory yr(t), a control u(t) can be defined that can provide perfect tracking. The control law is a function of the internal stateη and hence depends upon η(0).

A mathematical equation that is used to find the output of a system y(t) from an input time history, u(t), can simply be a representation of the dynamics of the system. Equation (3.19) is performing the inverse of it; it takes the desired output to generate an input that can produce that output. Equation(3.19), can therefore, be called inverse dynamics of the system [Slotine and Li (1991)]

Above discussion shows that inverse dynamics/model control is not confined to pole-zero cancellation idea, it can be extended to versatile ideas that may be used in nonlinear control. It should be noted that perfect tracking controller cannot be designed for a non-minimum phase system.

3.5 RRIM Control The nonlinear control applied in the military engine under consideration is called the Rolls-Royce Inverse Model (RRIM) control. The controller applies the engine model to calculate the amount of fuel for any acceleration demand i.e., the inverse of what an

38

engine does hence the name inverse model control. The following block diagram (Figure 3.2) shows a simple form of the RRIM controller [French (RR)].

Current fuel flow demand

Nhdot demand

-

+

Nh

Nhdot/dF

Nh

Fss

1/u

CL Fuel demand

(from EEC)

+

Nhdot/dF

Nhdot

Nhm

Nhdot/dF

+ dF

Fss Fss

Figure 3.2 Basic RRIM control structure.

3.5.1. Advantages Expected from RRIM Control The engine is a nonlinear system and a general concept of a good controller for a nonlinear system is that the controller should also be nonlinear in order to track the nonlinear behaviour of the system. The RRIM, being a nonlinear control has this capability. The RRIM controller knows, through the dynamic table, that the amount of fuel required to fulfil the Nhdot demand significantly varies with the power level and environmental conditions. The controller that ‘knows’ the system can, therefore, generate a fuel command that matches the engines requirement.

RRIM can compensate for inaccuracies in the engine model; hence may suit, in some developed form, to a particular build of engines. Further experience with the RRIM may lead to a life long control design of engines.

3.5.2. The RRIM Control Procedures Figure 3.2 shows how the RRIM control works. The RRIM controller works on acceleration demand and computes the corresponding amount of fuel using the model of the system in the form of two lookup tables:

Fss Vs Nh Nhdot/δF Vs Nh

where Nh is the high pressure spool speed and Nhdot is the acceleration the high pressure shaft experiences as a result of fuel increment δF. Fss is the steady state fuel consumption at any spool speed. These two graphs/tables can be achieved by running the engine in steady state and transient modes. The first table may be called the static and the second, the dynamic table.

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The dynamic table, which is a measure of the acceleration achieved by unit over-fuelling, can be sorted using Nh to find the corresponding value of Nhdot/δF. This quantity, when inverted, can be used to find the amount of over-fuelling, δF, necessary to achieve the desired Nhdot. This value can be added to current fuel flow demand and sent to the fuel metering system to update the fuel valve position. The story could finish here if RRIM were a perfect model of the engine, which is practically impossible because of numerous reasons, e.g.,

The engine is a nonlinear system and the relation between the demanded acceleration and the corresponding amount of fuel to fulfil that demand is highly nonlinear. The RRIM graphs may typically represent as many as hundred operational points. The controller is, therefore, left with no choice other than the use of interpolation and possibly extrapolation as well.

The engine model changes with the environmental changes due from hot to cold days and due from sea level to cruise height. All environmental conditions cannot be put into the model.

Even if there were no other reason, the model that is exact today wouldn’t be any more after, for instance, 1000 hr running time; on-wing is different from on-bed engine. Component properties change with time due to wear and tear in the dynamic components leading to maintenance activities. Extremely high temperatures in turbine-associated components lead to changes in physical properties.

It can be concluded that obtaining an exact model of the engine is almost impossible. As a result, the dynamic table in the RRIM control will not generate an accurate amount of overfueling. The spool speed achieved would, therefore, be lesser or greater than that required. Consequently, the response will never settle to a zero steady state error.

3.5.3. Why Modelled Speed in RRIM? Modelled HP spool speed, Nhm incorporates in the RRIM controller the ability to compensate for the model inaccuracies. To investigate how this happens, consider Figure 3.3 a simplified control loop with no sensor or actuator. Notice the difference of the RRIM in Figure 3.2 and Figure 3.3. The RRIM tables in Figure 3.2 are interpolated using measured Nh and not a modelled Nh. The acceleration demand coming from EPR error is multiplied by the inverse of Nhdot/dF obtained by interpolating the dynamic response table. The steady state response table will add to the fuel increment the steady state amount of fuel. If the two tables are accurate, this control loop should, at least philosophically, give the same response as that from Figure 3.3.

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Ref. EPR Nhdot Demand

-

+

Nh

Nhdot/dF

Nh

Fss

1/u

Fuel Command

+

Nh Nhdot/dF

+

Fss

EPR

Engine

K

EPR Error

Figure 3.3RRIM control loop with measured Nh.

Now consider the case when RRIM is not accurate. Let EPR error be zero at some time, i.e., the dynamic response table is inactive and steady state fuel generated by the steady state response table is a value for which EPR = Ref. EPR. At any time, all of the output variables are consistent with each other and so is the HP spool speed, Nh with EPR. Since the two tables are inaccurate, the value of steady state fuel flow, Fss generated by the steady state response table is not consistent with EPR or Nh. Rather, it is either higher or lower than that required value to maintain the reference EPR as steady state value. The state of the engine with zero EPR error is, therefore, a transient state of the engine and EPR would never stabilize at the reference EPR.

To avoid the above problem arising from model inaccuracies, RRIM works on the modelled spool speed, Nhm instead of actual spool speed, Nh. The actual spool speed, in this case, remains consistent with EPR and all other outputs even if modelled spool speed is different from actual spool speed.

The static response table, combined together with the dynamic response table, is used for modelling Nh. The steady state fuel demand from the static response table is subtracted from the present fuel flow to generate a difference that is multiplied with Nhdot/δF from the dynamic response to give Nhdot. This is the modelled acceleration that is integrated to produce, the modelled spool speed, Nhm. This modelled spool speed is then used, in feedback, to interpolate further into the two tables.

NB: Another advantage of modelled Nh is that it is a direct measure of model accuracy. Modelling error can be quantitatively found from the difference of Nh and Nhm.

3.5.4. Source of Nhdot Demand The RRIM controller in Figure 3.2 works on HP spool speed acceleration demand, Nhdot. This acceleration is produced by multiplying the error in the demanded and the measured

41

value by a gain, K. The gain KEPR may be a single value for the whole operating range or in general, a gain schedule as the engine goes from idle to the maximum power level. Here comes the reduction in controller parameters to be tuned where one, instead of three in the case of traditional control under consideration, parameter needs to be tuned.

Figure 3.4 shows the RRIM controller doing EPR correction in closed loop.

RRIM KEPR EPR Demand

EPR

-

+ Engine

Nhdot Demand

Fuel Demand

Fuel System

Error Fuel Command Fuel

Figure 3.4 RRIM controller in closed loop.

The pilot’s demand on thrust appearing as EPR in Figure 3.4 is not the only source of Nhdot demand, the limiters and acceleration and deceleration control units also send their own acceleration demands. The demands coming from all loops are processed by the loop selection logic.

3.5.5. Functional Description of Gain The RRIM, in combination with gain, comes up as a RRIM controller in nonlinear RRIM based controller. The controller uses the demand on acceleration of high pressure (HP) spool acceleration. The demand is generated by a gain with the control error no matter what the control parameter is. In most of the cases, a constant gain performs adequately over a wide range of variations in operating point. In case of a demand arranged from thrust request (EPR loop in most of turbofans), a gain schedule may be used instead of a constant gain over the whole range. The purpose of gain is to generate an appropriate acceleration demand. The dynamics of the controller are in the RRIM and are based upon the engine dynamics. The way the demand is fulfilled is, therefore, automatically appropriate. That is why it is believed that RRIM is easy to tune.

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Chapter 4 RRIM Control Design

The advanced RRIM control design is based upon Rolls-Royce Inverse Model (RRIM) as has been introduced in Chapter 3. The practical procedures followed in the design of the RRIM controller and its implementation in a simulation-based Electronic Engine Control (EEC) of a Trent series engine are explained in this chapter. The contents of this chapter are kept in sequence followed in the replacement of an existing traditional controller in the EEC with the RRIM controller.

The inverse model/dynamics are introduced in the controller in the form of two relations:

relation between acceleration per unit fuel flow increment and spool speed. relation between steady state fuel flow and corresponding spool speed.

The RRIM controller design, therefore, starts from synthesising RRIM itself. The parameters of the traditional controller are scheduled in the form of lookup tables. Following the same conventional style, these relationships are constructed as lookup tables.

4.1 RRIM Tables Inverse model of the engine in the RRIM control requires two lookup tables:

Nhdot/δF Vs Nh and Fss Vs Nh

where Nh is the HP spool speed and Nhdot is the corresponding acceleration produced by a fuel injection of δF (lb/hr) when engine is operating at steady state fuel flow Fss. What the length of these two tables could be? On a simulation bench like MATRIXx using the Rolls-Royce Aero-thermodynamic Performance (RRAP) model, as many steady state conditions as thousand is not a problem but an actual engine may not be run to give this many steady state points. The real engine may be run to generate as many as fifty points on a full range from idle to max speed. The intermediate points may be generated using interpolation. Quadratic interpolation can also be used because it is an off-line step in the design procedure but since a RRIM control can cope with model inaccuracies in some appropriate limits, linear interpolation is also supposed to work at the first stage. A similar procedure can be adopted in the control design based on a RRAP model allowing choosing steady state points as low as twenty.

43

4.1.1. Transient Response To accelerate the engine, RRAP program should be in transient mode, though a steady state mode run is also necessary to attain valid start point for the transient mode. To run the engine model for the full range of operation, a double power code is used, e.g., a power code that combines together fuel flow and thrust as primary power code. The first power code relating to fuel flow will run the program to a maximum level of fuel flow (21,000 lb/hr). The corresponding thrust at this power level can be regarded as the maximum thrust. The second power code will take the engine from maximum thrust to a thrust required for the idle condition (5% of maximum value). The two extreme conditions can then be used in shaping an appropriate fuel input for the transient mode to run the engine from idle conditions to maximum fuel conditions just in one go (see Appendix C-2).

A fuel schedule that is capable of driving the engine from idle to maximum power is shown in Figure 4.1.

0 2 4 6 8 100

0.5

1

1.5

2

2.5x 104 Fuel Schedule for Transient Response

Time (s)

Fuel

(lb/

hr)

Figure 4.1 Fuel schedule for the transient response.

The corresponding values of HP spool speed are shown in Figure 4.2.

The spool speed has been shown in percentage of an absolute maximum value of 13,300 rpm. It is worth noting that spool speed takes the same shape as the fuel schedule. This fuel schedule cannot take the speed to 100% because the model does not allow a 100% spool speed at static sea-level (SLS) conditions in either transient or steady state mode.

To find Nhdot from this plot, backward difference can be used in the first order approximation of the derivative operator on Nh, i.e.,

44

[Nh(i) - Nh(i-1)]Nhdot = t∆

where “∆t” is the sampling time (25 ms). HP spool acceleration, obtained in this way, is shown in. Figure 4.3.

0 1 2 3 4 5 6 7 8 9 1065

70

75

80

85

90

95

100HP-spool Speed

Time (s)

Nh (%

)

Figure 4.2 HP spool speed from idle-to-max fuel schedule.

0 1 2 3 4 5 6 7 8 9 1 0-1

0

1

2

3

4

5

6

7

8

9N h A c c e le r a t io n

T im e (s )

Nhd

ot (%

/s)

Figure 4.3 HP spool acceleration in transient response.

The acceleration goes up and comes down because the engine has been accelerated for an idle condition to settle the speed at about maximum. It remains on maximum for more than 2 s and this data is not of any interest.

45

4.1.2. Steady State Plot The second relation is:

Fss Vs Nh

where Fss is the steady state fuel flow when high-pressure spool speed is Nh. This can be easily found by running the program in steady state mode. The program can take Nh as the power code. The Nh vector obtained in transient response can be passed to the steady state mode to produce the corresponding values of steady state fuel (see Appendix C-3). Figure 4.4 shows the fuel demand in steady state as a function of steady state spool speeds.

65 70 75 80 85 90 95 1000

0.5

1

1.5

2

2.5x 104 Steady-state Fuel Demand

Nh (%)

Fss

(lb/h

r)

Figure 4.4 Steady state fuel schedule.

The fuel demand in this case should be less than the demand for the transient case, the difference being called over-fuelling. This fact is exploited to find out dynamic response curve.

4.1.3. Dynamic Response Curve The second relation is,

Nhdot/δF Vs Nh

where δF represents over-fuelling that is the fuel flow increment necessary to produce the acceleration for high pressure spool, Nhdot, when it is running at Nh.

Figure 4.5 combines in the fuel demands in steady state and transient modes to enhance the difference between the two (shown as an upward arrow at speed of about 73%).

46

65 70 75 80 85 90 95 1000

0.5

1

1.5

2

2.5x 104 Transient / Steady-state Response Vs Nh

Nh (%)

Fss,

F (lb

/hr)

TransientSteady state

Overfueling

Figure 4.5 Comparison of fuel demand in transient and steady state modes.

The same difference is called over-fuelling, δF, that can be used to produce the acceleration. Nhdot is divided by δF to give Nhdot/δF, a plot of which is shown in Figure 4.6. The severe oscillations and extremely high values at the two ends may be coming from taking the ratio for an overfueling δF that is too small to be practically considered.

65 70 75 80 85 90 95 1002.5

3

3.5

4

4.5

5

5.5x 10-3 Nhdot/Overfueling Vs Nh

Nh (%)

Nhdo

t/dF

(%/s

)/(lb

/hr)

Figure 4.6 The dynamic response of the engine.

Let y (Nhdot/δF, for example) is the engine data scheduled against any variable x (normally Nh). The following are some key points of implementation of (x,y) data tables in real engine control.

For practical use, data may be discretized over 1 to 5% Nh step. The value of y for intermediate values of x is calculated by linear interpolation.

47

Extrapolation may be performed for any exterior point calculation below the first and above the last data point, or the end point values of y may simply be repeated to extend the table.

The available data for RRIM tables should now be analysed in the light of these comments. The following procedures can, immediately, be adopted:

The data at the edges should be dropped on basis that a minimum required overfueling has not been used to accelerate the engine.

There are some small discontinuities at other points. Consider the jump in dynamic response ratio at about 70% Nh. In discrete sense, it is equivalent to a double valued function. A simple choice to select the value of ratio for this speed is to select an average of the two. This idea implies to all discontinuities and legitimises the use of curve-fitting to find a polynomial function as a global average of data.

Considering these two approximations, a third order polynomial can be used to give a reasonable curve i.e.,

Y = a*X3 + b*X2 + c*X + d

where X is the Nh data and Y represents Nhdot/δF values. The curve is shown in Figure 4.7. The values of coefficients are:

a=1.7230e-7 b=-4.0264e-5 c=3.0320e-3 d=-6.9275e-2

65 70 75 80 85 90 952.5

3

3.5

4

4.5

5

5.5x 10-3 Nhdot/Overfueling Vs Nh

Nh (%)

Nhdo

t/dF

(%/s

)/(lb

/hr)

ActualPolyFit

Figure 4.7 Smoothing dynamic response using curve fitting.

