enhancements of an auto- thrust function using fuzzy logic761371/fulltext01.pdfenhancements of an...

Enhancements of an auto-thrust function using fuzzy logic

G U S T A V Ö M A N L U N D I N

Master of Science Thesis Stockholm, Sweden 2014

Enhancements of an auto-thrust

function using fuzzy logic

G U S T A V Ö M A N L U N D I N

Master’s Thesis in Systems Engineering (30 ECTS credits) Master Programme in Aerospace Engineering (120 credits) Royal Institute of Technology year 2014

Supervisor at Airbus was Matthieu Barba Supervisor at KTH was Per Engvist Examiner was Per Engvist TRITA-MAT-E 2014:59 ISRN-KTH/MAT/E--14/59--SE Royal Institute of Technology School of Engineering Sciences KTH SCI SE-100 44 Stockholm, Sweden URL: www.kth.se/sci

Enhancements of an auto-thrust function using fuzzy logic.

Acknowledgements

First of all I would like to thank Matthieu Barba for giving me the opportunity to work with this projectand for patiently guiding me through the jungle that is aircraft control, in addition to being a goodsupplier of ideas and a sounding board for my own. For their shared thoughts and fruitful discussionsregarding the A/THR and manual piloting, I thank engineers Jean Muller, Fabien Guignard, and LilianRonceray, as well as test pilots Jacques Rosay and Martin Scheuermann.

Furthermore, I thank service manager Emmanuel Cortet together with the rest of EYCDR forwelcoming me into the service and inspiring me in my day-to-day work during my six months atAirbus Operations S.A.S.

I would also like to thank Per Enqvist and the School of Engineering Sciences (SCI) at the RoyalInstitute of Technology (KTH) for helping me through the administrative circus and for giving me theopportunity to study abroad and to write my master's thesis in France.

Last but not least, my ever helpful and cheerful colleagues with whom I shared the o�ce duringmy time at Airbus; namely Victor Gibert, Josep Boada-Bauxell, Alexandre Desbiez, Vincent Bassien-Capsa, and Marcos Medrano.

Toulouse, October 5, 2014Gustav Lundin

1


Abstract

This master's thesis aims to investigate how fuzzy logic can be used to adapt the tuning of aspeed control law during certain conditions such as turbulence. The objective is to lower the speedovershoot caused by the auto-thrust function as well as the general engine agitation. The mainmodi�cations studied are direct lowering of the closed loop gains, hybridisation and �ltering of thelongitudinal acceleration estimation. Finally, saturations or limits on the control signal as well ason the coordination with the longitudinal control law are studied in order to cope with the possibleconsequences of a softer control law.

To detect the turbulence, an already existing turbulence detector is used. In addition, a windgradient detector is designed in order to increase the gain during such wind conditions to counterramp errors.

It is found that a general lowering of the closed loop gain in combination with a slow hybridisa-tion, all proportional to the detected turbulence level, together with a limitation of the coordinationgives a satisfactory result. In scenarios including severe turbulence and wind gradients, the forcedlimits are shown to be indispensable.

A conclusion is drawn that the fuzzy tuning is better adapted to turbulent conditions but thatthe wind gradient detection and the forced limits must be studied further. It is also concluded thatthe coupling between the closed loop gain and the acceleration hybridisation can be interesting toinvestigate. Moreover, additional realistic scenarios should be simulated in order to further validatethe design.

For future studies on the subject; it is recommended that the controller tuning is validated withthe help of expert knowledge. Alternatively, the tuning could be handled by an ANFIS (AdaptiveNeuro Fuzzy Inference System). Finally the tuning of the controller should be validated for a widerrange of �ight points, most importantly the forced limits since the engine response varies a lotbetween di�erent points in the �ight envelope.

Keywords: Fuzzy logic, aircraft speed control, turbulence

Note: Some tuning values, �gures, and graph scales have been removed in this version due to

con�dentiality reasons.

2


Contents

1 Symbols and acronyms 7

2 Introduction 8

3 Problem 83.1 Problem description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Method 114.1 Fuzzy logic - What? How? Why? Where? . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.1.1 What is fuzzy logic (FL)? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.1.2 How does it work? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.1.3 Why use a fuzzy logic controller (FLC)? . . . . . . . . . . . . . . . . . . . . . . 154.1.4 Where to use fuzzy logic? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.2 Generalised speed control (A/THR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.3 Control strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.3.1 Approach speci�c strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.3.2 Cruise speci�c strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.4 Application of fuzzy logic in the A/THR . . . . . . . . . . . . . . . . . . . . . . . . . . 194.4.1 Nx estimation hybridisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.4.2 Closed loop gain modi�cation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.4.3 Limiting the command: N1,c limits . . . . . . . . . . . . . . . . . . . . . . . . . 334.4.4 Limiting the command: Adaptation to glide slope deviations . . . . . . . . . . 374.4.5 Limiting the command: Feed forward Nz,c limits . . . . . . . . . . . . . . . . . 39

4.5 Simulation,validation, and evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.5.1 Variables for evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.5.2 Scenarios for validation and evaluation . . . . . . . . . . . . . . . . . . . . . . . 414.5.3 Simulation environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5 Results 445.1 Non-retained solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.1.1 Higher order Nx estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.1.2 Variable stop/pass frequency in the Nx,est hybridisation . . . . . . . . . . . . . 445.1.3 Glide slope deviation adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.2.1 Generic turbulent approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.2.2 Approach: Perpignan, recorded wind 2010-01 . . . . . . . . . . . . . . . . . . . 475.2.3 Approach: Recorded severe turbulence . . . . . . . . . . . . . . . . . . . . . . . 495.2.4 Oscillating wind - No ANTIAIO . . . . . . . . . . . . . . . . . . . . . . . . . . 51

6 Conclusion 52

7 Discussion - Way forward 53

8 Appendices 55A Pilot discussion 250414 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55B Pilot discussion 210514 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56C Modi�cation summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

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List of Figures

1 Upper: Typical severe turbulence representation (pilot agreed); Lower: Up-chirp oscil-lating wind (0.009→0.06Hz). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Comparison of wind- and A/THR-caused speed deviations during turbulence and oscil-lating wind. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Engine agitation during turbulence and oscillating wind. . . . . . . . . . . . . . . . . . 114 Fuzzi�ed input membership functions for input 'sky'. . . . . . . . . . . . . . . . . . . . 125 Fuzzi�ed output membership functions for output 'weather'. . . . . . . . . . . . . . . . 136 FIS output function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Example of an (optimistic) FIS (rule 1 weighted by 0.2). . . . . . . . . . . . . . . . . . 148 FIS output function (rule 1 weighted by 0.2). . . . . . . . . . . . . . . . . . . . . . . . 149 Implementation of the FIS in the (very) simpli�ed aircraft model. . . . . . . . . . . . . 1510 Simpli�ed model of longitudinal aircraft dynamics. . . . . . . . . . . . . . . . . . . . . 1611 Singular values for the sensitivity function SGSC , in approach. . . . . . . . . . . . . . 1812 Comparison of di�erent τ in medium turbulence. . . . . . . . . . . . . . . . . . . . . . 2113 Comparison of di�erent τ in severe turbulence. . . . . . . . . . . . . . . . . . . . . . . 2214 Bode diagram comparing complementary high pass �lters with di�erent τ . . . . . . . . 2315 Nx,est hybridisation coe�cients as a function of turbulence (TURBLVLDET). . . . . . . 2416 Implemented band-stop and band-pass �lter. . . . . . . . . . . . . . . . . . . . . . . . 2517 Comparison of �rst and second order complementary washout �lter. . . . . . . . . . . 2618 Membership functions for ω as a function of turbulence (TURBLVLDET). . . . . . . . . 2719 Comparison of di�erent gains in medium turbulence. . . . . . . . . . . . . . . . . . . 2820 Comparison of di�erent gains in severe turbulence. . . . . . . . . . . . . . . . . . . . . 2821 Singular values corresponding to the gain at di�erent turbulence levels in approach. . 2922 Fuzzy gain as a function of turbulence. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3023 Bode diagram of the adaptive band stop-/pass �lter for di�erent ω. . . . . . . . . . . . 3124 Wind gradient detection overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3225 Evaluating simulation of the wind gradient detector. . . . . . . . . . . . . . . . . . . . 3326 Limits of N1,c during speed deviations in approach. . . . . . . . . . . . . . . . . . . . 3427 Limits of N1,c near the edges of the �ight envelope. . . . . . . . . . . . . . . . . . . . . 3528 Consistent speed deviation con�rmation. . . . . . . . . . . . . . . . . . . . . . . . . . . 3629 Limits due to consistent speed deviations, triggering and implied N1,c-limits. . . . . . . 3630 Glide slope deviation scenario. The dashed line shows the target glide slope. . . . . . . 3731 Limit of N1,c when in underspeed and over the glide slope. . . . . . . . . . . . . . 3832 Limit of N1,c when in overspeed and under the glide slope. . . . . . . . . . . . . . 3833 Classical A/THR limits on Nz,c. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3934 Fuzzy A/THR limits on Nz,c for light, medium, and severe turbulence. . . . . . . . . . 4035 Implemented limit on |Nz,c| as a function of turbulence (TURBLVLDET) for di�erent

speed deviations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4036 'Pilot agreed turbulence' and detected turbulence level (TURBLVLDET). . . . . . . . . 4237 Turbulence classi�cation in approach for fuzzy controller input. . . . . . . . . . . . . 4338 Closed loop simulator SIMBOX, simulink based controller. . . . . . . . . . . . . . . . . 4339 Closed loop simulator SIMPA, compiled C-based controller. . . . . . . . . . . . . . . . 4440 ATHR-caused speed deviation as a function of the turbulence level. . . . . . . . . . . . 4541 Typcal time series (m = 330t) for VCAS during medium (top) and severe (bottom)

turbulence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4642 Fan speed standard deviation as a function of the turbulence level. . . . . . . . . . . . 4643 Typical time series (m = 330t) forN1 during medium (top) and severe (bottom) turbulence. 4744 Mean closed loop pulsation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4745 Approach Perpignan: WX,0, TURBLVLDET, and KWINGRADDET. . . . . . . . . . . . 4846 Approach Perpignan: VCAS and N1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4947 Recorded severe turbulence: WX,0, TURBLVLDET, and KWINGRADDET. . . . . . . . . 5048 Recorded severe turbulence: VCAS and N1. . . . . . . . . . . . . . . . . . . . . . . . . . 50

4


49 Oscillating wind: WX,0 and TURBLVLDET. . . . . . . . . . . . . . . . . . . . . . . . . 5150 Oscillating wind: VCAS , ∆VCAS,A/THR, and N1. . . . . . . . . . . . . . . . . . . . . . . 52

5


List of Tables

1 Implemented Nx,est hybridisation time constants. . . . . . . . . . . . . . . . . . . . . . 222 Baseline ω as a function of �ight phase. . . . . . . . . . . . . . . . . . . . . . . . . . . 273 Gain as a function of turbulence level. . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 Wind gradient detector, turbulence acceleration threshold. . . . . . . . . . . . . . . . . 325 Wind gradient detector, conversion from wind acceleration to severity factor. . . . . . 326 Examples of the ratio σ(Nz,est)

σ(Nz,c)for di�erent turbulence severities. . . . . . . . . . . . . 40

7 Wind speed standard deviation as a function of the turbulence level. . . . . . . . . . . 418 Summary of fuzzy A/THR modi�cations. . . . . . . . . . . . . . . . . . . . . . . . . . 579 Summary of switching between classic and fuzzy A/THR tunings. . . . . . . . . . . . . 57

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1 Symbols and acronyms

Acronym Full form

A/THR Auto-thrustGSC Generic Speed ControllerFL Fuzzy LogicFLC Fuzzy Logic ControllerFIS Fuzzy Inference SystemMF Membership FunctionFDBK FeedbackDSPDCASDMD Speed deviation in A/THR (VTGT -VCAS)DCASTGT Speed deviation (VCAS-VTGT )GSDEV Glide Slope DeviationSymbol Description Unit

N1 Engine fan speed (percentage of max) [%]m Aircraft mass [kg]g Gravitational acceleration [m/s2]VTAS Aircraft true airspeed [m/s]VCAS Aircraft calibrated airspeed [m/s]VTGT A/THR reference speed [m/s]VGND Aircraft ground speed [m/s]VLS Lowest selectable speed [m/s]VMO Maximum operating speed [m/s]Wx,0 Longitudinal wind speed (rel. to the aircraft) [m/s]S Aircraft reference area (wing surface area) [m2]ρ Air density [kg/m3]ρ0 Air density at Standard Sea Level conditions [kg/m3]Cx Total drag coe�cient [-]Cz Lift coe�cient [-]F, c Engine thrust, commanded [N]f Lift-to-drag ratio [-]γ Flight path angle (rel. to the ground) [rad]θ Total aircraft pitch angle [rad]Nz,c Vertical load factor, feed forward [-]Nz,FDBK Vertical load factor, feedback [-]Nx,est Longitudinal load factor, estimated [-]ω Closed loop pulsation [rad/s]ζ Closed loop damping coe�cient [-]ETOT Total energy [J]

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2 Introduction

The speed is one of the most critical parameters to control when �ying an aeroplane. Naturally, thespeed monitoring therefore requires a lot of attention from the pilot. Airbus has developed a genericspeed controller (GSC) with two objectives, to attain a certain speed and to maintain it. There aretwo ways to control the speed of the aeroplane, either by the engines using the throttles or by theelevators using the stick. The GSC is basically a linear PID-controller together with a feed forwardterm to coordinate the thrust control with the longitudinal control law, i.e. the elevators.

For a linear controller it is well known that tracking and disturbance must be weighted against eachother due to the relation between the sensitivity function and the complementary sensitivity function.The speed control law in use today is heavily tuned towards reference following. It is known that sucha control law can have an unsatisfactory behaviour regarding disturbance attenuation. Although thecurrent tuning gives a robust behaviour for speed acquisition and maintenance it comes at the cost oflarge control signals in some situations.

This master's thesis aims to study whether the tuning of a speed control law during turbulence canbe improved by the use of fuzzy logic. Possible gains of a control law based on fuzzy logic could be toget an adaptive control whose parameters are optimised for the current circumstances. Presumably itwill be possible to reduce the control signals under certain conditions while maintaining the robustnessof the current tuning.

Initially, the reader will be introduced to the equations governing the speed dynamics and thestructure of the generic speed controller as well as the concept of fuzzy logic. Thereafter, the controlstrategy during approach and cruise and some proposed solutions will be discussed. Finally the resultswill be presented, along with a discussion regarding the advantages, disadvantages, and possible futuredevelopment.

3 Problem

3.1 Problem description

When �ying through turbulent air, where the wind speed varies in an oscillatory manner as depictedin Figure 1 for the case of pure turbulence and an analytic oscillating wind, there are two main issuesthat a�ect the speed control.

8


Figure 1: Upper: Typical severe turbulence representation (pilot agreed); Lower: Up-chirp oscillatingwind (0.009→0.06Hz).

The �rst one is that the A/THR creates deviations in the speed during oscillating winds in additionto the deviations caused by the wind itself. These oscillations are found notably around 0.03Hz for thecurrent A/THR, as can be concluded from the lower plot in Figure 2. Note that in the �gure below,WX,0 > 0 is de�ned as a headwind in the aircraft frame of reference to and will therefore lead to anincrease of the airspeed.

9


Figure 2: Comparison of wind- and A/THR-caused speed deviations during turbulence and oscillatingwind.

The second problem is that the A/THR sometimes over-agitates the engines during turbulence,which can be seen in the upper plot in Figure 3. This kind of behaviour can wear out the enginesfaster than if they would remain close to their stationary speed for the current �ight condition. Sinceturbulence phenomena are usually near zero-mean (or small in comparison to the amplitude), it mightbe interesting to dampen the A/THR response when �ying in such wind conditions. Furthermore,traces of Auto-thrust Induced Oscillations, AIO, can be seen in the lower �gure of Figure 3 as anincrease of the engine speed amplitude.

10


Figure 3: Engine agitation during turbulence and oscillating wind.

In the A/THR in use today, the issue of AIO is handled by a feedback consisting of a series of binaryactivation logics and non-linear �ltering, called simply ANTIAIO. Although robust in performance, ithas been proven rather complicated to tune. Therefore, this study also aims to see if it is feasible toreplace the ANTIAIO with a controller based on fuzzy logic.

The main issue when dampening the A/THR is that it must still be able to compensate quicklywhen the aircraft is struck by a non-null average wind (e.g. a wind gradient or gust). Hence thesewinds must be detected and distinguished from the turbulence in order to adapt the A/THR responseaccordingly.

3.2 Objective

The objective of the adaptive A/THR can be summarised as follows:

1. Requirements: While tracking the reference airspeed closely:

(a) Limit speed deviations caused by the A/THR.

(b) Limit engine agitation.

2. Prerequisites: To achieve the above, it is imperative to:

(a) Detect turbulence and wind gradients.

(b) Adapt the control law accordingly.

4 Method

This section presents a short introduction to fuzzy logic and some of its applications along withequations governing the GSC. This is followed by a reasoning concerning the control strategy and�nally a presentation of the actual uses of fuzzy logic in the A/THR.

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4.1 Fuzzy logic - What? How? Why? Where?

The central control concept in this master's thesis is fuzzy logic (FL), implemented in fuzzy logiccontrollers (FLC), through the use of fuzzy inference systems (FIS). The FIS engine used is the FuzzyLogic Toolbox in MATLAB provided by The MathWorksr.[2]

4.1.1 What is fuzzy logic (FL)?

Fuzzy logic is essentially human reasoning in mathematical form. Imagine looking out the window atthe sky, trying to judge the weather outside is suitable for an outdoors activity (e.g. �ying, to usean unrelated example). If the sky is clear blue and the sun is shining, it is most likely 'good'; if it iscloudy, it might be 'acceptable'; �nally, if it is raining, it is likely 'bad'. However, we all know thatthere are certain degrees of cloudy and rainy. If this would be fuzzi�ed on a scale from 0 to 10, where0 is rainy and 10 is clear, it might look like the curves in Figure 4.

Figure 4: Fuzzi�ed input membership functions for input 'sky'.

This function is called the antecedent and can be seen as the possibility of a certain input variable('sky') belonging to a certain fuzzy set made up by {rainy, cloudy, clear}, called membership functions.Moreover, a simple model of the human reasoning could be de�ned by the following rules:

1. If 'the sky is rainy', then 'the weather is bad'.(weight = 1)

2. If 'the sky is cloudy', then 'the weather is acceptable'. (weight = 1)

3. If 'the sky is clear', then 'the weather is good'. (weight = 1)

The set {bad, acceptable, good}, called the consequent, is fuzzi�ed in the same manner as the antecedent.They might be represented by the membership functions in Figure 5. Moreover, the weight added toeach rule represents how prioritised or important a certain rule is. For example, an optimist might puta lower weight on rule number 1, while a pessimist would put less weight on rule number 3.