The curve does not fit well to the data below 70% Nh. Other solutions can be sought for this, for instance, dividing the original data into two blocks and using separate curve-fitting for the two. The two curves can be joined by taking a average of the value at 70% Nh but this procedure will keep up a discontinuity in the data.

48

4.1.3.1. Another Approach to Dynamic Schedule

Nhdot/δF component of the dynamic schedules can also be arranged by applying a step fuel input, ∆F, from one steady state value to the other and noting the acceleration obtained immediately after the step is applied. Figure 4.8 shows this idea giving two steady state points for which fuel values are Fss(i) and Fss(i+1). These values can be used to define the step for a transient run, as given below:

∆F=Fss(i)-Fss(i+1)

Nh (rpm)

Fss (lb/hr)

Transient response

Steady-state point Fss(i+1)

Steady-state point Fss(i)

Step fuel input

Figure 4.8 Relation between steady state fuel flow and HP spool speed.

Transient response to this step may have any number of points on the curve but only the first two points will be used to find the acceleration, Nhdot, i.e., using the first order approximation for differentiation,

Nhdot(1)=[Nh(2)-Nh(1)]/ts (4.1)

where ts is the sample time in the transient simulation. At the end,

Nhdot/δF=Nhdot(1)/∆F (4.2)

NB: A small fuel step ∆F will produce a small acceleration and a large fuel step will produce a large acceleration. The analysis of the effect of step size on the ratio Nhdot/δF should be made. This approach has not been followed in the first implementation of the RRIM.

4.1.4. Traditional Scheme in Fuel Scheduling The above sections take the absolute values of fuel spool speed to discuss various issues on constructing the two lookup tables for the RRIM. Traditionally, steady state fuel schedule is taken in the form of Fss/(delta*√theta) where

delta = intake pressure / 14.696

49

theta = intake temperature / 288.15

where 14.696 psi is the standard pressure while 288.15 K is the standard temperature at static sea level.

Dynamic schedule is modified to Nhdot/(δF/√theta). It is not known that why the dynamic schedule does not have a delta-correction. The HP spool speed is also replaced by the aerodynamic counterpart, Nhdot/√theta so that the two tabular relations used in the RRIM take the forms:

Nhdot/(δF/√theta) Vs Nh/√theta Fss/(delta*√theta) Vs Nh/√theta

In static sea-level conditions, delta and theta are unity. The above corrections are made in the implementation of the RRIM.

4.2 From Traditional to RRIM Once the RRIM tables have been constructed, the Rolls-Royce scheme of inverse modelling finishes and the RRIM is there to replace the traditional controller. Figure 4.9 shows, in block diagrams, the change from the traditional to the RRIM control design as proposed by their implementation in the EEC.

Figure 4.9 divides the control into two categories with respect to the structure of the control loop. The rate control is in one category and the limits and thrust control are in the second.

As explained in Chapter 2, thrust control takes reference input from pilot’s thrust request or a steady state LP spool speed schedule. The limiter loop follows a reference that is a limit for a specific control parameter.

The inverse model (RRIM) is common to all loops and will replace the integrator.

Following the changes proposed in Figure 4.9, the next change, from the traditional to the RRIM controller, is the change made in the demands of the ACU, the DCU and the Backup ACU demands. The ACU and the DCU of the existing traditional controller manage a demand on rate of change of fuel flow. The reference input for the ACU and the DCU of a RRIM controller should be a demand on acceleration. Strictly speaking, designing a reference schedule (demand) is not a part of control design, rather it is a part of defining functional requirements for the engine.

Fortunately, the rate of change of fuel flow demand in the traditional controller is also calculated from a basic acceleration demand. The ACU and the DCU demand can, therefore, be arranged in the form of acceleration by a slight modification in the ACU and the DCU demand generator of the traditional controller as explained from the following sections.

50

SS/Limit Error

SS/Limit Error

Accel/Decel. Error

T1s+1 T2s+1 K

LSL

Fdot Demand

1 s

Fuel Command

Accel/Decel. Error K

LSL

Nhdot Demand

RRIM Fuel Command

K 1 s

K

Fdot Demand

Nhdot Demand

Figure 4.9 Change from traditional to RRIM controller.

4.2.1. ACU Demand The ACU in classical design controls the rate of change of HP shaft speed (Nhdot) to an Nhdot schedule. Figure 4.10 shows a simple picture of the ACU in classical control ignoring any trims and correction factors.

H

W

ACU Nhdot Schedule

Altitude ACU Fdot

demand KACU

+ Nh/ theta

ACU Nhdot demand limit Nhdot

-

ACU Fdot/F Schedule

P20

Nh

+

+

Fuel flow demand

ACU Fdot

Figure 4.10 ACU demand generator in classical control.

The ACU rate of change of fuel flow demand is calculated using two schedules, the ACU Nhdot schedule and the ACU Fdot/F schedule. The ACU Nhdot schedule is compared with an ACU Nhdot demand limit in a highest wins function. The resultant is then multiplied with an ACU gain KACU, to give an ACU Fdot demand. The ACU Fdot/F schedule is corrected by multiplying with the fuel demand to produce Fdot demand. The overall ACU Fdot demand is the sum of Fdot demand coming from the basic ACU Nhdot schedule and the ACU Fdot/F schedule.

51

A simple modification to the ACU in classical control to fit it to the RRIM controller is to make it a one-schedule functional, i.e., the function of only the basic ACU Nhdot schedule. Figure 4.10 is, therefore, a subset out of Figure 4.11.

H

W

ACU Nhdot Schedule

Altitude

ACU Nhdot demand

Nh/ theta

ACU Nhdot demand limit

Figure 4.11 ACU demand in RRIM control.

4.2.2. DCU Demand The DCU in classical design controls the rate of change of HP shaft speed (Nhdot) to a Nhdot schedule. Figure 4.12 shows a simple picture of the DCU in classical control ignoring any trims and correction factors.

L

W

DCU Wfdot demand

KDCU +

Nh/ theta

DCU Nhdot demand limit Nhdot

-

DCU Wfdot/Wf Schedule

P20

Nh

+

+

Fuel flow demand

DCU Wfdot

DCU Nhdot Schedule

Figure 4.12 DCU demand generator in classical control.

The DCU rate of change of fuel flow demand is calculated in the same way as the ACU demand, as can be seen in the simplified diagram of Figure 4.12. Following a similar procedure as in the case of the ACU, the DCU Nhdot demand can be arranged simplifying the rate of change of fuel flow demand. Figure 4.13 shows how the DCU Nhdot demand is generated.

H

W

ACU Nhdot Schedule

Altitude

ACU Nhdot demand

Nh/ theta

ACU Nhdot demand limit

Figure 4.13 DCU schedule in RRIM control.

52

4.2.3. The Control Loop Structure in Rate Control Not only the thrust loop and the limiters but also the ACU, the Backup ACU and the DCU in the RRIM controller have a structure different from that of the traditional controller (see Figure 4.9). The ACU and the DCU loops in the RRIM controller have the structure of Figure 4.14.

Nhdot

Nh ACU/ DCU Schedule

+ Engine

FMS d dt -

Nhdot Demand Fuel

Command

RRIM K s Kf

Figure 4.14 ACU and DCU loop structure in RRIM controller.

The control loop structure of the ACU and the DCU includes an integrator. The basic ACU and the DCU schedule in the traditional controller is an Nhdot schedule that is compared with the actual Nhdot response to compute the control error. This error is multiplied with a gain (K in Figure 6.15) to generate a rate of change of fuel flow demand, Fdot. The rate of change of fuel flow demand is integrated to inject the commanded fuel flow into the engine using the Fuel Metering System (FMS).

In the case of increasing speed, if acceleration is the same as the demanded acceleration, error will be zero and integrator will send a constant acceleration demand to the RRIM that would be converted to an equivalent fuel flow command. The acceleration command will change as soon as the acceleration becomes higher or lower than the demanded acceleration. The following points should be noted:

In case the error is zero, integrator will maintain an acceleration demand on the engine. For a nonzero reference, the engine will be in permanent acceleration and engine speed will continue to increase until the fuel flow command reaches a maximum and saturates there for a maximum allowable fuel flow. Of course, it is not always desirable to operate the engine on a limit. In a practical situation, Nhdot command of the integrator is received by the Loop Selection Logic (LSL) where it is compared with the other acceleration demands in a lowest-wins function. The acceleration command of the thrust control loop, for example, may be zero and that will win through the loop selection logic. The engine, will, therefore, not go to the limit.

If RRIM were a perfect model of the engine, it could be able to command fuel that can cause the real acceleration to be the same as the commanded acceleration. This could allow an open loop design, in which the acceleration demand could be fed into the RRIM

53

to generate an equivalent fuel flow demand. But since RRIM is not a perfect one, the actual acceleration would be different from the demanded acceleration.

In the selector control of the engine, none of the control loop remains in control all the time in a transient. In a situation when the acceleration loop, for example (and the same is true for deceleration loop) is not in control, a non-zero error will persist at the input of integrator. The integrator output will wind up to a very large number. This is a problem similar to the classical problem in PI controller when actuator operates on the limit. As a practical solution to this problem, the following actions can be taken.

Integration should be disabled and acceleration and deceleration demands should directly be connected to the loop selection logic to be compared with the other acceleration demands.

The integrator should be initialised to the modelled acceleration, Nhdotm from within RRIM itself when the acceleration or deceleration loop is selected. The integration action would be enabled to re-initialise the feedback control at this point.

4.2.4. Backup ACU The Backup ACU rate of change of fuel flow demand is a functional requirement of the engine that will replace the ACU rate of change of fuel flow demand in certain cases. This function is defined by the engine design group on the basis of some practical tests on the real engine. The Backup ACU in classical design is a Backup ACU Fdot/F schedule that is multiplied by the current fuel flow demand to generate a rate of change of fuel flow demand. Figure 4.15 shows a simple picture of the Backup ACU in classical control ignoring any trims and correction factors.

ACU Wfdot/Wf Schedule

P20

Nh

Fuel flow demand

Backup ACU Wfdot demand

Figure 4.15 Backup ACU in classical control.

The rate of change of fuel flow demand effectively controls the acceleration of the engine. There was no question of designing the Backup ACU in the absence of the Backup ACU acceleration demand. The traditional design, on the other hand, shows that the engine may not function appropriately at the start of acceleration, in the absence of the Backup ACU. In the absence of a reference for the Backup ACU, three options are available in the RRIM control design:

54

OPTION 1

The Backup ACU may be ignored pretending that the ACU is appropriate at all times in normal (steady-state) mode and need not be replaced by the Backup ACU.

OPTION 2

The ratio between rate of change of fuel flow demand produced by the ACU and the Backup ACU can be found from the available traditional control design of the EEC. If Rfr is the ratio defined as:

ACU from demand flow fuel of change of RateACU Backup from demand flow fuel of change of RateR fr = (4.3)

This ratio can be thought as a correction factor for the ACU, which is applied at the start of an acceleration only and disabled afterwards. It can, then, be assumed that acceleration demands, in the case of the RRIM controller, should maintain the same ratio. Then the Backup ACU schedule can be computed as:

ScheduleNhdot ACU*RScheduleNhdot ACU Backup fr= (4.4)

NB: To find Rfr, all the inputs of demand generators of the ACU and the Backup ACU, as given in Figure 4.10 and Figure 4.15 should be realistic, i.e., arranged from the engine model tests because they should all be consistent with each other.

OPTION 3

The existing Backup ACU in the original form should be, in some way, adjusted in the RRIM design.

The first option is the easiest one because the Backup ACU loop can simply be removed from the EEC simulation. The third option demands a two-stage loop selection logic so that one-stage can process the acceleration demand of steady state or limiter loop while the other can process rate of change of fuel flow demand of the Backup ACU. This approach may be regarded as a two-stage selector control and can be extended to incorporate the ACU and the DCU from the traditional design.

4.2.5. Two-stage Selector Control Figure 4.16 through Figure 4.19 represent pictorial view of a two-stage selector. Figure 4.16 represents a simplified view of the LSL in the traditional control.

The integration action, in discrete implementation is as simple as follows:

F(t)=F(t-1)+Fdot*ts=F(t-1)+∆F (4.5)

where ts is the sample time and ∆F is the fuel flow increment command of the controller. This is shown pictorially in Figure 4.17.

55

LSL Fdot Demand

Fdot Demand 1

s Fuel Command

All Loops

Figure 4.16 Simplified view of traditional selector control.

F(t-1)

LSL Fdot Demand

Fdot Demand

F(t)

All Loops

z -1

+

+ ts

F

Figure 4.17 Digital implementation of integrator.

The selector control is designed using If-Then-Else rules to allow the highest or lowest value. As for as the idea of loop selection logic is concerned, there is no harm in computing the fuel flow increment before the LSL, as shown in Figure 4.18. Figure 4.16 and Figure 4.18 will give entirely the same result. Practical implementation follows Figure 4.16 because it does the same job with lesser computational burden.

F(t-1)

LSL Fdot Demand F(t)

All Loops

z -1

+

+

ts

Demand F Demand

F

Figure 4.18 Loop selection logic based upon fuel flow increments.

The idea of designing the LSL based upon fuel flow increments, presented in Figure 4.1, can be extended to RRIM control. Compare the RRIM action with that of its counterpart in the traditional controller (the integrator). RRIM receives a fuel feedback from the fuel metering system and computes an absolute value of fuel command. If F(t) is the fuel command computed by RRIM at time t and F(t-1) is that computed at previous sample time, then effective fuel flow increment commanded by RRIM can be given as:

∆F=F(t)-F(t-1) (4.6)

This is shown as ‘∆F demand’ in Figure 4.19.

56

Demand F

F(t-1)

F(t)

Fdot Demand

Nhdot Demand

LSL ‘1’

Nhdot Demand

Thrust and Limits

z -1

+

-

ts

RRIM

LSL ‘2’

Demand F

Fuel Demand

ACU,DCU Bkup ACU

Figure 4.19 A two-stage selector control in RRIM controller.

Once the fuel flow increment commanded by the RRIM controller is known, it can be compared with the fuel flow increments commanded by the ACU, the Backup ACU and the DCU of the traditional controller. Equation (4.5) is valid for all the control loops including the Backup ACU. Let ∆FBACU is the increment generated by the Backup ACU, then

∆FBACU=(Fdot)BACU*ts (4.7)

Similar equations can be written for the ACU and the DCU

∆FACU=(Fdot)ACU*ts

∆FDCU=(Fdot)DCU*ts (4.8)

The separate LSL for acceleration and deceleration control allows, in general, mixing of the traditional control loops with the RRIM control loops. This introduces another flexibility in selector control design of a gas turbine engine in that the designer can select, for some reason, any of the two control techniques for each control loop.

4.2.5.1. Loop-in-Control Index in Two-stage Selector Control

In practical implementation of the EEC, each loop is labelled with a unique index. The logic that indicates the label of the loop is called Loop-in-Control Index (LCI) logic. This logic compares the output of the LSL with all its inputs, turn by turn, until it finds the two to be equal. This is a simple search procedure for the control demand that passed through the LSL.

The LCI logic applied to a two-stage selector control needs acute modification in the existing LCI of the traditional control in order to incorporate two, instead of a single variable. The variable processed in the first stage of the selector control is acceleration while that processed by the second stage is the fuel flow increment. This logic is very helpful in fine-tuning the gains in time domain to track the loop in control and must be modified in the two-stage selector control accordingly.

57

After making the above changes in the existing traditional controller, the next step towards the RRIM controller design is then gains tuning.