12


Figure 5: Fuzzi�ed output membership functions for output 'weather'.

These three components yield the FIS, depicted as the output function curve below in Figure 6.

Figure 6: FIS output function.

An interpretation of the above graph could be that when starting to rain heavily or it gets veryclear, the weather is most possibly bad or good respectively. On the other hand , a smaller change inthe cloudiness of an already cloudy sky will not change the perception of the weather as much.

4.1.2 How does it work?

As mentioned in the previous section, fuzzy logic is an intuitive form of logic. This means that everystatement is always true to a certain degree (which can of course be zero). A membership functionas depicted in Figure 4 will take a truth value between 0 and 1 depending on how much the input isa member of that set. The rules are then resolved to relate the antecedents to the consequents. Theconsequent MF of a rule will be true to the same degree as its corresponding MF for the antecedent.

By introducing some refreshing mathematical notations; a MF A of an input x ∈ U is denotedµA(x). In the example above, this gives the set of MFs {µrainy(sky), µcloudy(sky), µclear(sky)}, andsky ∈ [0 10].

For example, if the input 'sky' is judged as 2.5, the fuzzi�cation gives µrainy(2.5) = 0.5, µcloudy(2.5) =0.5, and µclear(2.5) = 0. The rules above then give the consequent as

• The weather is bad to a degree of 0.5.

• The weather is acceptable to a degree of 0.5.

13


• The weather is good to a degree of 0.

Each truth value will then be multiplied by its corresponding rule weight. Thereafter, the consequentof each rule will be represented by the surface covered by the corresponding MF integrated along thevertical axis from 0 to the weighted truth value. Since multiple rules a�ect the same output, the rulesmust be aggregated to get a weighted output that represents the fuzzy inference. Normally, this isdone by calculating the position of the mean center of gravity of the total surface (centroid method);however any other method can be used that better suits the controller design (such as bisector ormiddle-of-maximum). An illustration of this simple example is seen in Figure 7 below.

Figure 7: Example of an (optimistic) FIS (rule 1 weighted by 0.2).

This gives in turn the FIS output function seen in Figure 8.

Figure 8: FIS output function (rule 1 weighted by 0.2).

In case a rule includes logical operators (AND, OR, NOT) relating the MFs µA(x), µB(x), the totaltruth value of its antecedent is calculated by the following relations [1]:

µA∪B(x) = max[µA(x), µB(x)]

µA∩B(x) = min[µA(x), µB(x)]

µ 6A(x) = 1− µA(x)

it is trivial to mention that this works for any combination of any number of arbitrary MFs.

14


4.1.3 Why use a fuzzy logic controller (FLC)?

Depending on the nature and complexity of the controlled system or the stated performance require-ments, it might be more or less suitable to use a FLC. For a simple SISO system or nearly decoupledlinear MIMO systems, it is likely that a simpler controller can be easily tuned to give a satisfactorybehaviour. However when the system complexity increases or the underlying dynamics become lessclear, it is possible that a controller based on for example FL is a better choice. As an example, anysystem which is manually controlled by a human with no deeper understanding of the system dynam-ics, can be suitable for fuzzy control. In fact, one of the main applications of FLCs is where a humanbehaviour and reasoning would normally give a satisfactory result, e.g. robots, automatic steering, etc.

In this master's thesis, a typical example is studied. It is well known that a pilot is more thancapable of controlling the speed of an aircraft without knowing neither the exact dynamics of theengines, nor the value of every single parameter that a�ects the speed. Furthermore, the pilot canfor example have knowledge and experience of how the winds are up ahead and so has the ability toanticipate the control in a way a normal linear controller cannot.

As described in section 2, the A/THR reacts somewhat opposite to a human pilot during turbulenceby trying to compensate for the oscillating airspeed rather than not reacting and instead watching theairspeed so that it stays within acceptable limits. The problem is of course that the pilot's workloadis very high during some �ight phases, which is one reason why the A/THR is used. Since there is aquite signi�cant discrepancy between the pilot's and the A/THR's behaviour, it might be interestingdo make the A/THR behave more "human" under certain circumstances.

4.1.4 Where to use fuzzy logic?

In the �eld of aircraft speed control, a fuzzy logic controller can either be implemented as a completespeed controller or as an adaptive part of a more classical controller. This master's thesis discusses thelatter example, i.e. fuzzy logic is used to augment a linear controller. However there exists researchon the use of a FLC to control the glide slope and vertical speed of an aircraft during the descent andlanding.[3]

The adaptation of the controller parameters can be done either by feedback or feed forward. Inthe case of this study, the general approach is feed forward, although the speed deviation is used as aninput. The implementation is illustrated by the simpli�ed model in Figure 9.

Figure 9: Implementation of the FIS in the (very) simpli�ed aircraft model.

4.2 Generalised speed control (A/THR)

The forces a�ecting an aircraft �ying through the atmosphere are shown in Figure 10 below.

15


Figure 10: Simpli�ed model of longitudinal aircraft dynamics.

Recalling that the dynamic pressure q = 12ρV

2TAS and starting from the drag equation, assuming a

small �ight path angle, gives the equation

mVTAS = −1

2ρSV 2

TASCx + F −mgγ. (1)

Together with the assumption of stationary �ight (i.e. no acceleration in Z)

mg = L =1

2ρSV 2

TASCz ⇒1

2ρSV 2

TAS =mg

Cz(2)

Equation 1 becomes

mVTAS = −mg CxCz︸︷︷︸1/f

+F −mgγ = −mgf

+ F −mgγ. (3)

The command to the engine is given on the form

Fc = k1∆V︸︷︷︸Direct

+ k2VTAS︸︷︷︸Damping

+mg2

VTASNz,c︸︷︷︸

Feed forward

(4)

where the three parts represent a proportional compensator (∆V = VTGT −VCAS), a desired dampingand a compensation for the vertical load factor commanded by the longitudinal law. Furthermore, thespeed control works under the following assumptions:

• Constant aircraft mass and lift-to-drag ratio.

• Small FPA (sin γ ≈ γ).

• Ideal engine response (F = Fc).

• Perfect longitudinal control (Nz = Nz,c, normally NzNz,c

= 11+τp but τ is negligible in comparison

to the engine time constant).

Time derivation of Equation 3 gives

mVTAS = −˙(mg

f

)︸︷︷︸

=0

+F −mgγ. (5)

16


Which, together with the expression for the vertical load factor

Nz =VTAS γ

g⇒ γ =

gNz

VTAS(6)

yields the expression

mVTAS = F − mg2

VTASNz. (7)

Under the ideal engine assumption above, Equation 4 inserted in Equation 7 gives

mVTAS = k1∆V + k2VTAS . (8)

By taking the Laplace transform of this equation, its frequency domain representation becomes

mp2VTAS = k1∆V + k2pVTAS . (9)

Hence the speed transfer function can be de�ned as

G :=VCASVtgt

=k1

mp2 − k2p+ k1. (10)

remembering that VCAS =√

ρρ0VTAS . For an harmonic damped oscillator, the transfer function is

H =ω2

p2 + 2ζωp+ ω2.

The coe�cients k1 and k2 can then easily be identi�ed as

k1 = mω2

k2 = −2mζω.

Together with Equation 4, this yields the �nal expression for the (open loop) command as

Fcmg

=1

VTAS

[ω2

gVTAS∆V − 2ωζ

gVTASVTAS + gNz,c

]. (11)

The current GSC uses an ω of X in approach and a ζ of X, this gives the closed loop transfer functionGGSC and the related sensitivity function SGSC = 1−GGSC below.

(Removed for con�dentiality reasons) (12)

Since disturbance attenuation is one of the main topics studied in this project, it can be interesting tolook at the singular values of the sensitivity function. These can be seen in Figure 11 for the frequencyrange 0.1→1Hz.

17


Figure 11: Singular values for the sensitivity function SGSC , in approach.

From the singular values, it is clear that the overshoot during the oscillating wind shown in section3.1, Figure 2, is caused by bad disturbance attenuation due to the tuning as described in section 2.

4.3 Control strategy

The main advantage of using a FLC instead of a classic controller is that it can easily adapt todi�erent conditions without the need of several separate control laws. As mentioned above, the controlparameters can easily adapt according to the current state; however the question is when and howto change the parameters. One large disadvantage on the contrary is that such a controller needs tobe tuned with the help of expert knowledge (e.g. pilots and control law experts in this case) to beoptimally tuned, it is not always an easy task to tune it with respect to classical control parameters.Furthermore, a FLC does not give any guarantee of stability or robustness for the closed loop system;however it is not said that these criterion cannot be achieved with an adequate tuning.

The main topics studied is the case of a turbulent approach with or without wind gradients. Sincethe current A/THR is well tuned for reference tracking, the fuzzy logic controller will not alter thecontrol law during speed changes or in calm air when a larger control signal (N1) is more preferable.This can be formulated as the following logical statement:

• If ' no speed change is being e�ectuated' and 'no wind gradient present', then 'fuzzy A/THRtuning is used', else 'classic tuning is used'.

This essentially means that as soon as the aircraft switches from speed tracking to speed hold, theA/THR switches to fuzzy tuning.

Since the aircraft speed response is non-linear and non-symmetric, it could be interesting to includesome parameters in the fuzzy controller that are not used in the classic A/THR. The parameters whichmight be interesting will depend on the current �ight phase (i.e. cruise, approach).

4.3.1 Approach speci�c strategy

During the approach phase, the aircraft is descending at a certain glide slope. If the current �ight pathangle would be too steep, the pilot must perform a nose up action, and vice versa if the slope would

18


be too �at in order to get back to the reference glide slope. This allows the pilot to also control thespeed in some cases without using the throttle.

Nonetheless it is imperative to ensure a minimum level of performance when the aircraft is nearthe edges of its �ight envelope. In approach the aircraft is most likely to get close to or below VLS .This is handled by the 'guaranteeing principle' for the thrust derivative described in 4.4.3.

4.3.2 Cruise speci�c strategy

During cruise at altitude and speed hold it is not possible to control the speed with the �ight pathangle as it would lead to the a con�ict between the two laws. However, according to pilot feedback(see Appendix A) it is less important to have a very responsive A/THR during cruise since the speedis relatively far from both VLS and VMO. Therefore larger speed variations, up to a certain level, canbe allowed in order to reduce engine agitation. Conclusively, this means that more authority is givento pacifying the A/THR (by modifying Nx,est and reducing ω) than ensuring that the speed deviationis kept small.

4.4 Application of fuzzy logic in the A/THR

The idea of using fuzzy logic in the speed control is to tune the response of the A/THR such that itsbehaviour is more intuitive and it corresponds better to that of a human pilot. There are two mainapplications where fuzzy logic can be used to modify the control law, one in the derivative term ofEquation 11 and one directly in the closed loop transfer function in Equation 10. In the derivativeterm it is in the estimation of the longitudinal load factor Nx. Obviously the frequency content ofthe estimated acceleration will a�ect the frequency content of the control signal. For example, a veryturbulent Nx estimation will lead to a heavily oscillating thrust. From Equation 11, the feedback partcan be isolated as the two �rst terms on the right hand side, i.e.(

Fcmg

)FDBK

=

{Nx =

VTASg

}=ω2

g∆V − 2ωζNx. (13)

It is clear that reducing ω will directly reduce the A/THR agitation since the control signal is pro-portionally reduced. Furthermore, it is interesting to imitate the pilot's behaviour in situations whereeither the engines are not used to maintain the speed or where the pilot would have commanded moreor less thrust than the A/THR in order to avoid excessive under- or overspeeds. This is done by undercertain conditions implying certain limits directly on the thrust command derivative, given as N1,c.

4.4.1 Nx estimation hybridisation

The main idea concerning of the Nx estimation is to combine air- and ground accelerations by using acomplimentary �lter, in order to get an estimation of the real acceleration.

General principleThe relation between the airspeed and the ground speed can be written as

VTAS = VGND +Wmean + v, (14)

where the wind is represented by an average wind, Wmean, plus a white noise, v, representing theturbulence. Derivation with respect to time yields

VTAS = VGND + Wmean︸︷︷︸=0

+w. (15)

To get a state space representation, the state is chosen as x = VTAS , the input as u = VGND, and theoutput as y = VTAS + w. Under the assumption that the aeroplane acceleration only depends on theground acceleration, the system becomes

x = VTAS = VGND = Ax+Bu

y = Vest = VTAS + w = Cx+ w (16)

19


where A = 0, B = 1, and C = 1. Since the output disturbance w is considered to be Gaussian whitenoise, the state is optimally estimated with a Kalman �lter on the form

˙x = Ax︸︷︷︸=0

+Bu+Ka (y − Cx) . (17)

With Equation 16 inserted, this becomes

pVest = pVGND +Ka

(VTAS − Vest

). (18)

Rewritten on transfer function form, this gives

Vest =p

p+KaVGND +

Kap

p+KaVTAS =

p

p+Ka

(VGND +KaVTAS

). (19)

The �lter gain Ka in is inversely proportional to the time constant τ as τ = 1/Ka. In addition, thehorizontal load factor is Nx = V /g. Equation 19 can therefore be written as:

Nx,est =p

p+ 1τ

(VGND +

1

τVTAS

)1

g(20)

Nx,est fuzzi�cationFor the load factor estimation above, there are at two ways to use a fuzzy approach. First of all,the washout time constant can be modi�ed to alter the ratio of air/ground frequency content in thesignal. This could be useful in turbulence where the high frequency content of the air accelerationsignal increases but that of the ground acceleration remains relatively slow varying.

In addition to the fuzzy time constant, a band stop/pass-�lter can be implemented at the inputof VGND and VTAS in order to attenuate the auto-throttle induced oscillation described in section 3.Finally, it is possible to replace the �rst order washout �lter in Equation 20 with one of second orderin order to get a steeper frequency cut-o�.

Washout time constant hybridisationGiven the high pass �lter

H(p) =p

p+ 1τ

(21)

there are two ways to modify the "e�ective" time constant. One is to directly change the time constantvia a command of the form "If 'turbulence is XX' then 'τ is YY'". This can be easily implemented in afuzzy controller and gives a simple control architecture. However, this approach implies that the �ltermust be reinitialised every time the time constant changes, which can be often by the nature of thefuzzy controller. Thus it might prove hard to implement this approach in practice. Another way is torun the signal through several washout �lters in parallel and then use the fuzzy controller to determinehow much "weight" should be given to each washed signal. I.e if the signals {s1, . . . , sN |si ∈ R} area discrete set of washed signals and the coe�cients {c1, . . . , cN | 0 ≤ ci ≤ 1,

∑k ck = 1}, then the

resulting signal will be

sres =

N∑i=1

cisi. (22)

For example, the time constants τ = {5, 10 15} are used, giving the Nx estimations: Nx,5s, Nx,10s, andNx,15s. The total estimation becomes

Nx,est = c5sNx,5s + c10sNx,10s + c15sNx,15s

The coe�cients c5s, c10s, and c15s can in turn be related to a speci�c turbulence severity, e.g. lightturbulence gives {1, 0, 0}, medium gives {0, 1, 0}, and severe gives {0, 0, 1}. Any intermediary levelwould give a combination of the three, respecting that the sum must be 1.

20


The advantage of this method is that it is much easier to implement and is more robust due tothe use of constant time constants in parallel. It is however slightly more computational heavy asit will calculate all washed signals regardless of whether they are in use or not for the moment. Byde�ning the set of di�erent hybridisations as {medium, medium− slow, slow, very slow}, the fuzzyrules governing the hybridisation can be expressed as follows.

• If 'no turbulence' then 'the hybridisation is medium'.

• If 'the turbulence is light' then 'the hybridisation is medium-slow'.

• If 'the turbulence is medium' then 'the hybridisation is slow'.

• If 'the turbulence is severe' then 'the hybridisation is very slow'.

In order to determine which τ is appropriate to use for each turbulence level, a series of simulationwith a �xed τ were performed and evaluated for speed maintenance and engine agitation. For mediumturbulence, the curves in Figure 12 were obtained.

Figure 12: Comparison of di�erent τ in medium turbulence.

Furthermore, the curves obtained during severe turbulence are shown in Figure 13.

21


Figure 13: Comparison of di�erent τ in severe turbulence.

A τ of 100 seconds is clearly too large, since it corresponds to a cuto� frequency of 0.01Hz, the signalwill be dominated by the ground acceleration, i.e. the inertial acceleration of the aeroplane. Since thisacceleration is loosely coupled with the air acceleration, it risks giving a very sluggish response in theairspeed, which is seen in the �gure above during severe turbulence.

For the other τ above, the curves are almost identical, which basically means that an arbitrary τin the span of those values can be used. However, since the engine agitation is a secondary objective,as described in section 3, a smaller τ is preferable. The τ chosen for the hybridisation are seen belowin Table 1.

Medium Medium-slow Slow Very slowτ [s] τ0 2τ0 4τ0 10τ0

Table 1: Implemented Nx,est hybridisation time constants.

These di�erent τ correspond to the Bode diagrams in Figure 14.

22


Figure 14: Bode diagram comparing complementary high pass �lters with di�erent τ .

It is reasonable to assume that a lower frequency limit for wind classed as turbulence is around0.03Hz (referring to Figure 1). With this in mind, it is quite clear that a time constant of 50s givesa signal which is heavily dominated by ground content. Although since the disturbance attenuationis relatively large at low frequencies, it is possible that such a high time constant is unnecessary.Conclusively, Figure 15 shows the membership functions of the respective hybridisation coe�cients asa function of the detected turbulence level.

23


Figure 15: Nx,est hybridisation coe�cients as a function of turbulence (TURBLVLDET).

Band-stop/pass �lterThe idea of using a band-stop/pass �lter is to attenuate the 0.03 Hz oscillation which causes airspeedovershoots in the classic A/THR and compensate the lost frequency content with the ground speed.By starting with the transfer function (VGND, VTAS)→ Vest from Equation 20 and rede�ning VTAS :=GBSVTAS +GBP VGND, the transfer becomes

Vest =p

p+ 1τ

VGND +1τ

p+ 1τ

(GBSVTAS +GBP VGND

)=

p

p+ 1τ

(VGND +GBS

VTASτ

+GBPVGNDτ

). (23)

A bode diagram of the band-stop (GBS) and band-pass (GBP ) �lters of Equation 23 are shown inFigure 16 below.

24


Figure 16: Implemented band-stop and band-pass �lter.