4.3 Fuel Feedback to RRIM RRIM computes the amount of fuel flow that can fulfil an acceleration demand using the modelled HP spool speed (see Chapter 3). To compute a modelled spool speed, it uses fuel feed back. There are many options for the fuel feedback to the RRIM, at least in the simulation based EEC, as shown in Figure 4.20.

Engine

FMS Nhdot Demand

Fuel Command

RRIM

(a) (b) (c) (d)

Limiter

Feedback Options

Figure 4.20 Options for fuel feedback to RRIM.

The fuel feedback to the RRIM could be from any of the following systems in the control loop:

(a) The RRIM itself (b) The FMS output. (c) The fuel limiter output. (d) The engine fuel output

The option (a) excludes the dynamics of all the other systems in the control loop from the fuel feedback. It is practicable from the control implementation point of view and is one of the settings that should be analysed for stability and performance. The FMS out put in the option (b) is more realistic to be used as fuel feed back because it represents the actual amount of fuel injected into the engine. The actual fuel that is injected into the engine is different from FMS when limiter is active and the option (c) provides the actual amount of fuel in this case. It, however, introduces a saturation nonlinearity in the control loop in addition to that of fuel metering valve in the FMS, when the fuel flow commanded by the FMS crosses limits. The option (d) is purely theoretical because there is no physical sensor in the real life control that will measure the fuel as the engine ‘output’. The only reason to use/discuss the option (d) during a simulation based analysis and design is , perhaps, that it looks a traditional approach to the feedback design.

The option (a) was also tested in the EEC and the option (d) was analysed in finding nominal loop transfer function for frequency domain analysis. As far as the simulation is

58

concerned, this does not make any notable difference in time domain or frequency domain analysis. The option (b) is the same as the option (c) because the steady state fuel flow used in finding the nominal model is always within the limits. The option (b) has been selected in the final implementation of the RRIM controller because it is the most logical option from implementation point of view in the real engine.

4.4 Tuning Gains in Frequency Domain In the linear control design, frequency domain analysis helps finding gain margin, phase margin and bandwidth of the system. These parameters relate to relative stability of the system and reflect robustness properties of the control design. The RRIM is a nonlinear controller and the frequency domain analysis of the control loop is only possible if the control loop is linearized.

4.4.1. Why Frequency Domain Analysis? There were two motives of frequency domain analysis in the RRIM control design.

4.4.1.1. Robustness Analysis

A control design is, in general, incomplete without a robustness analysis. The RRIM control is a patent of Rolls-Royce and no procedure has been proposed by Rolls-Royce for the robustness analysis of the control design. Robust nonlinear control is an advanced area of research and no procedure could be sought from the nonlinear control literature that could be tailored to the RRIM control design during this project. In the absence of any other way to ensure robustness of the RRIM controller, the conventional linear approach to the robustness problem was the only way to ensure a robust control design.

4.4.1.2. Control Design Specifications

The design specifications for the control system of the engine under consideration (see Chapter 2) were also given in terms of phase margin, gain margin and bandwidth etc. These specifications urged to linearize the control loop and analyse the control design for stability margins and bandwidth. It was also required to complete the comparison of the RRIM controller with the traditional controller.

4.4.2. Linearization Procedures The two nonlinear components of the control loop are the RRIM controller and the engine. Linearization of the control loop, therefore, comprises the following steps:

Linearize the engine at reasonable number of operating power levels, e.g., at a regular 5% Nh step.

Linearize the controller for the Nh values selected in step 1.

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4.4.2.1. Linearization of Engine

The linear model of the engine was found using Xmath and the linear model in transferred to Matlab. The RRAP engine model is implemented in FORTRAN and has a user front of SystemBuild. The model can be accessed using Xmath only. Linearization of the engine model is also restricted to Xmath environment where special functions are used to access the model for this purpose.

The nonlinear model of the engine has 38 states (Appendix D-2). Xmath allows the user to activate some of the states and leave the others in linearization process simply by using zero perturbations on the states that are not activated by the user. There are some problems in activating the intermediate pressure (IP) compressor volume. The other volumes and heat soaks can also be ignored in the control system design as they have little effect on the engine power as compared to the shaft speeds. The only states that are selected for control system design are the states representing shaft speeds. The resulting state space (A, B, C, D) model will have the following dimensions:

States: Nl, Ni, Nh Output: 105 (all the outputs of engine model as given in Appendix D-3) Inputs: Fuel, VIGV angle

For internal settings of the IGV angle, only one column of the B matrix in state space model has nonzero entries. In the SISO control of the engine, output vector has two entries: one for the fuel, F that may be fed back to the RRIM controller (see section 4.3) and one for the exit point pressure of the low pressure (LP) turbine, P50 that is used to calculate the EPR. The fan inlet pressure, P20 at sea level static (SLS) is fixed. The reduced model for EPR loop will, therefore, have the following dimensions:

States: Nl, Ni, Nh Output: P50, F Inputs: Fuel

NB: The transfer function between the fuel input and the fuel output can be expected to be unity but it does not come out to be. It is rather a strictly proper system with 3 poles and three zeros almost cancelling each.

4.4.2.2. Linearization Of RRIM

RRIM is linearized in Matlab separately as a two input one output system. The linear model of the RRIM has the state space form as given below:

Ar = [a] Br = [0 b]

Cr = [c] Dr = [d 0] (4.9)

This gives rise to the following structure of linear RRIM.

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Fuel Feedback

RRIM Fuel Command

Nhdot Demand

+

+

+

+ d

1 s

a

b c

FMS

Figure 4.21 Linear model of the RRIM in feedback with FMS.

4.4.2.3. The Loop Transfer Function

Figure 4.21 also shows the feedback arrangement for RRIM. Since feedback to RRIM comes from fuel metering system (FMS), linear RRIM model makes a feedback structure with FMS. The equivalent feedback transfer function of the RRIM and FMS, Gra(s) is found from the corresponding feedback diagram.

The transfer function Gra(s) is in series with the engine model and the pressure sensor. The equivalent loop transfer function is found by cascading the three transfer functions. The sensor has a pole at s=100 and unity steady state gain. Other transfer functions are computed at each operating point and combined together, through block diagram manipulations, to represent the loop transfer function to be used in the stability analysis.

NB: The RRIM and the FMS can also be connected together for linearization in Matlab. This was, however, avoided due to practical problems in linearization of the RRIM in combination with the FMS. It reveals from the functionality of the RRIM and its linearization as described above that it has a persistent pole at s=0, at all nominal points. This pole is disturbed in numerical computations of the linear model when the RRIM and the FMS are put together in the linearization scheme. As a result, instead of a pole at s=0, a positive or negative pole appears near the origin of the s-plane. To avoid this difficulty in using the computational method of linearization, the RRIM is linearized separately and then combined with the other linear systems through block diagram manipulations.

4.4.2.4. Stability Margins

The detailed analysis of the control loop for all nominal points is excluded from this report. Only two nominal points have been discussed in Appendix E, the first is that for 60% Nh and the second response is that for 95% Nh. The first nominal point lies at about the idle speed requirement of the engine while the second response corresponds to a speed near to maximum take off (MTO) speed at static sea level (SLS). The loop transfer

61

function is nonminimum phase (NMP) type at 60% Nh while a mimimum phase (MP) type at all other nominal points.

A summery of the gains selected on the basis of 3dB bandwidth requirement is as below: Table 4.1 Gains in the RRIM controller for a 3 dB bandwidth.

Nh (%) Gain Phase Margin

(deg.) Gain Margin

(dB) Band-width

(rad/s) 60 2213 63.8 12 0.8 65 1549 139.4 Inf 3 70 923 115.3 Inf 3 75 484 100.0 Inf 3 80 269 94.2 Inf 3 85 186 94.8 Inf 3 90 135 94.5 Inf 3 95 176 108.0 Inf 3

The NMP systems have a bandwidth that is function of the zero’s position in the right half s-plane. That’s why the system has a lower bandwidth at 60% Nh. The following points can be noted from Table 4.1.

The linear system has infinite gain margin (except at 60% Nh). Phase margin is much more than required (almost 50 to 100% more). Loop gain could be increased as high as eight to ten times the gain at 3 rad/s

bandwidth before the phase margin becomes an issue.

It is, therefore, only the performance (bandwidth, noise rejection etc.) that would help select or reject any gain. The performance may be measured in terms of bandwidth or in terms of rise time, settling time, steady state error etc. in time domain.

The following section introduces gains selection process based upon rise time, overshoot, smoothness of the response and some engineering instincts.

4.5 Gains Tuning in Time Domain Gains may be tuned on the basis of shape of the response i.e., rise time, settling time and overshoots. The RRIM controller is found very easy to be tuned to satisfy the time domain specifications of the engine under consideration. There are two motives to tune the gains in time domain.

4.5.1. Verification of Frequency Domain Analysis Frequency domain analysis is not possible for the nonlinear systems and the system is, therefore, linearized to ensure bandwidth, gain margin, phase margin etc. But are the specifications for the time response e.g., rise time, settling time and overshoot, fulfilled or not? Is there any need of further tuning, using the nonlinear model, keeping in view the allowable range of the gains based upon frequency domain analysis? Yes, the response of

62

the nonlinear system should be analysed for the gain schedule decided in frequency domain analysis. Gains are verified for the EPR loop at each operating point used as a nominal point in linearization.

Linearization uses small perturbations around the nominal point and the model is valid for small perturbations only. To keep up this ides in nonlinear control loop, the EPR step was kept as low as 0.1% of the the operating range that gives a variation on EPR of about 0.4. A total perturbation of 0.0004 EPR about the operating point allows an EPR step of just 0.0002 EPR on both sides of the steady state operating condition as shown in Figure 4.22.

20 s

0.0004 EPR 0.0002 EPR Steady-

state EPR

0 s

Figure 4.22 EPR step input for verification of controller gains.

The closed loop system is allowed to settle at steady-state EPR corresponding to the nomiunal point. A step of 0.0002 is added to the reference and time is allowed for the response to settle with no oscillation or EPR error. A negative step of 0.0004 will take the response in the opposite direction at 0.0002 EPR from the operating point.

4.5.2. Avoiding Linearization Another possible approach to tuning gains for the RRIM controller is to keep the analysis procedures strictly in nonlinear domain. Experimental procedures can be adopted to estimate gain margin, phase margin and bandwidth. Settling time reflects the bandwidth of the nonlinear system. A wide variation of the controller gain gives an estimate of the gain margin. Similarly, phase lag can intentionally be introduced in the control loop and varied to observe phase margin. Moreover, if there is no linear model involved in the control design procedure, there are lesser parameter errors that should be compensated for in terms of phase margin.

Strictly speaking, the step response methods used for the analysis of linear systems are, however, confined to linear systems only. This is because the model of a nonlinear system changes with change in operating point. For a nominal linear system, the size of the step does not affect the dynamics of the system. For a nonlinear system, the first step in time domain analysis is to decide the size of the step.

What should be the criteria for tuning gains in time domain? The following section provides a discussion on the step size in tuning gains for the EPR control loop.

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4.5.3. Criteria for Tuning a Nonlinear Control System There are many arguments on the size of step used as reference input to observe time domain characteristics. One argument that applies in general to all nonlinear systems is that step size to observe the step response should be small enough to keep the operating range small. The following points should be noted:

The RRIM is a nonlinear controller and a large reference input, e.g., a step increase of 0.2 EPR changes the operating point.

The RRIM, on the other hand, is a robust controller (as observed in its application to the Trent engine in this project) and can perform satisfactorily with a constant gain over a wider operating range as compared to the traditional linear controller. This allows a large step size used to observe step response.

In any case, the whole range can be divided into regular 5% Nh intervals so that gain can be scheduled as a function of Nh. The choice of Nh step, instead of EPR step is for two reasons, firstly, because it is a conventional approach seen in the existing traditional control of the engine under consideration and secondly, because the RRIM tables are constructed for upon and scheduled across the Nh response of the engine.

On the basis of above arguments, the following options are available:

OPTION 1

Define steps over EPR that correspond to 5% Nh steps as shown in Table 4.2. Table 4.2 EPR steps in tuning gains for the EPR loop.

No. Nh (%)

Fuel (lb/hr) EPR ∆EPR

1 55 824.3 1.00425 - 2 60 1053.04 1.00639 0.00176 3 65 1417.4 1.00933 0.00294 4 70 2110.93 1.01833 0.0135 5 75 3621.71 1.04646 0.02673 6 80 6044.94 1.09337 0.04584 7 85 9597.36 1.16825 0.07403 8 90 14447.6 1.28342 0.010854 9 95 20285.1 1.43062 0.11905

The reference will be given as:

EPRRef=EPR+∆EPR (4.10)

where both EPR and ∆EPR correspond to the same row in Table 4.2. In steady state at EPRRef, the speed will rise by 5%Nh. The size of the step, ∆EPR varies drastically from idle to maximum power as shown in Figure 4.23.

64

EPR steps in gains tuning for EPR loop.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

55-6

0

60-6

5

65-7

0

70-7

5

75-8

0

80-8

5

85-9

0

90-9

5

Nh Range (%/s)

EPR

Figure 4.23 EPR changes for 5% Nh step.

The reason why this issue comes into discussion in tuning the gains using nonlinear engine model, on the basis of time domain specifications, is that the RRIM controller is nonlinear that responds to Nhdot demand. Nhdot demand is computed from the control error as follows:

Nhdot=K* (EPR Error)=K*(EPRRef-EPR)=K*∆EPR (4.11)

The idea is that a single gain should work appropriately over 5% Nh rise or drop. The gain at the end is assigned to the middle of the Nh range when scheduled as a function of Nh/√θ where θ is defined as

Theta (θ)=T1/288.15 K

T1 is the fan entry temperature.

OPTION 2

The EPR step, ∆EPR should not be fixed upon 5% Nh increment, rather it should be a percentage of EPR at operating point. The two choices in fixing the step size could be as follows:

A fixed step size of reference EPR in tuning gains at different power levels is can replace unequal EPR steps used in the option 1. This fixed step size may be a fixed percent of the EPR rise from idle to maximum speed. This, for example, could be 1% (0.004) of the EPR rise (approximately 0.4) from idle to maximum power level.

A variable step on EPR can be defined depending upon the EPR level the engine is operating on. This for example, would be 0.1 (1% of 0.1) when engine steady state is 1.1 EPR and 0.003 (1% of 0.3) when engine steady state is 1.3 EPR.

In all cases gain will be scheduled as a function of Nh/√θ.

65

All the limiters, the ACU and the DCU were designed in time domain using a different step sizes for the reference. A constant gain was selected for each of the control loop for the whole operating range. The following table lists up the gains for different control loops other than the EPR loop (see Chapter 2 for the engine control parameters). Table 4.3 RRIM controller gains for limits and demands.

No. Control Loop Gain

1 Nlmax limiter 1.0

2 Nlmin limiter 0.5

3 Nimax limiter 4.0

4 Nhmax limiter 0.5

5 Nhmin limiter 5.0

6 P30max limiter 0.2

7 P30min limiter 0.2

8 Acceleration demand (ACU) 0.20

9 Deceleration demand (DCU) 0.25

Note that there are two limits on one parameter. The gain is different for the minimum and maximum limiter for the LP spool speed Nl and the HP spool speed. There is no limiter for the idle (minimum) IP spool speed parameter. The HP compressor delivery point pressure, P30 has the same gain for the minimum and the maximum limiter.

4.6 Summary The acceleration and the deceleration demand schedules in the ACU and the DCU in the traditional controller are also derived from a basic spool acceleration demand. This allowed a full-scale design purely based upon the RRIM controller.