The respective transfer functions are

GBS = (Removed for con�dentiality reasons) (24)

GBP = (Removed for con�dentiality reasons) (25)

(26)

Just as for the nominal case, the complementary �lter could optionally be replaced by a higher orderone.

Higher order washout �lterAs mentioned above, it might be interesting to use a higher order washout �lter for the complementary�lter. This is possible due to the fact that the high pass �lter

H2(p) =p2

p2 + 2ζωp+ ω2. (27)

has the relative degree zero, i.e. the output must be derived zero times in order to see the inputsignal.[4] When using a higher order washout, the frequency cut-o� will be much more distinct andthus the damping will be greater at the lower frequencies, see Figure 17 below. However, this might notbe favourable during for example a wind gradient as it is desirable that the aeroplane reacts quickly tosuch phenomena. Note that the cut-o� frequency is the same in both cases. However, it is importantto notice that the cut-o� frequency in Equation 21 is de�ned as ωc = 1/τ and in Equation 27 asωc = 2π/τ . This means that the 'e�ective' τ will not be the same in the two cases.

25


Figure 17: Comparison of �rst and second order complementary washout �lter.

Clearly the problem with the substitution of a �rst order high pass �lter for a second order one isthat more phase lead is introduced. This could potentially be compensated for with a phase laggingall-pass �lter. Although this approach might work in practice, a more proper solution would be toderive a second order Kalman estimation. Such a solution would also require information about thederivative of the disturbance (i.e. wind acceleration). This means that the assumption of a mean windWmean is no longer valid and that the wind must be added as a state equation in Equation 16.

The implementation of a higher order washout focuses on when to switch between the �rst andsecond order hybridisation. This requires that both turbulence and wind gradients are detected withprecision since a second order �lter will radically dampen the estimated acceleration signal at lowerfrequencies (where wind gradients usually reside).

4.4.2 Closed loop gain modi�cation

Since the regulation of the Nx estimator is not applied directly on the closed loop transfer function,it will not a�ect the overall performance of the control law as much as modifying ω but rather helpto cancel out any anomalies in the control signal. Therefore it is interesting to modify the closed loopdynamics directly in order to handle the overall response of the control law. The two parameters toalter as described above are the pulsation and the damping. For the aeroplane to have a su�ciently fastresponse to speed changes, the gain must be high, although in turbulence the gain should be reducedto avoid engine agitation. Furthermore in wind gradients where the speed relative to the air changesslower than during turbulence, the gain must also be high in order to maintain the commanded speed.This boils down to a few simple rules regarding the general adaptation of the gains:

• If 'no turbulence' then 'the gain is high'.

• If 'wind gradient' then 'the gain is high'.

• If 'turbulence' then 'the gain is lowered'.

These rules can be directly translated into fuzzy rules, which is very handy for the implementation. Inaddition, the damping will be left rather unchanged (0.7 normally, a little higher during approach orin high lift con�guration), thus the gain will be proportional to the pulsation ω. An obvious problemwith this control is the scenario of a wind gradient in turbulence. The turbulence can quite easily be

26


detected since it has high frequency content whereas the wind gradient does not and might not bedetected in the case of this unfortunate combination.

For the case of turbulence, it is important that it is detected and classi�ed accordingly. Theturbulence level is basically the normalised di�erence between the largest and smallest measured windacceleration during a short period of time. The signal is then �ltered to get a good estimation ofthe turbulence severity.[5] However, since the signal is �ltered, the estimation has a convergence time(depending on the �lter) before it delivers a just estimation. For a �rst order �lter at τ seconds, thistime is roughly 3τ seconds.

In general there are three levels of turbulence: light, medium, severe. The turbulence level dependson the standard deviation of the assumed Gaussian wind speed. In addition to these three, extremeturbulence is essentially the case of severe turbulence at high altitude. To counter these levels ofturbulence, it can be suitable to associate each level with a corresponding gain, i.e. in order not toparalyse the control as soon as there is a little turbulence. A simple and intuitive way to do this isaccording to the following rules:

• If turbulence is light, then the gain is medium.

• If turbulence is medium, then the gain is low.

• If turbulence is severe, then the gain is very low

These rules correspond to the membership in Figure 18.

Figure 18: Membership functions for ω as a function of turbulence (TURBLVLDET).

The baseline gains chosen for approach, high-lift, and clean are shown in

Approach (APP) High lift (HYP) Cruise (CRZ)ω0 [rad/s] 0.16 0.14 0.1

Table 2: Baseline ω as a function of �ight phase.

27


For the de�nition of the fuzzy set {high, medium, low, very low}, simulations with a �xed ω wereperformed, as seen in Figure 19 and Figure 20. For medium turbulence, the following curves wereacquired:

Figure 19: Comparison of di�erent gains in medium turbulence.

In addition, the curves obtained during severe turbulence were the following:

Figure 20: Comparison of di�erent gains in severe turbulence.

It is clear that the both the speed deviation and the engine agitation are improved when the gainis lowered to a certain limit. From the above curves, the following gains can be derived as appropriatefor the di�erent levels of turbulence.

28


Turbulence None Light Medium SevereGain High Medium Low Very lowω [rad/s] ω0 0.75ω0 0.5ω0 0.375ω0

Table 3: Gain as a function of turbulence level.

As an illustration, singular values of the sensitivity functions to Equation 10, i.e. |S| = |1−G|[4],for the above ω are shown in Figure 21.

Figure 21: Singular values corresponding to the gain at di�erent turbulence levels in approach.

The peak frequency of the sensitivity function is directly proportional to ω. As described in theproblem section, the problem frequency for the classic A/THR is around 0.03Hz, which also is thefrequency in the Nx estimation around which the band stop/pass �lter is centred. This means thatit could also be interesting to adjust the centre frequency as a function of the current ω, indirectly asa function of turbulence. Not doing so means that the double hybridisation would only be optimalfor the nominal gain case during approach and its impact would be degraded as ω changes due toturbulence. This further means that the engine agitation would not be lowered as much during severeturbulence as during lower levels of turbulence. Another factor which is a�ected by the frequencyshift of the singular values is the Nx estimation. Lower frequency content is ampli�ed more at higherlevels of turbulence and is also included to a greater extent due to the increase of the complementaryhigh pass �lter time constant. This means that the total "ampli�cation" at low frequencies risk beingworsened by these two factors, and thus further motivates additional �ltering in order to reduce thee�ect on the airspeed.

The FIS output function concerning the closed loop gains is illustrated in Figure 22.

29


Figure 22: Fuzzy gain as a function of turbulence.

Since the fuzzy controller will be deactivated as soon as a wind gradient is detected, the gain willautomatically be high. It might however be interesting to increase the gain in situations of excessivespeed deviations, since lowering the engine agitation is a secondary objective.

Adaptation of Nx,est hybridisation due to gain loweringAs mentioned above, a possible issue when lowering the closed loop gain is that the hybridisation usingband stop/pass �lters, meant to dampen the resonance peak in the sensitivity function, becomes lesswell adapted. Since the resonance frequency is proportional to the closed loop pulsation, a formulaeto alter the centre frequency can be written as

ωadapt = ωresω

ω0(28)

where ωres is the resonance frequency to the sensitivity function in Equation 12 (i.e. the nominal centrefrequency which varies with the �ight phase: cruise, high lift, approach), ω is the current gain, and ω0

is the nominal gain as per Table 2. Together with the general transfer functions for band-stop/pass,this gives

HBP =2kpζωadaptp

p2 + 2ζωadapt + ω2adapt

, HBS =ks(p

2 + ω2adapt)

p2 + 2ζωadapt + ω2adapt

(29)

where ks and kp are arbitrary constants related to the maximum/minimum �lter gain. It is clear thethe band-stop �lter has its zeros on the imaginary axis, therefore it can be interesting to add a �rstorder term as in Equation 26 in order to get LHP zeros and to "soften" the frequency response. Addingthe term 0.03 ω

ω0to the nominator in HBS (the term ω/ω0 maintains the relation between the real and

imaginary part of the zeros for all ω) and choosing k = 1 yields the Bode diagram below for di�erentmodi�ed ω.

30


Figure 23: Bode diagram of the adaptive band stop-/pass �lter for di�erent ω.

Theoretically this should give a better adapted hybridisation, especially for very low ω. As anexample, in severe turbulence (ω = 0.06) the static hybridisation will take 0.537 parts of the airacceleration around the resonance peak (which has moved to 0.0088Hz) while the adaptive hybridisationwill use 0.108 parts. It can however be argued whether the low frequencies are already dominated bythe ground accelerations and thus the adaptation will have very little impact on the closed loop.

Wind gradient detectionBoth the Nx estimation and the closed loop gain modi�cation require that superposed winds duringturbulence are detected in order for the speed control law to remain well adapted to the currentconditions. It is therefore interesting to investigate by which parameters such a wind is distinguishedand how to estimate its acceleration. As mentioned above, a wind gradient during turbulence canbe di�cult to detect and anticipate. However, with the help of the turbulence detector, it should bepossible to get a rough estimation of the current wind condition with the following procedure:

De�ne the wind speed asVw,est = VGND − VTAS

To get a distinction between the low and high frequency contents of the wind, it is �ltered inparallel at 1 and 10 seconds. Since the interesting content is mostly at low frequencies, the �lteredwind is pseudo-derived using a high pass �lter at 1 second.

The amplitude of the 10 seconds �ltered signal is then compared to the presumed turbulenceacceleration amplitude given the estimated turbulence level. If the �ltered signal amplitude is largerthan the turbulence induced one, it is assumed that a wind gradient is detected. The wind gradientacceleration is then taken as the 1 second �ltered wind acceleration. Below in Figure 24 is a schematicoverview of the wind gradient detector.

31


Figure 24: Wind gradient detection overview.

The lookup table TURBLVLDET TO DVWPTEST for the wind acceleration threshold uses the valuesin Table 4.

TURBLVLDET 0 0.2 0.5 1 1.5 2DVWPTEST 0 0.3 0.5 0.6 0.7 0.8

Table 4: Wind gradient detector, turbulence acceleration threshold.

The lookup tableWINGRADACC TO KWINGRAD for converting the wind gradient acceleration intoa corresponding severity factor uses the values in Table 5

WINGRADACC 0 0.3 3KWINGRADDET 0 0 1

Table 5: Wind gradient detector, conversion from wind acceleration to severity factor.

As a concluding example, Figure 25 shows a simulation that illustrates the function of the windgradient detector.

32


Figure 25: Evaluating simulation of the wind gradient detector.

There are two major drawbacks with this method. Firstly, it's error is heavily dependent on theturbulence estimation. This can be problematic during the transient phases where turbulence is presentbut has not yet been detected due to the "settling time" of the turbulence detector. Since this meansthat the turbulence threshold will be close to zero in the wind gradient detector, any turbulence willbe detected as a wind gradient. This further implies that the closed loop gain will be kept on a higherlevel than the turbulence detector would normally propose. On the bright side, the A/THR responsewill not be worse than that of the classical since the gain will never be higher than the baseline.

Secondly, the estimated wind gradient acceleration is strongly in�uenced by the turbulence acceler-ation. A consequence is that an increasing wind amplitude might not be detected until it has surpassedthe amplitude of the turbulence. This makes the detection rather slow in severe turbulence, as shownby Figure 25 where the detection is lagging behind by around 5 seconds.

4.4.3 Limiting the command: N1,c limits

With the above approach of pacifying the A/THR, there is a risk that the command becomes too slowin the case of heavy turbulence and wind gradients and hence does not react fast enough when theaircraft approaches VLS or VMO or when it gets too far from its target. It is therefore imperative tointroduce boundary conditions for the command as a function of the speed in comparison to the threeaforementioned speeds VLS , VMO, and VTGT . In a turbulent approach, which is the case primarilystudied in this master's thesis, it is more important to privilege overspeeds than underspeeds since thespeed is close to VLS , according to pilot input (see Appendix A). During cruise, larger speed deviationscan normally be accepted, however close to VMO the overspeed limit should be tighter instead.

The control signal limitations should be activated at the same premises as the fuzzy A/THR tuning,with the exception that the control signal should not be limited in calm air. Formulated as a logicalrule this can be written as:

• If 'fuzzy A/THR tuning is used' and 'turbulence is detected' then 'then N1,c is limited.'

33


A problem that can arise when applying forced limits is that it can easily create an over- or undershootof the target speed. This is due to the linear control law (Equation 11) not being capable of compen-sating the thrust deviation (compared to the linear response) caused by the forced limits. The forcedlimits must therefore be applied tight enough on VCAS to avoid too large deviations, yet loose enoughto avoid shooting past VTGT . One solution is to have a tighter limit on over-/underspeed where theA/THR is not allowed to command an acceleration/deceleration and a looser limit which forces theengines to decelerate/accelerate. Formulated as a fuzzy rule, this so called "guaranteeing principle"can be written as:

• If 'the underspeed is small' then 'the thrust derivative is at least slightly negative'.

• If 'the underspeed is large' then 'the thrust derivative is greater than zero'.

• If 'the overspeed is small' then 'the thrust derivative is at max slightly positive'.

• If 'the overspeed is large' then 'the thrust derivative is less than zero'.

The values of the forced thrust derivative for large speed deviations should correspond to the valuewhich the classical A/THR would have commanded. Using adequate values, the guaranteeing principleis illustrated in Figure 26 below in the case of an approach.

Figure 26: Limits of N1,c during speed deviations in approach.

As can be seen in the above �gure, the lower limit is closer to zero than the upper limit. This isdue to the fact that the speed during approach equals VLS + 5kt. Moreover, a rule of thumb is toallow 1/3 of the speed deviation in underspeed and 2/3 in overspeed when �ying close to VLS , which isre�ected by the above limits. In the normal case where the aircraft is not �ying near VLS , e.g. duringcruise, the two facing curves above would be symmetrical.

In addition to the guaranteeing principle for speed deviations, the limits when surpassing VLS orVMO are formulated as:

• If 'the speed is con�rmed (2 seconds) under VLS', then the thrust derivative is greater than zero'.

34


• If 'the speed is con�rmed (2 seconds) over VMO', then the thrust derivative is less than zero'.

The above rules are illustrated in Figure 27 below.

Figure 27: Limits of N1,c near the edges of the �ight envelope.

In case the linear law does not manage to compensate the steady state error during turbulence,i.e. the speed variations are not centred around zero, an additional condition is needed in order toavoid ending up in a general overspeed or underspeed. This condition re�ects the pilot's reaction toslightly adjust the throttle when noticing a stationary speed deviation and was described during thepilot discussions (see Appendix B). In fuzzy terms, this can be expressed as

• If 'the speed deviation is consistently greater than zero', then 'the thrust derivative is at themaximum slightly positive'.

• If 'the speed deviation is consistently less than zero', then 'the thrust derivative is at the minimumslightly negative'.

This is implemented by integrating the speed deviation and activating the limits when the integrationreaches a certain threshold (ex. 2kt overspeed during 10 seconds). The integration is reset to zeroif the speed deviation or the speed derivative changes sign, or if they have the same sign. Once thethreshold has been surpassed, the limits are deactivated only when the speed deviation and the speedderivative get the same sign again. An illustration of these limits are shown below in Figure 28. Notethat DSPDCASDMD is positive in underspeeds and negative in overspeeds.

35


Figure 28: Consistent speed deviation con�rmation.

The e�ect of these limits are seen in Figure 29 for an example of severe turbulence.

Figure 29: Limits due to consistent speed deviations, triggering and implied N1,c-limits.

As can be seen in the �gure above, the main function of of these limits is to compensate for thesluggishness of the modi�ed linear law in the event of a consistent speed deviation. The tendency ofthe linear law in this case is likely due to the speed deviation term in Equation 11 is linear in ω2. Thismeans that in severe turbulence, the weight of ∆V is heavily reduced leading to a slower attainmentof the reference speed.

Conclusively, the objective of the forced limits is to assure a certain increase or decrease of thethrust when the speed strays from the target. In addition, the application of these limits is softenedby the use of several levels of implication (e.g. 'don't accelerate' to 'decelerate'). If the conditions

36


described above are not met, the limits are set to their default values.

4.4.4 Limiting the command: Adaptation to glide slope deviations

According to test pilots (see Appendix B), the A/THR risks compensating too much when the longitu-dinal control is tracking a given glide slope (GS) during a turbulent approach. The most obvious casesare the combinations of underspeed and over glide or over speed and under glide where it often su�cesto do a nose down or up action respectively to regain the target speed and the reference glide slope.Since this is the natural reaction of the longitudinal control, the A/THR risks overcompensating thespeed, causing an over- or undershoot and working against the pilot (manual or automatic).

The hypothesis in this case is that the longitudinal control (pitch up/down) will naturally compen-sate the speed under certain conditions. In order to �nd in which conditions the longitudinal controlwill su�ce, start with the expression of the total energy given a certain �ight point (VCAS , VTGT , h,m)

Etot =1

2mV 2 +mgh. (30)

De�ne two points A and B, as in Figure 30 below, where A is the deviated point and B is at thetarget speed and glide slope.

Figure 30: Glide slope deviation scenario. The dashed line shows the target glide slope.

Given that the glide slope deviation is small (ρA ≈ ρB), the energy di�erence between the twopoints can be written as

∆E =1

2m(V 2CAS − V 2

TGT

)+mg∆h. (31)

For the longitudinal law alone to be able to attain and retain the target speed and glide slope, thisdi�erence must obviously be zero. However, since the zero condition is not likely to be met in practice,it is more realistic to check if the energy di�erence is greater than zero, i.e. whether it is possible toreach the target values (not necessarily in steady state).

The limits would logically be applied to N1,C as for the guaranteeing principle. It is easy to writea fuzzy statement based on the above reasoning:

• If 'in underspeed' and 'over the glide slope' and 'the total energy di�erence is equal to or greaterthan zero', then N1,C is upper limited.

• If 'in overspeed' and 'under the glide slope' and 'the total energy di�erence is equal to or greaterthan zero', then N1,C is lower limited.

Since it has not been investigated how much the longitudinal law can compensate speed deviations, asmall margin is left around zero. Figure 31 and Figure 32 illustrate the implemented limits. The curveschange very little with variations in the glide slope and speed variations, which is why the �gures belowonly show the curves for a single value of DCASTGT and GSDEV respectively.

For the case of underspeed and over the glide slope, the following applies:

37


Figure 31: Limit of N1,c when in underspeed and over the glide slope.

Additionally, for the case of overspeed and under the glide slope, the following applies:

Figure 32: Limit of N1,c when in overspeed and under the glide slope.

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4.4.5 Limiting the command: Feed forward Nz,c limits

A problem that can arise when softening the A/THR response according to the above techniques(lowering of ω and modi�cation of Nx,est) is that the feed forward term (gNz,c) in Equation 11 becomestoo in�uential. Since this term is used to compensate for any longitudinal command (e.g. pitch up ordown) in order to maintain the speed, it will naturally be proportional to the glide slope deviation inapproach. For simplicity, the ratio between the commanded vertical load factor Nz,AT and the feedforward one, Nz,c, can be called the relative authority.