To include the Backup ACU in the RRIM design, a mixed approach was developed in which the ACU, the DCU and the Backup ACU from the traditional controller could work together with the RRIM controller for all the other loops.

Gains of the RRIM controller can be tuned both in time domain with the nonlinear control loop and in frequency domain with the linearized control system. Frequency domain tuning was adopted for the EPR loop because it helped satisfying the control specifications of gain margin, phase margin and bandwidth defined for the traditional control design. The gains that satisfy the frequency domain characteristics were also found satisfying the time domain requirements were applied in the final implementation of the RRIM controller in Electronic Engine Control. No frequency domain analysis was carried for the limiters, the ACU and the DCU. The gains for these loops are based upon simulation experiments in the time domain.

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Chapter 5 Performance of RRIM Control

This project is the first implementation of the RRIM controller and was basically aimed at assessing the feasibility of the new control scheme in high bypass ratio turbofans used in the civil aircraft. The first stage was to make the new scheme functional in the EEC of the engine under consideration. The Electronic Engine Control (EEC) of the Trent series was already in place and supposed to perform satisfactorily.

5.1 The Analysis Procedures The performance of the advanced nonlinear RRIM controller is compared with that of the traditional controller in the light of criteria defined in actual pass-off tests of the engine. The comparison of the two controllers is done for the following tests:

Slam acceleration Slam deceleration Slow ramp acceleration Slow ramp deceleration

The slow action (acceleration/deceleration) is basically a test of the main control loop that is engine pressure ratio (EPR) control. The EPR is an indicative of the thrust/power of an engine.

The slam action activates the other loops i.e., the limiters and the acceleration/deceleration control loops governed by the acceleration and the deceleration control units (ACU and DCU respectively).

The section corresponding to each test describes the pass-off test criteria before the comparison. In each test, EPR is the indicative of power and the high pressure (HP) spool acceleration and deceleration will be considered as the parameter of interest in discussing acceleration and deceleration of the engine.

In addition to the conditions of the pass-off tests, the response has also been compared on the basis of surge margin. Briefly stated, a higher surge margin is preferable from the safety point of view. Moreover, a surge margin of 0.2 (20%) can be considered as a crude approximation of the minimum acceptable surge margin at all operating points. A zero surge margin means the engine will surge and may also be operating at stall (see Chapter 2, ‘Compressors’ for details of surge and stall). The initial stage of a compressor being in stall may be occasionally acceptable. A low value of surge margin for the low pressure

67

(LP) compressor (the inlet fan) may not be as objectionable and is less likely to occur in the by-pass engines. The surge is, however, of serious concern in operational safety in the intermediate pressure (IP) and high pressure (HP) compressor.

Moreover, the surge margin should not be related to the gain and phase margin (relating to the stability issue) because the (nominal) engine system with high gain and phase margin can exhibit surge and stall.

Besides the performance issue, the two control techniques have also been analysed for the computational burden.

Brief attention is given to the issue of vulnerability to sensor noise. The noise rejection property of only the RRIM controller is observed. No comparison is made with the traditional control in this issue.

A short list of the acronyms and abbreviations used in this chapter are given in Table 5.1. Table 5.1 Important abbreviations and acronyms.

Abbreviation Description TRA Throttle Resolver Angle (the same as PLA)

PLA Pilot Lever Angle

EEC Electronic Engine Control

SLS Static sea level

EPR Engine pressure ratio

BV Bleed Valve

HB Handling Bleed

VSV Variable Stator Vane

HP High pressure

IP Intermediate pressure

LP Low pressure

Nl LP spool speed

Nh HP spool speed

Ni IP spool speed

Different control loops take over the control of the engine at different times when the power level of the engine is changed. Different control loops are identified by an index, called the loop-in-control index, in the EEC.

5.2 Loop in Control Index The response of the engine, in general, is a cumulative response of many controllers. It is, therefore, important to view loop-in-control index to know of which controller remained

68

in control at what time. Table 5.2 gives a full list of the loop-in-control index used to label different control loops.

The loop-in-control index will be plotted in many cases in the analysis of performance of different control loops in the relevant sections and Table 5.2 will facilitate to identify the loop in control. Table 5.2 Loop-in-control Index.

Index Loop in Control 1 Minimum P30 acceleration / rate of change of fuel flow demand in control.

2 Minimum Nl acceleration / rate of change of fuel flow demand in control.

3 Idle Nh acceleration / rate of change of fuel flow demand in control.

4 Steady state EPR acceleration / rate of change of fuel flow demand in control.

5 Maximum Nl acceleration / rate of change of fuel flow demand in control when reverse thrust is selected.

6 Maximum Nl acceleration / rate of change of fuel flow demand in control limited by maximum Nl red line speed limit.

7 Maximum Ni acceleration / rate of change of fuel flow demand in control.

8 Maximum Ni acceleration / rate of change of fuel flow demand in control.

9 Maximum P30 acceleration / rate of change of fuel flow demand in control.

10 Maximum ground start TGT acceleration / rate of change of fuel flow demand in control.

11 ACU acceleration / rate of change of fuel flow demand in control.

12 Backup ACU acceleration / rate of change of fuel flow demand in control.

13 DCU acceleration / rate of change of fuel flow demand in control.

14 Fuel flow demand limited by scheduled maximum fuel flow limit.

15 Fuel flow demand limited by scheduled minimum fuel flow limit.

16 Steady state Nl acceleration / rate of change of fuel flow demand in control in reversion mode when reverse thrust is not selected.

17 Fuel flow demand limited by absolute maximum fuel flow limit.

18 Fuel flow demand limited by starting fuel flow or absolute minimum fuel flow limit outside of starting mode.

19 Steady state Nl acceleration / rate of change of fuel flow demand in control when neither reversion mode nor reverse thrust is not selected.

20 Not used

21 Maximum Nl acceleration / rate of change of fuel flow demand in control limited by Ni/√θ.

22 Idle Nh acceleration / rate of change of fuel flow demand in control set by T30 minimum limit for water ingestion.

23 Fuel dip in progress.

Sections 5.3.1 and 5.4.1 define tests and subsequent validation procedures for the EEC response to slam PLA manoeuvres at sea level static (SLS) conditions.

69

5.3 Slam Acceleration A sudden demand of increasing the engine power from idle to maximum level will cause slam acceleration. The pass-off test criteria for slam acceleration is as follows:

5.3.1. Pass-off Test Criteria for Slam Acceleration Test

Set the High/Low idle switch to select high idle and allow the simulation to settle at high idle speed.

Perform a slam acceleration by ramping PLA from idle to maximum forward in one second. Continue the simulation untill the response settles at maximum conditions.

Analysis

(a) Verify that the value of EPR command ramps as required by the EPR-TRA relationship of the selected rating from idle to maximum take-off.

(b) Verify that during acceleration, the fuel demand is scheduled smoothly with no discontinuities. There may be small discontinuities at Bleed Valve closing points.

(c) Verify that actual EPR does not exceed the EPR command by more than 0.02 EPR during the transient nor 0.01 EPR for more than 3 second at maximum take-off.

(d) Verify that any transient overshoot of the engine speeds is within 0.5% and TGT overshoot within 12.5 K.

(e) Verify that at stabilised maximum take-off, EPR is controlled to 1.337±0.005 EPR.

(f) Verify that the engine simulation reaches ≥ 35% of maximum take-off thrust within 4 seconds, and ≥ 95% within 8 seconds (± 1 second tolerence allowed).

(g) Verify that Bleed valve scheduling is as defined by Performance Group, and that all Bleed valves are closed at Maximum Take-off condition.

(h) Verify that Variable Inlet Guide Vane (VIGV) scheduling is as defined by Performance Group, and that the position reads -5.73 deg. at maximum take-off conditions.

5.3.2. Comparison in Slam Acceleration The response of the acceleration control unit (ACU), as shown in Figure 5.1 in the traditional controller can be seen from slam action input i.e., by giving step demand from idle to maximum power.

The condition (a) of the pass-off test criteria is a requirement on EPR command (the reference in Figure 5.1 that it should ramp according to a selected EPR-TRA relationship

70

known as the ratings function. The TRA is moved from 5 deg to 90 and the generated EPR command comes out to be different in the RRIM and the traditional control. Since the definition of the ratings function is not known, the source of this difference is not known. It will, however, be supposed that the condition (a) is satisfied in both cases.

5 10 15 20 250.9

1

1.1

1.2

1.3

1.4

1.5EP

R

RRIM Vs trad. controller: Slam deceleration

Time(s)

TraditionalRRIM

Figure 5.1 RRIM Vs Traditional Controller: slam acceleration.

Continuity of Fuel

The fuel is scheduled by the two controllers at the values shown in Figure 5.2. The condition (b) of the pass-off test criteria requires the verification that during acceleration, the fuel demand is scheduled smoothly with no discontinuities. As can be seen in Figure 5.2, , there are small discontinuities at two points between 12s and 14s in the response under the traditional controller. In the case of the RRIM controller, fuel input is not smooth at the maximum value.

0 5 10 15 20 250

0.5

1

1.5

2

2.5x 104

Fuel

(lb/

hr)

Time(s)

RRIM Vs trad. controller: Slam acceleration

TraditionalRRIM

Figure 5.2 RRIM Vs Traditional Controller: fuel shape in slam acceleration.

71

The size of the fuel discontinuities in the traditional control can be estimated from Figure 5.3. The magnitude of fuel flow oscillates in the range 400 to 800 lb/hr at two points during slam acceleration.

10 12 141.02

1.04

1.06

1.08

1.1

1.12

1.14

1.16

1.18

1.2

1.22

EPR

Time (s)10 12 14

0.4

0.6

0.8

1

1.2

1.4

1.6x 104

Time (s)

Wf (

lb/h

r)

Figure 5.3 Traditional control: fuel oscillations during slam acceleration.

A fuel oscollation/discontinuity is allowed at Bleed Valve (BV) closing points. The HP and the IP bleeds are indicated as bleed flow fractions in Figure 5.4.

0 5 10 15 20 250

0.02

0.04

0.06

HP

Ble

ed F

low

Fra

ctio

n

Trad. controller: Bleed valve operation in slam acceleration.

0 5 10 15 20 250

0.05

0.1

0.15

0.2

Time (s)

IP B

leed

Flo

w F

ract

ion

Figure 5.4 Traditional control: HP/IP Bleed Valve operations in slam acceleration.

It can be seen in Figure 5.4 that the first fuel oscillation appears just after Bleed Valve closing point but there is no Bleed Valve operation at the second oscillation. The cause of the first oscillation may also be other than Bleed Valves.

Overshoots

Verification required under the condition (g) of the pass-off test criteria is that actual EPR should not exceed EPR command by more than 0.02 EPRduring the transient nor 0.01

72

EPR for more than 3 second at maximum take-off. In the case of the traditional scheme, this is satisfied at maximum take off (MTO) because there is no overshoot. The EPR glinch at about 13s may be objectionable. In the RRIM control, this is satisfied during rise up and at maximum take off (MTO) because the maximum overshoot is 0.0084 EPR and the overshoot duration is less than 3s.

Steady State EPR

The steady state EPR, EPRss is 1.3382 EPR in the traditional control and 1.3369 EPR in the RRIM control. These steady state EPR values satisfy the requirement in the condition (e) of the pass-off test criteria saying that at stabilised maximum take-off, EPR should be controlled to 1.337±0.005 EPR. EPRss is achieved in about 14s in the traditional control and in about 12s in the RRIM control.

Thrust Rise Timings

Requirements on rise time are defined in the condition (f) that the engine simulation should reach ≥ 35% of maximum take-off thrust within 4 seconds, and ≥ 95% within 8 seconds. From Figure 5.1, thrust rises by 35% after 8.0s and by 95% after 11.75s. In the case of the RRIM control, thrust rises above 35% after 7.2s and above 95% after about 9.3s.This condition is better satisfied by the RRIM control of the engine.

The ACU Performance

The acceleration control unit (ACU) is the most active component of the EEC in slam acceleration as indicated by the loop-in-control index in the lower window of Figure 5.5. The loop-in-control index for ACU is 11 as can be found from Table 5.2.

0 5 10 15 20 25-5

0

5

10

15

Nhd

ot (%

/s)

Traditional control: ACU performance

DemandResponse

0 5 10 15 20 254

6

8

10

12

Time (s)

Loop

-in-c

ontr

ol In

dex.

Figure 5.5 Traditional control: the ACU performance in slam acceleration.

73

There are severe oscillations in the acceleration response of the engine to ACU command in the traditional control of the engine. A steady state error to a non-zero reference at maximum power is legitimate because it is not the ACU loop that is in control after 14s.

There oscillations in the acceleration response of the engine to ACU in the RRIM control are more severe in the case of the RRIM control as shown in Figure 5.6. The control shifts, as could be expected, to the EPR loop at steady state.

0 5 10 15 20 25-5

0

5

10

Nhd

ot (%

/s)

RRIM control: ACU performance

DemandResponse

0 5 10 15 20 254

6

8

10

12

Time (s)

Loop

-in-c

ontr

ol In

dex.

Figure 5.6 RRIM control: the ACU performance in slam acceleration.

ACU loop is in control during steep acceleration only both in the case of the traditional and the RRIM control.

Surge Margins

Lesser rise times in the case of the RRIM controller are obtained at the cost of higher acceleration which results in lower surge margins. Surge margins in slam acceleration are shown in Figure 5.7. The figure shows that the surge margin in slam acceleration is better for LP compressor only in steady state while almost the same for IP and HP compressors.

74

0 5 10 15 200

0.1

0.2

LP S

urge

Mar

gin

RRIM Vs Trad. Controller: Surge Margin in slam acceleration

TraditionalRRIM

0 5 10 15 200

0.5

1IP

Sur

ge M

argi

n

TraditionalRRIM

0 5 10 15 200

0.2

0.4

HP

Surg

e M

argi

n

Time (s)

TraditionalRRIM

Figure 5.7 RRIM Vs Traditional Controller: surge margins in slam acceleration.

5.4 Slam Deceleration A sudden demand for decreasing the engine power from maximum to idle will cause slam deceleration. The pass-off test criteria for slam deceleration is as follows:

5.4.1. Pass-off Test Criteria for Slam Deceleration Test

Set the High/Low idle switch to select high idle and allow the simulation to set at maximum stable condition.

Perform a slam deceleration by ramping PLA maximum forward to idle in one second. Simulation is continued untill the response settles at high idle.

Analysis

(a) Verify that the value of EPR command ramps as required by the EPR/TRA relationship of the selected rating from maximum take-off EPR to high idle EPR.

(b) Verify thet during deceleration, the fuel demand is scheduled smoothly with no discontinuities. There may be small discontinuities at Bleed Valve opening points.

(c) Verify that Bleed Valve scheduling is as defined by Performance Group.

(d) Verify that actual EPR does not exceed EPR command by more than 0.02 EPR during the transient, nor 0.01 final state EPR for more than 3 seconds.

75

(e) Verify that thrust delay times are as follows (within ± 1s):

30%FNT at 1.6s

75%FNT at 4.0s

90%FNT at 7.5s

where FNT is defined for the thrust, FN of the engine as follows:

%FNT=100*[(FN Take-off)-FN]/ [(FN Take-off)-(FN-Idle)]

The condition (c) is supposed to be satisfied in the absence of any comment from the Performance Group. For clasue (e), the Engine Pressure Ratio (EPR), will b etaken as indicative of engine thrust (FN).