In calm air or in very light turbulence this is not an issue due to the size of the feedback. Howeverin heavier turbulence it is clear that the engine agitations will be caused primarily by the feed forwardcommanded by the longitudinal law since Nz,AT will be small due to ω being lowered, hence it can beinteresting to limit the feed forward under certain conditions.

The current limits on Nz,c are de�ned according to Figure 33 below

Figure 33: Classical A/THR limits on Nz,c.

According to the above reasoning, the feed forward command should be limited when the relativeauthority becomes too small, that is when the feedback becomes small or the feed forward becomeslarge. Since the amplitude of the feedback term in the fuzzy controller will increase with the turbulenceseverity but will decrease due to ω being lowered, it can be reasonable to assume that it will follow asimilar curve as the classic A/THR. Additionally, the feed forward term will increase monotonicallywith the turbulence level. Therefore, the feed forward should be limited tighter at low turbulence levelsand should gradually be loosened with the turbulence in order to maintain roughly the same relativeauthority for all levels of turbulence. This can be formulated with the following fuzzy rules:

• If 'the turbulence is light' then 'the Nz,c limit is tight'.

• If 'the turbulence is medium' then 'the Nz,c limit is loose'.

• If 'the turbulence is severe' then 'the Nz,c limit is very loose'.

• If 'the speed deviation is excessive' then 'the Nz,c limit is nominal'.

These rules are illustrated in �gure Figure 34 below, using adequate values (not the actual tunedvalues) for the limits.

39


Figure 34: Fuzzy A/THR limits on Nz,c for light, medium, and severe turbulence.

A possible issue when limiting the feed forward can be that the glide slope deviation becomes toolarge during heavy turbulence. Therefore the feed forward needs a certain authority to compensatethe longitudinal law commanding Nz which give a non-negligible impact on the speed.

Taking the above observations into account, the limit as seen in Figure 35 on the absolute value ofNz,c was implemented.

Figure 35: Implemented limit on |Nz,c| as a function of turbulence (TURBLVLDET) for di�erent speeddeviations.

In the above FIS, the speed deviation is used directly as an input, although it can be discussedwhether it would be better to use the glide slope deviation instead. For this application the speeddeviation is used since it makes it easier to tune the FIS over a larger �ight envelope. As a concludingexample, Table 6 shows the relative authority expressed as the ratio between the standard deviations ofNz,AT and Nz,c, for three di�erent levels of turbulence. The fuzzy controller includes the modi�cationfor ω and Nx,est as described in sections 4.4.2 and 4.4.1.

Turbulence Light Medium SevereClassic 2.16 2.33 1.86Fuzzy 1.37 0.99 0.85Fuzzy (Nz,c limited) 2.25 3.09 2.37

Table 6: Examples of the ratio σ(Nz,est)σ(Nz,c)

for di�erent turbulence severities.

With the implemented limits, the ratio between the feedback and the feed forward are slightlyincreased which means that the modi�cations of Nx,est and ω will maintain their impact on the engine

40


agitation during turbulence as desired.

4.5 Simulation,validation, and evaluation

4.5.1 Variables for evaluation

As mentioned above, the objective of the fuzzy logic based A/THR is to reduce the speed overshootcaused by the engines, as well as the engine agitation. The A/THR-caused speed deviation is givenby the absolute value of the calibrated airspeed minus the target speed and the projected wind in theaeroplane frame of reference, i.e

∆VCAS,A/THR = |∆Vtotal − Vwind| = |VCAS − VTGT − VGND + VTAS |. (32)

Intuitively, it is the mean value of this variable that is interesting to look at during turbulence.For the engine agitation it is mainly the variation of the engine fan speed that is important, i.e.

the standard deviation of N1. However, in a scenario which is not purely turbulent (e.g. when a windgradient strikes or a speed change is commanded), neither the mean value of N1, nor of ∆VCAS,A/THR,will be centred around a certain steady state value. This means that such scenarios must be evaluatedqualitatively using entire time series.

4.5.2 Scenarios for validation and evaluation

The main interest is to improve the A/THR response during turbulence. Hence di�erent levels ofturbulence will make up the base in all simulations. The turbulence input is modelled as a zero-meanGaussian distribution and tuned in accordance with pilot experience to give a realistic aircraft response.At low altitude, the standard deviations corresponding to the di�erent levels are as follows.

Turbulence (TURBLVL) σx [kt] σy [kt] σz [kt] σp [deg/s]None (0) 0 0 0 0Light (1) 1 1.5 1.5 0.6Medium (2) 2.5 3 3 1Severe (3) 3 4.5 4.5 2

Table 7: Wind speed standard deviation as a function of the turbulence level.

This yields the following wind speed (in the aircraft frame of reference) and the correspondingturbulence severity detection when simulating on SIMPA.

41


Figure 36: 'Pilot agreed turbulence' and detected turbulence level (TURBLVLDET).

Furthermore, the following fuzzi�cation was used to classify the turbulence in approach for all fuzzycontrollers using turbulence as an input.

42


Figure 37: Turbulence classi�cation in approach for fuzzy controller input.

In addition to pure turbulence, it is also interesting to simulate more realistic scenarios, in particularcases in which a wind gradient is hidden in turbulence.

4.5.3 Simulation environments

Two di�erent simulation environments were used during the course of the project. For the preliminaryresults and testing of di�erent techniques and parameters, an environment called SIMBOX, consistingof a simulink model of the primary �ight computer connected to a �ight dynamics simulator was used,see Figure 38.

Figure 38: Closed loop simulator SIMBOX, simulink based controller.

For the �nalising of the tuning and simulation of the recorded winds, a closed simulator calledSIMPA (Simulation Pilote Automatique) was used, see Figure 39. This required the simulink modelsto be converted into C-code and compiled before they could be used for simulation.

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Figure 39: Closed loop simulator SIMPA, compiled C-based controller.

An issue when switching from one simulator to the other is that SIMPA does not use the sameprecision as SIMBOX regarding for example the comparison of two 'identical' values (e.g. when checkingspeed changes). SIMBOX uses the standard smallest number handled by MATLAB, ε = 2.2204∗10−16

while SIMPA works with tolerances of ε ≈ 10−5.

5 Results

5.1 Non-retained solutions

The modi�cations below were not implemented in the �nal controller for various reasons.

5.1.1 Higher order Nx estimation

Due to problems with modelling the the second order Kalman �lter and the increased phase lead, thesecond order Nx estimation has not been implemented.

5.1.2 Variable stop/pass frequency in the Nx,est hybridisation

Due to problems tuning the �lters properly and uncertain e�ects on the closed loop system, theproposition of using a varying centre frequency for the band stop/pass �lters has not been implemented.

5.1.3 Glide slope deviation adaptation

Due to di�culties when regulating the implied limits, the adaptation to glide slope deviations has notbeen implemented in the �nal controller design.

5.2 Simulation results

The below simulations were conducted on the platform SIMPA. In all simulations of the "FuzzyA/THR", the following modi�cations were in use:

Modi�cation In use Var. in SIMPANx,est hybridisation BADISATHRFUZZY

- Nx,est fuzzi�cation Yes- Band-stop/pass �lter Yes- Higher order washout �lter NoClosed loop gain modi�cation BADISATHRFUZZYGAIN

- ω lowering in turbulence Yes- Adaptation of Nx,est hyb. due to gain lowering NoN1,c and Nz,c limits BADISATHRFUZZYLIM

- N1,c limits Yes- Nz,c limits in turbulence Yes- Glide slope adaptation No BADISATHRGSDEVLIM

44


Additionally, the aircraft model used was an A380-800 with Rolls Royce engines.

5.2.1 Generic turbulent approach

Flight point: z0=4000ft, CONF=3, CG=36.5%, γglide = −3◦.Simulation sweep: m=uniform(260t,400t), TURBLVL={0; 1; 2; 3}

The injected wind is depicted in Figure 36 in 4.5.2.

ATHR-caused speed deviationThe average speed deviations caused by the ATHR, as per Equation 32, are seen below in Figure 40as a function of the turbulence level.

Figure 40: ATHR-caused speed deviation as a function of the turbulence level.

A typical time series for VCAS during medium and severe turbulence are shown in Figure 41 below.

45


Figure 41: Typcal time series (m = 330t) for VCAS during medium (top) and severe (bottom) turbu-lence.

Engine agitationThe standard deviation of N1 for di�erent levels of turbulence is shown in Figure 42.

Figure 42: Fan speed standard deviation as a function of the turbulence level.

For the cases of medium and severe turbulence, a typical time series is seen below in Figure 43.

46


Figure 43: Typical time series (m = 330t) for N1 during medium (top) and severe (bottom) turbulence.

The mean ω in these simulations can be seen in Figure 44.

Figure 44: Mean closed loop pulsation.

5.2.2 Approach: Perpignan, recorded wind 2010-01

Flight point: z0=4000ft, CONF=3, CG=36.5%, m=330t γglide = −3◦.

The wind used in the scenario is depicted below in Figure 45.

47


Figure 45: Approach Perpignan: WX,0, TURBLVLDET, and KWINGRADDET.

This wind yields the results seen below in Figure 46.

48


Figure 46: Approach Perpignan: VCAS and N1.