5.4.2. Comparison in Slam Deceleration The response of deceleration control unit (ACU) in the traditional controller can be seen from slam action input i.e., by giving step demand from idle to maximum power as shown in Figure 5.8.

The condition (a) of the pass-off test criteria is supposed to be satisfied, in both the RRIM and the traditional control because the definition of the ratings function is not known.

25 30 35 40 450.9

1

1.1

1.2

1.3

1.4

1.5

EPR

RRIM Vs trad. controller: Slam deceleration

Time(s)

TraditionalRRIM

Figure 5.8 RRIM Vs Traditional Controller: slam deceleration.

Continuity of Fuel

The fuel is scheduled by the two controllers at a value shown in Figure 5.9. The condition (b) of the pass-off test criteria requires verifying that during deceleration, the fuel demand

76

is scheduled smoothly with no discontinuities. In the case of the RRIM control, there is a small discontinuity at the point where the response converges to the idle speed.

20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2x 104

Fuel

(lb/

hr)

Time(s)

RRIM Vs trad. controller: Slam deceleration

TraditionalRRIM

Figure 5.9 RRIM Vs Traditional Controller: fuel shape in slam deceleration.

The size of the fuel discontinuity is small enough to be ignored. Moreover, a fuel oscollation/discontinuity is allowed Bleed Valve opening points. The HP and the IP bleed fractions during deceleration in the RRIM control of the engine are shown in Figure 5.10.

20 25 30 35 40 450

0.02

0.04

0.06

HP

Ble

ed F

low

Fra

ctio

n

RRIM control: Bleed valve operation in slam deceleration.

20 25 30 35 40 450

0.05

0.1

0.15

0.2

Time (s)

IP B

leed

Flo

w F

ract

ion

Figure 5.10 RRIM control: HP/IP Bleed Valve operations in slam deceleration.

It can be seen in Figure 5.10 that the fuel discontinuity occurs when bleeds are being controlled by the EEC.

Final State EPR

As for as final state EPR is concerned, it stays at a value required by the idle thrust setting. The idle setting of thrust can be low or high, depending upon the flight condition but the test statement of the pass-off test criteria demands a high idle setting. High idle

77

setting could not be made in the EEC and the final state EPR corresponds to low idle. The minimum TRA was set to 5 deg., which is lower than the value required for idle speed. This was just an approximate setting on safe side when EPR-TRA relationship was not available to be used for idle setting. The final EPR value, both in the traditional and the RRIM control can, therefore, be considered to be satisfying the requirement.

Thrust Drop Timings

The condition (e) of the pass-off test criteria for slam deceleration defines requirements on thrust drop requirements. Assuming a linear relationship between thrust and EPR, the same rules can be applied to EPR drop timings. Replacing thrust, FN by EPR in the formula:

%FNT=100*[(FN Take-off)-FN]/ [(FN Take-off)-(FN-Idle)]

the observed timings are

Percent of FNT Traditional RRIM 30%FNT 1.975 s 1.025 s 75%FNT 5.825 s 2.875 s 90%FNT 9.125 s 4.125 s

The required timings are 1.6s, 4.0s and 7.5s (±1s each) for 30%, 75% and 90% FNT respectively. This shows that thrust drop rate is faster, in the case of the RRIM controller, than the required drop rate.

The DCU Performance

The deceleration control unit (DCU) is the most active component of the EEC during slam deceleration as indicated by the loop-in-control index in the lower window of Figure 5.11 for the traditional controller and in Figure 5.12 for the RRIM controller.

78

20 25 30 35 40 45-10

-5

0

5

10

Nhd

ot (%

/s)

Traditional control: DCU performance

DemandResponse

20 25 30 35 40 450

5

10

15

Time (s)

Loop

-in-c

ontr

ol In

dex.

Figure 5.11 Traditional control: the DCU performance in slam deceleration.

There are some oscillations in the deceleration response of the engine to its DCU in the traditional control. A steady state error to a non-zero reference at maximum power is legitimate because it is not the DCU loop (loop 13) that is in control after about 38s.

There deceleration response of the engine to DCU in the RRIM control is quicker in convergence to the reference initially and remains on the reference for about 3s, as shown in Figure 5.12. The control shifts to minimum Nl (the LP spool speed) loop in the idle state.

20 25 30 35 40 45-10

-5

0

5

10

Nhd

ot (%

/s)

RRIM control: DCU performance

DemandResponse

20 25 30 35 40 450

5

10

15

Time (s)

Loop

-in-c

ontr

ol In

dex.

Figure 5.12 RRIM control: the DCU performance in slam deceleration.

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The DCU loop is in control during steep deceleration only both in the case of the traditional and the RRIM control.

Surge Margins

The higher magnitude of deceleration in the case of the RRIM controller may be causing lower surge margins particularly for the IP compressor. Surge margins in slam deceleration are shown in Figure 5.13. This can also be anticipated from the thrust drop times in the case of the RRIM controller, which indicate that the thrust drop is a bit quicker than the required drop rate.

25 30 35 400

0.1

0.2

LP S

urge

Mar

gin

RRIM Vs Trad. Controller: Surge Margin in slam deceleration

TraditionalRRIM

25 30 35 400

0.5

1

IP S

urge

Mar

gin

TraditionalRRIM

25 30 35 40

0.5

HP

Surg

e M

argi

n

Time (s)

TraditionalRRIM

Figure 5.13 RRIM Vs Traditional Controller: surge margins in slam deceleration.

Figure 5.13 shows that the surge margin provided by the RRIM control of the engine in slam deceleration may be objectionable in the case of the HP and IP compressor. The surge margin for LP compressor is however acceptable.

5.5 Slow Acceleration Slow acceleration of the engine means slow rise from idle to maximum engine power. The following is the pass-off test criteria for slow acceleration.

5.5.1. Pass-off Test Criteria for Slow Acceleration Test

Perform an acceleration action by ramping the simulation Pilot Lever Angle (PLA) from idle to maximum at 1 deg/s and allow the simulation to stabilize at maximum conditions.

Analysis

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a) Verify that the value of EPR command ramps in accordance with the EPR/TRA relationship for the selected rating.

b) Verify that during the acceleration, the fuel demand is scheduled smoothly with no discontinuities (other than the small discontinuities at Bleed Valve switch points).

c) Verify that Bleed valve scheduling is as defined by Performance Group, and that all Bleed valves are closed at Maximum Take-off condition.

d) Verify that the IP turbine cooling demand remains off.

5.5.2. Comparison in Slow Acceleration The response of the engine under traditional control is shown in Figure 5.14 for acceleration along a slow ramp reference. The response closely tracks the reference EPR that is a slow ramp in some portions and a constant value in the other parts of the curve. This shape of the reference curve is a result of EPR-TRA relationship defined under the ratings function. The condition (a) of the pass-off test criteria defines a requirement on this relationship and in the absence of an exact definition of the EPR-TRA relationship, the condition is presumed to be satisfied.

0 20 40 60 80 100 1200.9

1

1.1

1.2

1.3

1.4

1.5

Time(s)

EPR

Traditional control: slow ramp acceleration

ReferenseResponse

Figure 5.14 Traditional control: slow ramp acceleration.

The definition of EPR-TRA relationship is unknown and is usually quite complex being a function of engine and environmental parameters as well. Consequently, the EPR reference curve appeared to be different in the traditional and the RRIM controller although the TRA input is the same, as can be observed by comparing the reference curve in Figure 5.14 with that in Figure 5.15 that shows the response of the engine in the case of the RRIM control.

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Condition (b) of the pass-off test criteria is not strictly fulfilled, as can be seen in Figure 5.15 because the response has glitches at two points (power levels) between 22s and 44s during acceleration both in the case of the traditional and the RRIM EEC. The fuel schedule commanded by the controller can also be expected to be uneven. A selected portion of fuel is shown enhanced in Figure 5.16.

10 20 30 40 50 60 70 80 90 100 1100.9

1

1.1

1.2

1.3

1.4

1.5

EPR

Time(s)

RRIM control: slow ramp acceleration

ReferenceResponse

Figure 5.15 RRIM control: slow ramp acceleration.

20 30 40 503000

4000

5000

6000

7000

8000

9000

10000

11000

12000

Fuel

(lb/

hr)

Time(s)

Traditional

20 30 40 503000

4000

5000

6000

7000

8000

9000

10000

11000

12000

13000

Fuel

(lb/

hr)

Time(s)

RRIM

Figure 5.16 RRIM Vs Traditional control: fuel flow fluctuations.

There are small glitches in the fuel scheduled by the traditional controller whilst there are small oscillations in the fuel commanded by the RRIM controller. The time response of the traditional controller is, therefore, better than that of the RRIM controller at least in

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the time interval shown in Figure 5.16. A Bleed Valve (BV) operation, if there is any, can explain these fluctuations. The BV operation is the same in the traditional and the RRIM control and is shown in Figure 5.17.

0 20 40 60 80 100 1200

0.02

0.04

0.06

HP

Ble

ed F

low

Fra

ctio

n

Bleed valve operation in slow ramp acceleration.

0 20 40 60 80 100 1200

0.05

0.1

0.15

0.2

Time (s)

IP B

leed

Flo

w F

ract

ion

Figure 5.17 Bleed Valve operations in slow acceleration.

The HP and IP bleed flow fraction shown in Figure 5.17 can be supposed to be satisfactory under the condition (d) of the pass-off test criteria. The figure also confirms that the handling bleed (HB) control of EEC is activating the BVs between 180s and 200s. The fuel fluctuations of Figure 5.16 can, therefore, be ignored.

5.6 Slow Deceleration Slow deceleration of the engine involves a slow drop in EPR (the indicative of the engine thrust) from maximum to idle engine power. The following is the pass-off test criteria for slow deceleration.

5.6.1. Pass-off Test Criteria for Slow Deceleration Test

Perform a deceleration by ramping the simulation Pilot Lever Angle (PLA) from maximum forward to idle at 1 deg/s and allow the simulation to stabilize at low idle.

Analysis

(a) Verify that the value of EPR command ramps in accordance with the EPR-TRA relationship of the selected rating from maximum take-off to low idle.

(b) Verify that during the deceleration, the fuel demand is scheduled smoothly with no discontinuities (other than the small discontinuities at Bleed Valve switch points).

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(c) Verify that Variable Inlet Guide Vane (VIGV) scheduling is as defined by Performance Group, and that the position reads -5.73 deg. at maximum take-off conditions.

(d) Verify that the IP turbine cooling demand remains off.

Some details of the above criteria, such as the BV or VIGV setting (Part (c)), are beyond the scope of this project. Part (d) in acceleration and deceleration tests can be supposed to be satisfied in the presence of temperature and pressure limits. Otherwise, the reader can ignore it.

5.6.2. Comparison in Slow Deceleration The response of the engine in the traditional control is shown in Figure 5.18. The response follows the reference EPR closely. The reference is a slow ramp in some portions and a constant value in the other parts of the curve. This shape of the reference curve is a result of the EPR-TRA relationship defined under the ratings function. The condition (a) of the pass-off test criteria defines a requirement on this relationship. As in the case of slow acceleration, the condition is supposed to be satisfied in the absence of an exact definition.

100 120 140 160 180 200 220 2400.9

1

1.1

1.2

1.3

1.4

1.5

Time(s)

EPR

Traditional control: slow ramp deceleration

ReferenseResponse

Figure 5.18 Traditional control: slow ramp deceleration.

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Figure 5.19 shows the response of the RRIM control.

120 140 160 180 200 220 2400.9

1

1.1

1.2

1.3

1.4

1.5

EPR

Time(s)

RRIM control: slow ramp deceleration

ReferenceResponse

Figure 5.19 RRIM control: slow ramp deceleration.

The response is uneven for a portion of curve, both in the traditional and the RRIM EEC. The fuel schedule commanded by the controller can also be expected to be uneven. A selected portion of fuel is shown enhanced in Figure 5.20.

180 190 2001000

2000

3000

4000

5000

6000

7000

Fuel

(lb/

hr)

Time(s)

Traditional

180 190 2000

1000

2000

3000

4000

5000

6000

Fuel

(lb/

hr)

Time(s)

RRIM

Figure 5.20 RRIM Vs Traditional control: fuel flow fluctuations.

There are small glitches in the fuel scheduled by the traditional controller whilst there are small oscillations in the fuel commanded by the RRIM controller. The time response of the traditional controller is, therefore, better than that of the RRIM controller at least in the time interval shown in Figure 5.20. As in the case of slow acceleration, the Bleed Valve (BV) operation can explain these fluctuations. The BV operation is the same in the traditional and the RRIM control and is shown in Figure 5.21.

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100 120 140 160 180 200 220 2400

0.02

0.04

0.06

HP

Ble

ed F

low

Fra

ctio

n

Bleed valve operation in slow ramp deceleration.

100 120 140 160 180 200 220 2400

0.05

0.1

0.15

0.2

Time (s)

IP B

leed

Flo

w F

ract

ion

Figure 5.21 Bleed Valve operations in slow deceleration.

The HP and IP bleed flow fraction shown in Figure 5.21 can be supposed to be satisfactory under the condition (d) of the pass-off test criteria. The figure also confirms that the HB control of EEC is activating the BVs between 180s and 200s. The fuel fluctuations of Figure 5.20 can, therefore, be ignored.

5.7 Altitude Test All of the previous results were obtained and the subsequent comparison was made on the basis of a sea level data. The altitude test of the engine involves of testing the performance of the same controller at a higher altitude. The high altitude selected for this test is 35,000 ft that is the nominal cruise altitude for the aircraft using the engine under investigation.

RRIM tables can be reconstructed from the engine response for a higher altitude setting in the simulation. A harder test of the RRIM is performed here to see how robust the RRIM control is in the face of environmental changes. For this, the test-bed (or sea level) data is used to construct the RRIM tables and no subsequent changes are made accept that the two RRIM tables are interpolated across a normalized (quasi dimensionless) speed of the engine, Nh/√θ, called the aerodynamic speed, where

Theta (θ)=T1/288.15 K

In the above expression, T1 is the engine (the IP compressor) entry point temperature. The engine response in slam acceleration at high altitude is compared with that at sea level is compared in Figure 5.22.

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0 2 4 6 8 10 12 14 16 180.8

1

1.2

1.4

1.6

EPR

Altitude test of RRIM controller: Slam acceleration

Time(s)

Sea level35000 ft

0 2 4 6 8 10 12 14 16 180

1

2

3x 104

Fuel

(lb/

hr)

Time(s)

Sea level35000 ft

Figure 5.22 Altitude test of RRIM controller: slam acceleration.

The difference in the two responses is the difference of rise time and over shoots. Rise time for the sea level is greater than the rise time at 35000ft. This is an advantage because the RRIM controller response was sluggish than the one require in the pass-off test criteria. The overshoots are not apparent in Figure 5.22. The response is re-plotted for a smaller time scale in Figure 5.23.

10 12 14 161

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

EPR

Time(s)

Sea level35000 ft

10 12 14 160.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2x 104

Fuel

(lb/

hr)

Time(s)

Sea level35000 ft

Figure 5.23 Altitude test of RRIM controller: the overshoots.

The over shoot at sea level is 0.0085 EPR while that at high altitude is 0.0141 EPR. The overshoots in both cases are less than the allowable limit at seal level that is 0.002 EPR. The allowable limit at high altitude, if it is different from that at sea level, is not known.

A steeper acceleration at high altitude can, however, result in a lower surge margin. Surge margins in slam acceleration are shown in Figure 5.24. The figure shows that the surge

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margin in slam acceleration is better for LP, lower but acceptable for IP and almost equal for HP compressor.

0 5 10 15 200

0.1

0.2

LP S

urge

Mar

gin

Altitude test: Surge Margin in slam acceleration

Sea level35,000 ft

0 5 10 15 200

0.5

1

IP S

urge

Mar

gin

Sea level35,000 ft

0 5 10 15 200

0.5

1

HP

Surg

e M

argi

n

Time (s)

Sea level35,000 ft

Figure 5.24 Surge margins in altitude test of RRIM controller: slam acceleration.

In the case of deceleration, there are no overshoots and the response high altitude is almost the same as the response at sea level, as can be seen in Figure 5.25.

22 24 26 28 30 32 34 36 38 400.8

1

1.2

1.4

1.6

EPR

Altitude test of RRIM controller: Slam deceleration

Time(s)

Sea level35000 ft

22 24 26 28 30 32 34 36 38 400

0.5

1

1.5

2x 104

Fuel

(lb/

hr)

Time(s)

Sea level35000 ft

Figure 5.25 Altitude test of RRIM controller: slam deceleration.

The surge margins in slam deceleration are shown in Figure 5.27. The figure shows that the surge margin in slam deceleration is almost equal for the LP and HP compressors. The surge margin for the IP compressor is, however, unacceptable because it is almost zero at about 30s.

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25 30 35 400

0.1

0.2

LP S

urge

Mar

gin

Altitude test: Surge Margin in slam deceleration

Sea level35,000 ft

25 30 35 400

0.5

1

IP S

urge

Mar

gin

Sea level35,000 ft

25 30 35 40

0.5

HP

Surg

e M

argi

n

Time (s)

Sea level35,000 ft

Figure 5.26 Surge margins in altitude test of RRIM controller: slam deceleration.

The other issues like robustness (phase margin and gain margin in the linearized control loop) and bandwidth etc. have not been investigated. The time response of the RRIM controller designed for sea level is, however, adequate at high altitude.

5.8 Noise Test The main control loop is the EPR loop. Noise was added to EPR output. There is no noise signal available in MATRIXx (the software support of the engine model) to be added to the sensor output for noise test. The maximum required bandwidth of the control system is 3rad/s (0.477 cps). A triangular wave of high frequency (20 cps) was selected to mimic a noise frequency signal. The altitude was taken to be 0.02 EPR that is 5% of the approximate EPR rise (≈0.4 EPR) from idle to maximum power level. The added noise and the response of the RRIM controller are shown in Figure 5.27.

20 20.1 20.2 20.3 20.4 20.5-0.02

-0.01

0

0.01

0.02

Add

ed N

oise

(EPR

)

Noise Test of RRIM controller at sea level for the EPR loop.

20 21 22 23 24 25-3

-2

-1

0x 10-5

EPR

Noi

se (E

PR)

Time(s) Figure 5.27 Noise test of RRIM controller.

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The noise response (shown black in lower window) is obtained by subtracting the response without sensor noise from the response with sensor noise. The oscillations in the response are very small.

5.9 Response of Mixed Control Design Another approach to get a canned solution to ACU and DCU from the existing traditional EEC design is to use a mixed design approach that leads to tailoring the ACU and DCU of the traditional controller to fit to a RRIM controller (see Chapter 4 for a detailed discussion). For a time domain tuning of the EPR loop and all the limits involved in the control, the respose of the engine is shown in Figure 5.28 both for acceleration and deceleration.

Figure 5.28 Response of the controller using mixed design approach.

The idea was superseded after the pure RRIM based design was achieved. No stability margins have been found. It is included in this chapter to show that a mixed design approach, based upon the RRIM and the traditional controller also works and can be adopted, in some situation, after further analysis.

5.10 Computational Burdon Figure 5.29 is a duplicate from Chapter 2 (Loop Selection Logic) and can be used to estimate the computational burdon of the traditional and the RRIM controllers.

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Control Stage ‘1’

Controller Fuel Command Control

Stage ‘2’

Control Error

Control Demand

Figure 5.29 A two-stage control design used in selector control.

Stage 1 of the controller produces an intermediate demand on the engine. In the traditional controller, stage 2 is an integrator and control demand from stage 1 is the rate of change of fuel flow demand. In the RRIM controller, stage 2 is the RRIM itself and the demand on stage 2 is the deceleration demand. Stage 1 is designed separately for all loops and is the real source of computational burden.

Two types of numerical operations are performed by the digital controller in stage ‘1’:

Interpolating the control parameter tables Computing the control demand

5.10.1. Interpolating Tables In the traditional controller, for all the loops other than ACU and DCU, the demand is calculated by interpolating three tables:

Table for the lead time constant, T1 Table for the lag time constant, T2 Table for the proportional gain, K

For the ACU and DCU, only one table (for gain K) is interpolated. The minimum and the maximum limiters for any engine parameter have the same value of T1 and T2 but a different value of K. Table 5.3 summerises the number of tables used for all loops. Table 5.3 No of parameter schedules in traditional control.

Control Loop No of Parameters in Lead Component Gain

N1 limit (min/max) 2 2

N2 limit (max) 2 1

N3 limit (min/max) 2 2

P30 limit (min/max) 2 2

ACU 0 1

DCU 0 1

TOTAL 8 9

As the table shows, a total of 17 tables are interpolated for all control loops. How many of them are effectively used in evaluating a fuel command? The answer is, one to three. The

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rest of the computer effort remains unused (83% to 94% loss) each time control logic is executed. It is the minimum computational loss, in case when same lead and lag terms are used for minimum and maximum limits. The computational loss per execution increases when separate lead-parameters are used for minimum and maximum limits.

In the case of the RRIM controller, it is only the gain that is scheduled and many times it comes out to be a constant. Table 5.4 No of parameter schedules in the RRIM control.

Control Loop No of Gains/Schedules N1 limit (min/max) 2

N2 limit (max) 1

N3 limit (min/max) 2

P30 limit (min/max) 2

ACU 1

DCU 1

Nhdot/dF 1

Fss 1

TOTAL 9

The number of schedules to be interpolated to find the gain is 9, that is almost half the number of parameters in the traditional controller. This is only in case the same parameters are used for maximum and minimum limits in lead-term. In the other case, the difference of the number of tables to be interpolated will become more significant.

5.10.2. Computing Control Demand The lead action is implemented in discrete form in a digital controller. To compute the output of the lead-term, a minimum of four additions/subtractions and two multiplications/divisions are required. Similar calculations can be done, as given in Section 5.10.1, for all the control loops to show that the aggregate computational burden of the traditional controller in computing the control demand is much higher than that of the RRIM controller where only one multiplication is required for each control loop.

From the above arguments, it can be concluded that the computational burden of the traditional controller is significantly greater than that of the RRIM controller.

5.11 Conclusions Neither the traditional nor the RRIM control of the engine strictly obeys the conditions of the pass-off test criteria considered within the scope of this project. At some points, the RRIM control showed superior performance whilst the traditional controller was the

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winner in the context of some other pass-off test criteria. Most of the time, the performance of the two control schemes was comparable.

The engine power (indicated by EPR) fluctuates at some particular power levels during acceleration. The source of this fluctuation may not be the EPR control loop but rather some engine characteristic. The setting for a staged combustion may have been selected in the EEC. The fuel Metering System (FMS) used in both the traditional and the RRIM EEC is surely the one that supports the staged combustion. Nothing can be said for the design and performance of the existing FMS within the scope of this project. The concept that the inherent interference effect of a staged combustor can cause such oscillations should, however, be considered as a possible cause of the oscillations and glitches appearing in the slow and slam acceleration, both in the case of the traditional and the nonlinear RRIM control of the engine. The controller fuel update, in this situation, is utilized in filling the fuel pump of the new fuel stage and effectively not used in combustion.

The performance of ACU and DCU was poor, both in the RRIM and the traditional control of the engine acceleration/deceleration. Some mathematical analysis is needed to show that why both schemes are not able to track a reference acceleration demand adequately.

This is the first performance from the RRIM controller designed in a short period of time. The control loop for the thrust control was designed on the basis of frequency domain analysis performed at different operating points along the operating range. The other control loops were designed on the basis of the time domain tuning, analysing rise time, settling time and shape of the response etc. A lot of further work is needed to tune all the control loops to best possible values of controller parameter. Modifications in the control structure and the control loop may also be developed and analysed.

The altitude test of the controller indicates the robust performance of the controller in the presence of nonlinearities and environmental changes. An intuition-based tuning of the RRIM controller gives adequate performance, at least in the time domain. If further research work is done in the RRIM design area, particularly to formulate some sophisticated rules to tune the controller in the time domain, RRIM may prove a strong candidate in the area of civil gas turbine engines.

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Chapter 6 Conclusions and Recommendations

This project was aimed at implementing the Rolls-Royce Inverse Model (RRIM) control technique to a high bypass ratio turbofan of the civil aircraft. This report represents the first implementation of the new control technique in gas turbine engines used in a civil aircraft. The project was carried on an engine model implemented in MATRIXx. This chapter hilights some key points of the control design procedures adopted in the RRIM control design, allocates some problems and difficulties faced in MATRIXx procedures, brings up some critical issues of the engine control design and proposes solutions to some problems. Conclusions on each particular matter are drawn in each section and suggestions are given to investigate the issues that remained untouched or incomplete in this project. The conclusions at the end are the benefits of the new control technique that have been investigated, partially of fully, in this project.

All the aspects of a new control technique could not be investigated, in the limited time of the project, for a complex nonlinear system. A lot of work remained pending that could lead to a test-stage practical application on a real engine and finally to certification of the use of the nonlinear RRIM controller in gas turbine engines in civil applications. Hence, some of the material in this chapter not only recaps on previous chapters but also steps forward in resolving some issues, and is presented as a recommended course of action for further work. Students seeking, for example, an analytical basis of the RRIM controller will find the interpretations of the RRIM helpful. Future work on this project proposed at the end may prove helpful in further research on the RRIM control.

6.1 Using RRAP Models from Xmath The engine model used in this project is that of a Trent series engine that falls in the class of Rolls-Royce Aero-thermodynamic Performance (RRAP) models. The model can be accessed from both Xmath and SystemBuild. In both ways, some input parameters are passed to the model. Xmath invokes SystemBuild blocks with particular settings of the SystmBuild parameters. A new student should analyse the Xmath example program given in Appendix C to see how the program changes the settings in the SystemBuild provided for accessing RRAP models with different options.

The control, at the end is implemented as a part of a simulation used to implement the EEC in complete. The reader can assume that it is a very complex simulation provided by Rolls-Royce plc. to implement control laws and verify its performance in the presence of

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a number of ancillary functions and subsystems of the engine. These functions implement the engine control for startup, acceleration to idle, steady state control (idle to maximum speed), reverse thrust mode and much more. To explain this SystemBuild program, even in minor details, can take a full length chapter and is not a subject of this discussion. The RRIM has been implemented for the control of the engine in the normal operation only. A suggestion in using the program, that would help a lot in saving time and avoid difficulties, is to understand Xmath/SystemBuild in view to use it for the RRIM implementation. Partions of variables can be defined in Xmath to divide the variables into categories other than a ‘main’ category in Xmath. The EEC also has two partitions in Xmath, in addition to main, to declare variables, which are ‘EEC’, and ‘bs94mx’. The future students analysing his or her control design for the EEC may observe, at different parts of the EEC, as many as fifty variables. A general practice to do this is writing a mathscript file to plot these variables. It is a good practice in using Xmath to delete all those variables that are not inteded to be kept with the original program. The best way to do this is to use ‘delete’ command at the end of Xmath file to delete all the unwanted data. Another way is to view Xmath Workspace variable from the maneu bar and delete the variables that are not wanted. It is also fine to write, at Xmath command line,

delete main.*

before ending any session and storing any changes in the program. This helps a lot in saving time, specially on slow machines. Saving changes ‘without variables’ would be a fatal mistake for the next session because all of the three partions of variables would be lost and the provided program Similary, saving changes ‘with variables’ may increase the file size ten-fold. This will increase the time to reload file and save again proportionally. To summarize, the user SHOULD delete variables from the ‘main’ partion only and he or she SHOULD NOT delete all the variables, writing, for instance,

delete *

This command is, however, recommended before loading a new program to flush the variables from old Xmath sessions.

6.2 Using SystemBuild SystemBuild is similar to Simulink in that both are block diagram manipulation systems. The block diagram libraries of the SystemBuild Catalogue such as ‘Software Constraints’ are highly useful in introducing If-Then-Else conditions and maintaining computational sequence in block diagram manipulation. Albeit, it has lesser custom blocks and many blocks in the EEC are user customized. A customized user block is a combination of the custom blocks that is intended to perform a specific operation under a specific label or

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name that is unique within a simulation. A change in the customized SuperBlock will result in an automatic change in all its ‘copies’ within a simulation (see Appendix F-1).

The user of MATRIXx is recommended to make his or her own customized blocks. This apparently looks a slow procedure as compared to copying any existing blocks but is, in fact, advantageous in that it will help understand SystemBuild better and make the computations transparent to the user. An example presented in Appendix F-2 for the future students to show the sensitivity of SystemBuild to apparently small variations in setting the user options.

6.3 Modelling Errors in RRIM The RRIM produces fuel flow demand that can fulfil an acceleration demand. If a certain fuel flow produced a certain amount of acceleration, the acceleration, when placed as demand to the RRIM, should retrieve the fuel flow from the RRIM. In other words, fuel flow demand coming from the RRIM in Figure 6.1 should equal the fuel injected to the engine, assuming that the RRIM is a perfect model.

Engine Model RRIM

Nh

Nhdot

Fuel Injected

Fuel Demand

Modelling Error

-

+ Figure 6.1 Inverse model test of RRIM.

The Simulink block diagram given in Figure 6.2 can be used to model the situation of Figure 6.1. Data for Nh and Nhdot corresponding to any fuel flow is obtained from the engine model running in the transient mode. This data is loaded into the Simulink model from Matlab workspace using “From Workspace” blocks. The two look up tables of the RRIM are “fired” using Nh vector corresponding to Nhdot acceleration placed as a demand. The quantity obtained from the dynamic response table (Nhdot/δF Vs Nh) is Nhdot/δF, which is, as in the RRIM control, inverted to give δF/Nhdot. The Nhdot demand is the same as used to construct the dynamic response table. If this demand is multiplied by δF/Nhdot, the resultant would be δF that is added to the steady state fuel Fss coming from the second table. What is obtained at the end (Fss+δF) is the fuel flow that is needed to produce the demanded acceleration. This fuel flow demand should be the same as the one, on the record, used to produce Nhdot in first place.

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Figure 6.2 Simulink block diagram for finding modelling error in RRIM.

The fuel flow that is used to produce Nhdot (demand in Figure 6.2) is compared with the fuel flow demand coming from the RRIM in order to find the modelling error that is shown in Figure 6.3.

Figure 6.3 Error in the RRIM without curve-fitting and interpolation.

The error is negligibly small (and possibly comes from rounding off/truncation) if no curve-fitting is used to approximate the model. On the other hand, the error is relatively large with curve-fitting and reduced number of data points (Nh column of each of the two tables takes only 15 values ranging from 66% to 94% Nh). The error is shown in Figure 6.4.

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Figure 6.4 Error in the RRIM using curve-fitting to approximate the model.

The sources of error are:

approximating the static response (Fss Vs Nh) by a second order curve,

approximating the dynamic response (Nhdot/δF) by a third order curve,

approximating the derivative (Nhdot) from a first order difference,

interpolation and extrapolation.

The RRIM control is expected to compensate for the above modeling errors.

6.4 Linearization of RRIM Control Loop This section reveals some problems using Matlab (or MATRIXx) for linearization of the RRIM control loop and two possible interpretations of the RRIM controller from its linear version.

Matlab offers many commands for linearization such as linmod, linmodv5, linmod2, dlinmod, any of which may suit better for the control loop that has the RRIM controller as compared to others. An investigation of how these commands work and differ from each other is necessary. Linmod2 is an advanced version of linmod that simply does not support linearization of the RRIM controller. It is claimed by Mathworks that linmod that comes with Matlab R12 (version 6) generates exact linearization for most blocks. This command does not allow setting the step size for perturbation as does its Matlab 5 counterpart, linmodv5. The size of perturbation is, however, a secondary issue, the primary issue is that how does Matlab interpret the RRIM tables. For an analysis on this ground, it is recommended to linearize only the RRIM controller. There is only one state in the RRIM, comprised by the integrator, that will make linearization simple and transparent. From the implementation point of view, the RRIM is a two input one output system as shown in Figure 6.5.

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Figure 6.5 Linearization of RRIM in Matlab.

The model that is generated by the linmod (Matlab) command at 85% Nh (initial condition of the integrator) in the first case is as follows:

Ar = [-2.0646] Br = [0 0.0033]

Cr = [842.2095] Dr = [298.9606 0]

Where the state x in

xdot = Ar x + Br u

is the integrator output. The picture of the linmod output can be portrayed as in

Figure 6.6 The equivalent structure of the linearized RRIM.

The gains in Figure 6.6 can be explained as follows:

The following table gives the values from two tables when Nh is 85%.

Nh Fss Nhdot/δF

85% 9.7131266e+3 3.3449220e-3

When Nh is perturbed by 1e-5 of Nh in both directions, total perturbation, ∆x, is 1.7e-3 (2*1e-5*85). The corresponding perturbation from Fss-table comes out to be 1.4317561. The perturbation gain generated by the steady state table, therefore, is 1.4317561/1.7e-3 which is what comes out as C = 842.20. Hence the perturbed state ∆x (the output of the integrator) adds to the output C times its value.

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The gain produced by the second table is NOT calculated across a perturbation in Nh. The gain between input(1) and output is the inverse of what comes directly from the dynamic response table, i.e., 0.00334492 is not a perturbation gain but a value of Nhdot/δF for 85% Nh. The same value is used to obtain state feedback with a gain 2.8171 and as the input gain for input(2). Note that 2.8171 is obtained as: 842.20*0.00334492, and is different from the matrix Ar is 2.0646 (which it should not be). This indicates a numerical error of Matlab in handling objects. The following is the summary of these numerical problems:

Nh (%) ∆Nh (%) ∆Fss (lb/hr) ∆Fss/∆Nh δF/Nhdot

85% 1.7e-3 1.4317561 842.20 298.96

Figure 6.6 can be modified to Figure 6.7 to relate the gains to the RRIM tables more clearly.

Figure 6.7 Linearized RRIM in Simulink at 85%Nh.

Figure 6.7 shows that steady state table will be replaced by a gain that is obtained by perturbing the state while dynamic response table is replaced by its absolute table value. This is because the steady state table is a part of the integration loop while dynamic response interacts from outside this loop.

6.4.1. What is a RRIM Controller? Figure 6.7 introduces the general structure of the RRIM as given in Figure 6.8. At a particular power level, the lookup tables perform the function of simple gains.

Fuel Feedback

Nhdot Demand

-

+ 1/u

Fuel Command

+

dF

+ Fss

Ks 1 s Kd

1 Kd

Figure 6.8 Simplified structure of RRIM at any trim point.

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At any particular power level (operating point), the lookup tables simply perform the function of gains. The static response curve of the RRIM is a relation between Nh and Fss. Let Ks give the transformation from Nh to Fss for any particular value of Nh. The gain Ks, is a perturbation gain that can be calculated as follows:

Ks = ∆Fss/∆Nh (6.1)

The dynamic response curve of the RRIM is a relation between Nh and Nhdot/δF. Let Kd give the transformation from Nh to Nhdot/δF for any particular value of Nh. Then:

Kd = Nhdot/δF (6.2)

These gains combine together to generate the controller parameters. Figure 6.8 shows the RRIM structure with the modification that the RRIM tables have been replaced by gains. The dynamic response table performed two actions: it appeared as the integrator gain in the integration loop and it scaled the input demand to convert the Nhdot demand into an appropriate increment in fuel flow demand. The gain Ks appears as a proportional gain in the integration loop.

The overall gain of the integral loop is:

Ki = Ks Kd (6.3)

Integral loop, with unity negative feedback, has the following equivalent transfer function:

i

ir Ks

K)s(G+

= (6.4)

The input of Gr(s) is a positive feedback from the Fuel Metering System (FMS) that is an integrator with PI controller and has the following transfer function:

a 2

10s+5G (s)=s +10s+5

(6.5)

Let Kp represent the gain that scales the input. Then,

Kp = 1/Kd (6.6)

Gr(s)

Nhdot Demand +

+ +

Engine Kp Ga(s)

Figure 6.9 Simplified structure of RRIM at any trim point.

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The equivalent transfer function of the RRIM and FMS is a result of block manipulation of the RRIM in positive feedback with FMS and can be written as:

)5s)10K(s(s)Ks)(5s10(K)s(G

i2

ipar +++

++= (6.7)

where the subscripts ‘a’ and ‘r’ show actuater (FMS) and RRIM respectively.

Equation (6.7) shows that RRIM, in feedback configuration, has an intrinsic effect of introducing integrator in the loop transfer function. This ensures zero steady state error for a constant reference input. Gar(s) can also be used as the ‘trim point’ representation of the RRIM controller along with FMS in order to find gain and phase margin of the control loop at a perticulr value of Nh. The same structure has been used in robustness analysis of the RRIM, in order to find the gains that ensure a desired gain and phase margins and bandwith.

NB: In practice, a modelled HP spool speed Nhm, is the variable across which the tables are interpolated. The modelled and the actual spool speeds (Nhm and Nh respectively) are almost the same, depending upon how accurate the tables are, and their steady state values can replace each other.

6.4.2. Another Interpretation of RRIM Let the fuel feedback for the RRIM controller be taken from within the RRIM This will make the RRIM a SISO system as given in Figure 6.10.

Figure 6.10 RRIM with internal feedback.

In this case, the linear model comes out to be:

Ar = 0 Br = 1.00 Cr = 842.2095 Dr = 298.9606

Since Ar=0, there is no state feedback as shown in Figure 6.11.

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Figure 6.11 RRIM equivalent to self-tuned PI controller.

The numerical algorithm has altogether thrown away state feedback which does not look rational, but gives rise to another interesting interpretation of the RRIM controller that it is a PI controller with automatic nonlinear tuning functions, derived from the engine characteristics and arranged in the form of lookup tables, for the proportional and derivative actions.

This form of the RRIM is not implemented in the EEC and actually, has not been tested for its performance but still gives the reader a new direction to think of what this controller is? This also shows that RRIM may be implemented in different ways to form a control law that uses inverse dynamics of the engine to generate control action. Moreover, equation (6.7) can also be written as:

+++

+

+

=5s)10K(s

)5s10(s

)Ks(K)s(Gi

2i

par (6.8)

The above equation also supports the idea that RRIM is an auto-tuned PI controller. Equation (6.7) also shows the effect of the RRIM on the open loop poles of fuel metering system.

6.4.3. Auto Scheduling in RRIM Control Figure 6.11 shows the two parameters of the RRIM controller. The values of proportional and integral gains, Kp and Ki respectively, are shown in Figure 6.12. These are the two control parameters that are scheduled by the RRIM itself. The third parameter is the RRIM gain that converts the error into an equivalent Nhdot demand. The auto-scheduling of Kp and Ki is supposed to be the best for the RRIM controller.

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60 80 100180

200

220

240

260

280

300

320

340

K p

Nh (%)60 80 100

0

200

400

600

800

1000

1200

Nh (%)

K i

Figure 6.12 RRIM parameters in PI representation.

If the ‘shape’ of the curve for Kp and Ki shown in Figure 6.12 is presumed to be the best for an optimal performance of the controller, then the controller gain used to furnish the acceleration demand should be a constant over the whole range of operation as it is for most of the control loops in the military aircraft. It is only the engine power (or the parameter the engine power is almost in linear proportion to) for which the controller gain is most likely to be a schedule. This is because power, generally, is not linearly proportional the normal outputs (physical parameters like temperature, pressure, speed etc.) of a system. Power expressions usually have non-unity exponents (remember how voltage is related to electrical power) and a schedule may be a replica of these relations.

6.4.4. Verification of Linear Model To investigate how accurate the linearization process is, a comparison between the linear and nonlinear system for small perturbation input is a practical approach. Trusting linmod (of Matlab) to always produce a valid linear model is not a good idea, analysis of the linear model is also highly recommended. The linear and nonlinear RRIM models can be compared by using perturbation inputs. For this, RRIM integrator should be initialised at the initial condition for Nh and corresponding amount of steady state fuel flow must be added to input(2) and subtracted from the output in order to obtain a set-point response to perturbations only. This is illustrated in Figure 6.13.

The response of the linearized RRIM can be compared with the nonlinear RRIM in Figure 6.14. Besides some initial difference, the two curves almost overlap each other. Actually, the two responses exactly match if Ar is replaced by the pole of the RRIM (which is legitimate). The difference is, therefore, mainly because of the numerical problems arising in Matlab objects.

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Figure 6.13 Simulink block diagram used in investigating linearization error.

]

Figure 6.14 Comparison of RRIM with its linearized version.

6.4.5. Linearization in MATRIXx Xmath is used to linearize the engine model and there is no other choice for it because model is accessible in MATRIXx only. In the case of Rolls-Royce Inverse Model (RRIM), the choice is open; both MATRIXx and Matlab can be used. Since Xmath was more involved in academic coursework of this MSc, Matlab was preferred in the project whenever a choice was available just because of convenience due to a hand on experience with it. In the case of linearization of the RRIM, however, some differences were observed. In the case of PI structure (Figure 6.11), the linearized RRIM has the following transfer function:

+

=s

)Ks(K)s(G ipar (6.9)

and the values of Kp and Ki are summarized in Table 6.1.

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Table 6.1 Linearization difference in Matlab and MATRIXx.

Kp Ki Nh

Xmath Matlab Xmath Matlab 75 242.49 231.44 1.63 1.74 80 276.53 262.82 2.18 2.37 85 310.99 298.93 2.67 2.82 90 328.68 325.63 3.28 3.27 95 325.74 323.17 1.76 2.09

One possible source of this difference is that the RRIM tables have been implemented as a schedule of Nh with increment of 2% Nh in Xmath while an increment of 1% Nh in Matlab. A second source may be the method adopted for extrapolation (95% Nh) for the last point because the dynamic response table ends at 94% Nh. To extrapolate in Xmath table, edge values are repeated. Extrapolation function of Matlab may be different.

6.5 Error Analysis in ACU and DCU The acceleration and deceleration control problem handled by the ACU and the DCU respectively is different from the conventional tracking problem. In a classical tracking problem, the reference appears as a specified curve to be followed by the output, that is Nh in this case, and not its rate. In the acceleration/deceleration control of the engine, both the reference and the output are rate of change of the HP spool speed.

Before the design of the acceleration and the decelation control units (ACU and DCU respectively) for the RRIM based EEC, the design of the traditional ACU and DCU was analysed (see Appendix E-3 for the results). For this purpose, the ACU and the DCU loops were separated from the traditional EEC and individual loops for each of the two units were constructed as shown in Figure 6.15 in a simplified structure (see Chapter 4 for details).

Nhdot

Nh

ACU/ DCU Schedule

+

Engine

K 1 s FMS d

dt -

Fdot Demand

Fuel Command

Figure 6.15 Individual ACU/DCU loop of traditional controller.

It is not the output but the rate that is being controlled, therefore, the additional derivation is appearing with the engine system.

In the case of the RRIM ACU, the integrator of Figure 6.15 will be replaced by RRIM itself as shown in Figure 4.20 which is a duplicate from Chapter 4 (see Appendix E-3 for the results of the ACU and DCU control loop in the RRIM control design).

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Nhdot

Nh ACU/ DCU Schedule

+ Engine

FMS d dt -

Nhdot Demand Fuel

Command

RRIM K s Kf

Figure 6.16 Individual ACU/DCU loop of RRIM controller.

Closed loop transfer function for a system G(s) with unity negative feedback can be written as:

CLG(s)G (s)=

1+G(s) (6.10)

so that for a unit step reference, output error would be:

1 G(s) 1 1E(s)= 1s 1+G(s) s 1+G(s) − =

(6.11)

Steady state error, ess(t) can be computed from its Laplace transform using final value theorem, which, for E(s), can be expressed mathematically as below:

)s(sELt)t(eLt)t(e0stss →∞→

== (6.12)

so that for a step reference, the equation (6.12) can be written as:

+

=→ )s(G1

1Lt)t(e0sss (6.13)

Let Gp(s) represent the transfer function for all the systems other than the controller. It is found in the linearization of the control loop that there is no pole at s=0 in Gp(s). Due to the additional derivative, the transfer function that includes the derivation action for the rate output, Gd(s) can be written as:

)s(sG)s(G pd = (6.14)

6.5.1. Error in Traditional ACU/DCU Let G(s) be the loop transfer function for the ACU/DCU in the traditional control which can be written as (see Figure 6.15):

[ ] )s(KG)s(sGsK)s(G

sK)s(G ppd =

=

= (6.15)

so that in the absence of any pole at s=0 in the transfer function Gp(s), the equation (6.16) can be written as:

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)0(KG11

)s(KG11Lt)t(e

pp0sss +

=

+=

→ (6.16)

Equation (6.20) shows that:

Steady state error would tend to converge to a constant. The error will be small if ‘KGp(0)’ is high so that in the limit when ‘KGp(0)’ is

infinity, the error will become zero. This urges to increase the controller gain K to decrease error to a constant reference.

NB: It is more difficult to keep the error finite when reference is a ramp and further difficult when reference is an arbitrary trajectory that has minor discontinuities like that in the ACU/DCU schedule.

6.5.2. Error in RRIM ACU/DCU As shown in the Section 6.4.1, the RRIM introduces a pole at s=0. In the presence of an integrator, there are two poles at s=0, in the loop transfer function G(s) written from Figure 4.20. Let K(s) represent the transfer function introduced into the control loop by the insertion of the RRIM controller, the K(s) can be written as:

22

s)s(K)s(K = (6.17)

where K2(s) has no pole at s=0. Let G(s) be the loop transfer function for the ACU/DCU in the RRIM control which can be written as:

[ ]s

)s(G)s(K)s(sG

s)s(K)s(G

s)s(K)s(G p2

p22

d22 =

=

= (6.18)

For the RRIM controller, equation (6.13) can be written as:

0)s(G)s(Ks

sLt)t(ep2

0sss =

+=

→ (6.19)

where Gp(s) also does not have any pole at s=0. This analysis shows that the RRIM ACU (and DCU) will result in a zero steady state error for a constant reference rate. The steady state error will be constant for a ramp reference.

6.5.3. Open Loop ACU/DCU in RRIM Control The basic ACU and DCU demand in classical control is an acceleration demand, Nhdot scheduled on high-pressure spool speed and RRIM also receives the same demand. An immediate idea, that can drastically ease the job of designing the ACU and the DCU, could be as simple as directly using the ACU, the DCU or the Backup ACU Nhdot

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demand as the Nhdot demand on the RRIM controller as shown in Figure 6.17. The ACU/DCU schedule is a function of the high pressure (HP) spool speed, Nh that is measured from the engine output.

Nh E

ngine FMS

Nhdot Demand Fuel

Command

RRIM

ACU/ DCU

Schedule

Figure 6.17 Open loop ACU/DCU in RRIM controller.

If RRIM were a perfect replication of the engine, it could be the easiest solution for the ACU/DCU design. Although perfect engine model cannot be embedded into RRIM, still it would be interesting to see the response of open loop Nhdot demand control and here is one in Figure 6.18 that is obtained from the RRIM EEC, when a slam action is performed in both directions. The lower window in Figure 6.18 ensures that the ACU and the DCU did take the control of the engine but could not drive the engine through an expected change in power.

Figure 6.18 Open loop ACU and DCU response in RRIM controller.

It would also be interesting to see the control parameter, that is the HP spool acceleration Nhdot, to see how it followed the reference. Figure 6.19 shows the reference and achieved Nhdot along with the output error.

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Figure 6.19 Acceleration and deceleration in open loop ACU and DCU.

The result shows that this is not only the accuracy of the ‘inverse model’ that will ensure the accuracy of open loop acceleration control; the idea is appreciable at all. The error in open loop ACU and DCU design is sufficient enough to drop this idea.

6.6 Tuning RRIM Gains in Time Domain Rolls-Royce Inverse Model (RRIM) control works on a desired Nhdot demand. Tuning gains in time domain means to produce an appropriate acceleration demand that is defined as follows:

Acceleration Demand = Gain*Control Error (6.20)

The following points may help in tuning gains in time domain.

Physical relation between different parameters

The control error has the same physical units as the control parameter. Since Nh is measured as a percentage of its maximum, relation in equation (6.3) shows that whatever the units of controlled variable are, the units of error would be ‘%/s’. There is no mathematical logic behind it. The dimensions strongly conflict with each other. It is legitimate to say that the error should be considered a number instead of a physical quantity. The gain would be multiplied with this number to produce the acceleration demand.

A relation between Nh (or Nhdot) range and each engine parameter can, nevertheless, be sorted out in order to convert the engine parameter to an equivalent Nhdot demand. Data from the engine model can be analysed to find mapping from one engine parameter to another.

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The range of acceleration demand

It is important to note that the gain performs a purpose to convert the error into an equivalent acceleration, Nhdot. Nhdot is then multiplied with δF/Nhdot (coming from Nhdot/δF schedule) to produce the increment in fuel flow, δF that can produce the demanded acceleration. The larger the Nhdot demand is, the higher the required increment in fuel flow will be. Consider the case when engine is being controlled to EPR that can range from almost unity to almost 1.4 in a Trent engine. If the engine is running at EPR(1), that is being measured, it can be asked to produce any EPR(2), giving rise to a very small to a maximum possible EPR error (see Figure 6.20).

EPR(2) (demanded)

EPR(1) (measured)

Nh(2), F(2)

Nh(1), F(1)

K Max. allowed accel. demand

F= EPR Fmax

EPRmax

Figure 6.20 Tuning of gain in RRIM control.

There is a limit on the increment in fuel flow, ∆Fmax that can be introduced without causing surge. Let EPR(2) be the EPR corresponding to this increment in fuel flow and call it EPRmax. What the gain is supposed to do is to find an equivalent maximum possible acceleration corresponding to this maximum possible EPR. The fuel flow increment, ∆Fmax is given by:

∆Fmax=Kmax*Nhdotmax*(δF/Nhdot) (6.21)

where Nhdotmax is maximum possible acceleration produced by the fuel flow increment ∆Fmax when engine has a steady state speed Nh, at which δF/Nhdot can be found from dynamic response table. Maximum possible gain, Kmax can be found from equation (6.21).

Appropriate acceleration demand

The acceleration demand generated by the controller is proportional to the step size used as reference. Decide some criteria for the step size first and then look for the appropriate acceleration that the controller should demand. The acceleration demand of acceleration control unit (ACU) is a good guess. Once the acceleration demand and reference input step size is decided, the controller gain K can directly be found e.g., for EPR, as follows:

K=Error/Nhdot=(EPRref-EPR)/Nhdot (6.22)

Deciding the criteria for setting a reference step size is a main issue in time domain tuning of Rolls-Royce Inverse Model (RRIM) control.

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6.7 Why Splitting Control Action in Selector Control? The selector control is based upon loop selection logic. The logic can be built upon both the absolute value of the fuel flow and the rate of change of fuel flow. The engine is sensitive to both the absolute value of the fuel flow injection and its rare. The output of the controller is passed through a fuel flow limiter that blocks the amount of fuel flow above a maximum limit. But what is the measure on rate of change of fuel flow that must also be controlled?

To ensure that the rate of change of fuel flow is appropriate, the control action is divided into two stages. The first stage should generate a rate of change of fuel flow command while the second stage should convert the command of the first stage into a fuel flow command. The loop selection logic inserted between the two stages will ensure that the most suitable rate of change of fuel flow command will pass on to the second controller stage.

In the case of the traditional controller, the fist stage is a lead controller that generates exactly the rate of change of fuel flow command. It has been discussed in Chapter 4 (in the design of a two-stage selector control) that in the design of loop selection logic, a rate can be replaced by the corresponding increment. The increment in fuel flow ∆F is given as

∆F=Fdot*ts (6.23)

where ts is the sample time and Fdot is the rate of change of fuel flow. The increment in fuel flow equally represents its rate of change and will not affect the selection of the logical circuit.

Similar argument follows in the design of loop selection logic (LSL) for the RRIM controller. Although it is the arte of change of fuel flow that is aimed at to be controlled but the LSL can be based upon acceleration demands. This is because the increment in fuel flow generated by the RRIM controller as a response to acceleration demand is proportional to the acceleration demand. As increment in fuel flow can replace its rate in a loop selection logic, so does the acceleration demand because both are proportional to rate of change of fuel flow demand.

Velocity algorithm is also preferred where actuators are integrators, like motors in position control. In that case, there is no need to implement a numerical integrator. This may be a computational saving. A physical system working as integrator is, most of the times, a continuous integrator, which may be an advantage over a numerical integrator in terms of accuracy.

Moreover, it is also believed that tuning a PI controller as velocity algorithm is relatively easier than its tuning in conventional form [Astrom and Hagglund (1995)].

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6.8 Conclusions This project represented the first implementation of Rolls-Royce Inverse Model (RRIM) controller in the civil aircraft engine (a high bypass ratio turbofan). The project time was limited and there was a lot to do with the simulation environment of the real time engine control that took away a significant part of the project time. On the other side, the traditional controller has been designed with a higher level of satisfaction in tuning controller parameters in a due time length. RRIM is a new entry in the civil aircraft engines and can be expected to evolve, with time and experience, as a strong candidate to replace the traditional controller. This is because it puts forward a revolutionary control technique from many point-of-views such as:

It is simple in structure.

Think of the reasons why nonlinear control is not popular. One obvious reason is that very often the structure of nonlinear controller comes out to be undesirable. And think of the intuitive sense in the RRIM controller that every one feels analysing the its functionality. It is not a controller with terms (inputs, outputs or states) squared and/or having non-integral powers.

It is easy to construct.

Data required for RRIM tables can be obtained from a simple experiment.

It is easy to implement.

The controller parameters and hence the number of schedules for the controller parameters are much less than those in the traditional control scheme.

It is easy to tune.

The optimum of a single variable is easy to find by experiment. One may start from a low gain, increase it, see the response (rise time, settling time, overshoot etc. etc.) and stop wherever appropriate. He or she can go ahead increasing the gain to resolve the issue of local optimum (if speculated).

It has shorter design period.

Tuning just one, instead of, for example, three variables is a big time-advantage.

It reduces computational burden.

Three main points to be noted here are: firstly, lesser the number of parameter schedules, lesser the computer effort in finding control action, secondly, a schedule may be replaced by a single parameter giving further reduction in computational effort and thirdly, a simpler control structure involves lesser computations.

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It reflects system dynamics, i.e., it ‘knows’ the system.

Better one knows a system, easier would it be for him or her to tune a controller. RRIM brings into it the dynamics of the system and has, therefore, an exact lead action in response to an acceleration demand. In other words, it can anticipate the system response.

It doesn’t need conventional model of the system (transfer function or state space).

The model required for the RRIM controller is not a transfer function or state space model. All the difficulties in finding the (nominal) model of the system for classical control techniques used, for example, in the traditional PI-controller based gains-scheduling, are not there. The same difficulties are observed in pole-zero cancellation when they lie close to origin in s-plane.

It is robust against modelling mismatch.

The RRIM tables are not supposed to be exact and accurate to many decimal places. Dynamics of the engine can be captured even with low accuracy. Moreover, the way the controller is implemented also introduces some modelling inaccuracies. So the idea of an accurate model is not there in first place.

It is robust against environmental changes.

The altitude test shows that a ground level design is quite robust to the altitude variations.

It gives zero steady state error.

Although a PI controller can also eliminate steady state error, yet the saturation nonlinearity is a typical issue of integral windup in the PI controller. The integral action inherent in the RRIM controller is free from this trouble.

6.9 Further Work and Recommendations The following sections recommend some lines of action to carry on research on Rolls-Royce Inverse Model (RRIM) control from the point it ended in this project.

6.9.1. Linearization of the Control Loop Linear model of the engine should be analysed to quantify modelling error. The size of perturbation used in linearization should be observed and best available linear model should be used, particularly at low engine powers.

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6.9.2. Time Domain Tuning The RRIM is a nonlinear controller and the size of step input used to tune the controller in time domain ha drastic effect, at least in simulation, on the performance of the engine. A relatively very small gain is not acceptable in the case of a large step input while very large gain is acceptable for a very small step size. A criteria must be set on step size of the input in tuning such a nonlinear control loop in time domain.

6.9.3. Further Tuning It should be noted that the performance of the RRIM controller presented in this project is not the best possible using the RRIM controller; the controller may further be improved to (at least) an experimental optimum. The project time did not prove enough to tune the controller to a significant level of satisfaction.

6.9.4. Performance Analysis More work on RRIM performance in presence of disturbance and sensor noise, both on experimental and mathematical ground, is needed. Robustness analysis should be extended from experimental to analytical mode.

6.9.5. Singularities in Inverse Modelling Although the RRIM is an inverse model controller, experiment showed that it is not unstable even when the nominal model proved to be of non-minimum phase (NMP) type at 60 % Nh. There is, however, no surety that actual system is NMP at low powers. A research on conventional design of inverse model controllers, both for the linear and nonlinear systems, may reveal some new aspects of inverse modelling useful in the RRIM-idea. Up to the level the RRIM controller has been investigated in this project, there is no reason to reject all possibilities of facing singularities in the case of NMP systems. Think of, for example, numerical instability; who can say that there is no possibility of it.

6.9.6. Linearization of the Control Loop As long as control specifications are given in terms of phase margin, gain margin and bandwidth and there is no other way to ensure robustness of the control design, it becomes essential to linearize the control loop. Further analysis should be done in linearizing the control, specially resolving two issues:

Results are different in Xmath and Matlab

Appearance of unstable/non-zero pole close to origin when the nonlinear controller and fuel metering system are kept together.

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Moreover, the linearization of the nonlinear engine model in Xmath at low powers makes problems and special settings are made to achieve linear model. These problems should be sorted and linear model of the engine should be analysed before using it in control design/analysis.

6.9.7. Acceleration Demand in RRIM Controller In the RRIM control design, the engine is controlled to an acceleration demand. The acceleration demand in the present implementation of the RRIM controller is a demand on high-pressure (HP) spool speed. This is because shaft dynamics are dominant in the engine performance.

The Trent engine has three shafts, the low-pressure (LP), the intermediate-pressure (IP) and the high-pressure (HP) shaft. Although the dynamics of HP shaft are dominant over the other engine variables like temperature and pressure but are not dominant over the dynamics of IP and LP shafts. Why shouldn’t the engine be controlled to LP or IP acceleration instead of HP acceleration?

6.9.8. Different Rate Demands for Different Loops In the present implementation of the RRIM controller, all engine parameters are controlled through high-pressure (HP) spool acceleration demand. This is similar to the notion of controllability in linear systems where a number of states are controlled through a single input.

Extending the idea of 6.9.7 and looking at the RRIM controller, it seems that similar tables can be built for, e.g., P30. In this case, the two tables constructed on P30 would be:

P30dot/δF Vs Nh

P30ss Vs Nh

The idea of constructing RRIM tables on the same variable that is being controlled should also be investigated. Selector control will be changed accordingly and computational burden will increase but is there any performance improvement that is worth it.

6.9.9. RRIM-type Controllers The RRIM controller should be taken as an idea, not as a fixed structure, in inverse model control. New experiments should be made keeping up the structure and changing the variable the RRIM is built on. New structures can also be found and investigated theoretically, experimentally and/or logically. A logical explanation of the RRIM, for example, can be as given below:

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Consider the graphical relation between fuel flow and the resultant spool speed (Chapter 4, RRIM Tables); the relation is monotonic. Information up to the first derivative is enough for finding complete information from any monotonic relation; a second derivative is redundant. For the monotonic relation between fuel input, F and resulting spool speed, Nh, the two relations that are required are:

relation between F and Nh relation between dF/dNh Vs Nh

The first relation is the static response table of the RRIM and the second relation is modified as follows:

dF/dNh = (dF/dt)/(dNh/dt) = Fdot/Nhdot

Also

Fdot=dF/dt ≈ ∆F/∆t

and since ∆t (sample time in discrete systems) is constant, ∆F /Nhdot has the same information as Fdot/Nhdot. ∆F /Nhdot is then inverted to give Nhdot/δF and stored as dynamic response component of the RRIM.

If the relation between fuel flow and speed were not monotonic, there would be three, instead of two, tables in the RRIM. The third would define, in any form, the relation between fuel flow and second rate of speed. This argument keeps its validity for any order of the system with zeros anywhere in s-plane.

Similar arguments can be thought of to invent such simple control schemes.

6.9.10. MIMO RRIM Controllers Multi-input, multi-output (MIMO) systems are still a challenge in spite of the research in advanced control. The RRIM controller in this project was a single-input, single-output (SISO) system and proved a relatively simpler approach as compared to most of the conventional nonlinear control techniques. The idea should be extended to MIMO in order to investigate any break through in the problems of MIMO systems control.

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French, M. E. “A Brief Introduction to Rolls-Royce Inverse Model (RRIM)”, Report No. DNS50572, Issue 1, Rolls-Royce Property Data.

Kuo, B. C. (1995), Automatic Control Systems, Prentice-Hall Inc., New Jersey, U.S.A.

McClelland, D., RB211-TRENT: System Test Facility Pass-off Test Requirements, Report No. 12 DNS 60431, Feb.-02, 2002.

Oldfield, A. R., “Trent Functional Requirements Data”, Document no. DNS49507, Issue 4, Rolls-Royce Property Data.

Rolls-Royce (1986), “The Jet Engine”, The Technical Publications Department for Rolls-Royce plc, Derby, England.

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Walsh, P. P., and Flecher, P. (2000), Gas Turbine Performance, Blackwell Science Ltd, Osney Mead, Oxford OX2 0EL, England.