5.2.3 Approach: Recorded severe turbulence

Flight point: z0=4000ft, CONF=3, CG=36.5%, m=330t γglide = −3◦.

The wind used in the scenario is depicted below in Figure 47.

49


Figure 47: Recorded severe turbulence: WX,0, TURBLVLDET, and KWINGRADDET.


Figure 48: Recorded severe turbulence: VCAS and N1.

50


5.2.4 Oscillating wind - No ANTIAIO

Flight point: z0=4000ft, CONF=3, m=330t, CG=36.5%, level �ight.The wind used in this scenario is shown in Figure 49. The frequency sweep is 0.009Hz - 0.06Hz.

Figure 49: Oscillating wind: WX,0 and TURBLVLDET.


51


Figure 50: Oscillating wind: VCAS , ∆VCAS,A/THR, and N1.

6 Conclusion

The main issue when softening the A/THR during turbulence (5.2.1) is that the aircraft risk strayinginto under- or overspeed simply because the input signal (N1) is lowered in general. This issue ishandled as described above by certain rules making up the "guaranteeing principle" as described in4.4.3. However, the proposed rules only check speed deviations and do not take the �ight point intoaccount, which might cause them to be suboptimal for an extended �ight domain. It is clear duringsevere turbulence that the speed deviations caused by the A/THR are heavily reduced. The engineagitation is not reduced very much when looking at the quantitative results. However in the time seriesit is clear that the thrust oscillates in a much slower manner although with large variations.

In the high wind scenario (5.2.2), the problem of a large wind gradient hidden in turbulence isillustrated. When the wind gradient hits the aircraft at around 275s, the minimum under speed getsroughly 3kt below and the maximum overspeed gets roughly 5kt above the classic A/THR. Moreover,the average speed deviation is around 0.5kt larger in the fuzzy case. Conclusively this scenario reinforcesthe already stated fact that wind gradients must be anticipated in order to be e�ectively damped whenthe gain is low.

For the oscillating wind scenario, the fuzzy A/THR gives a better result in most aspects. However,in low frequency it dampens a bit less than the classic A/THR, most likely due the ampli�cation beingmuch higher at low frequencies than for the nominal case (see Figure 21) and is not reduced e�cientlyby the band stop �lter. This might then be reinforced by the fact that more ground content is taken forthe acceleration, i.e. low frequency. In addition, the a�ect of the ANTIAIO is almost negligible at lowfrequencies, seen as the di�erence between the classic and fuzzy compared to fuzzy with ANTIAIO andfuzzy without ANTIAIO. Although towards the very end of the tile series in Figure 50 the di�erenceis larger. That is also where the wind starts being interpreted as turbulence, why it can be questionedif it represents relevant results.

52


A general conclusion concerning the tuning is that it becomes hard to tune optimally for both thegain and the hybridisation together. This is likely due to the band stop/pass part essentially attacksthe peak in the speed sensitivity function which is then shifted when the gain is lowered. Thus thehybridisation of Nx,est becomes less in�uential when the turbulence increases.

7 Discussion - Way forward

Given the results presented and the conclusions drawn so far, it seems promising to use an adaptivecontroller based on fuzzy logic to adapt the speed controller's behaviour. There are, as mentioned inthe conclusion, a few points that need further investigation. For the implemented fuzzy A/THR, thefollowing points have been identi�ed so far:

• Improvement of wind gradient detection and anticipation. This is the key to using very low gains,which will re�ect the pilot's behaviour of being attentive instead of reactive during turbulence.It was mentioned by Jacques Rosay that the wind measured at the tower could be used to get abetter anticipation of the wind, since it is information available to the pilot.

• Further analyse the possibility of adapting the band pass/stop �lter in the hybridisation of Nx,est

to the current gain in order to better dampen the speed overshoot caused by the peak in thespeed sensitivity function.

• More precise and intuitive application of the guaranteeing principle. The implemented controlleruses many di�erent conditions, making it hard to know exactly which limit is active.

• Better adaptation of the forced limits to the current �ight point. As mentioned by test pilotMartin Scheuermann (see Appendix A), the engine response varies a lot between high/low altitudeand high/low thrust respectively. This could include adapting the underspeed limit in approachif the current approach speed di�ers from VLS + 5kt, i.e. include VCAS − VLS as an input for thelower limit.

In addition, some other tracks might be interesting to investigate:

• Validation and adaptation of the controller during cruise. Extension of validation to a larger�ight envelope.

• Use very low gains in spite of the wind gradient risk but tune the forced limits so that they ensurea small speed deviation. An idea is to use fuzzy logic during a speed deviation to get the speedclose to the reference using a high gain linear law, and then switch to a very low gain tuningwhen the speed is "attained". This has partly being discussed by Stéphane Delannoy for speedchanges.

• A long shot is to implement a neural controller based on fuzzy logic, a so called ANFIS, AdaptiveNeuro Fuzzy Inference System, which can learn how the pilot reacts in di�erent wind scenariosand then tune the fuzzy membership functions accordingly during turbulence. This can possiblybe a way for the A/THR to handle wind gradients hidden in turbulence. Some drawbacks arethat the method is computationally complex and not very good at handling monotonic functionsor discontinuous membership functions, such as the current gain reduction during turbulence.

Naturally such a tuning approach would require the pilot's reactions to be quanti�ed as a secondorder system from which new ω could be derived. In addition the non-linear behaviour re�ectedby the forced limits would have to be separated from the "linear" reactions. Alternatively thepilot is given an A/THR without the forced limits and gets to react in parallel with the A/THRin order to de�ne the MFs for the forced limits, which could essentially be something completelydi�erent than what is proposed in this study.

• A track not necessarily including fuzzy logic could be to study the implementation of a linearmodel predictive controller (MPC) in order to avoid large thrust variations by commanding 'just

53


enough'. Since the control signal is clearly limited and the aircraft is quite linear and naturallysampled in the case studied, a MPC could be fairly well adapted to the task. This would requirea representative model of the engines. Some work has been done to establish a third degreemodel of the engine response. [6]

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8 Appendices

A Pilot discussion 250414

Participants :Martin SCHEUERMANN, Experimental test pilotMatthieu BARBAGustav ÖMAN LUNDINFabien GUIGNARDLilian RONCERAY

Today's A/THR focuses mostly on reference following, i.e. the di�erence between the target speedand the current speed. Martin mentioned that the pilot has a much wider span of inputs when hemanages the throttles. For example how much the speed varies and how far he is from ex VLS or VMO.Furthermore he mentioned that when the speed varies around the reference, a rule of thumb is to keepthe speed 1/3 and 2/3 over or under depending on if the reference is near VLS or VMO.

i.e.

Some cases of speed perturbations are more alarming than other, especially in approach, which isthe phase where the A/THR is the most useful. For example, headwind + turbulence might not implyany pilot command since the TAS is increased by the headwind which is a command the pilot wouldnormally give in turbulence in order to stay clear of the red band. However a tailwind in approachimplies that the glide slope increases which implies a contradictory behaviour since the aeroplaneaccelerates and sinks faster due to the slope increase but decellerates due to the tailwind.Martin also proposes that the ATHR should take into and handle the energy and the air FPA insteadof just the velocity in order to get a better coherence with actual pilot behaviour. Moreover, it wouldbe good if it adopted to the current altitude in approach since it is more critical to maintain a referencespeed at under 500ft than at 2-3000ft. At lower altitudes it might also be interesting to use the spoilersfor speed control, however one needs to pay attention to where the nose points since a rising nose usuallyindicates a lowered speed which is then acted against although the opposite action is commanded bythe A/THR.In the long run (research) it may be interesting to keep the air FPA constant and instead vary theground FPA in order to get less high frequency variations on NXEST.Regarding FPA it is also important to take into account the engine response, or the possible engineresponse in di�erent �ight cases. For example at high altitude and low FPA, the engines are veryresponsive. Inversely at low altitudes, high FPA and idle engines, the response is much slower.Second part:M. BARBA; G. ÖMAN LUNDIN; F. GUIGNARDIdeas on closed loop simulations: Run simulations with several ω, ζ, τ and compare the engine agitationto �nd good boundary values for the fuzzy control. Compare changes in τ and ω.

CONCLUSIONFocus for the internship proposed to be changed to primarily the approach phase since that is whereMartin feels the need for a good A/THR is the greatest. He argues that during cruise it is not asimportant to exactly follow a given speed and this will naturally decrease the engine agitation. Pilotdiscussions 2-4 will show whether this is a widespread opinion.

55


B Pilot discussion 210514

Participants:Jacques ROSAY, Chief test pilotMatthieu BARBAGustav ÖMAN LUNDIN

In approach, the glide slope error can be used as an input to the ATHR. For example, if the commandedglide slope is X◦, the current glide slope is Y◦, and the speed gap is DVTGT, the ATHR can commandsomething/nothing according to:

• If Y<X and DVTGT<0, then do nothing.

• If Y>X and DVTGT<0, then do something. (ex. increase the thrust)

• If Y<X and DVTGT<0, then do something. (ex. decrease the thrust)

• If Y>X and DVTGT<0, then do nothing.

Note that this kind of control takes into account that the pilot reacts and changes the glide slope inorder to correct the speed since the A/THR does not have that authority. It is though a more intuitiveway to handle the A/THR in approach in order to not have a counteracting behaviour from the pilotand the A/THR.Furthermore it was discussed whether the authority of the ground speed in the A/THR is too largeat times. Jacques gave an example of an aeroplane which made a sharp turn towards a high wind,thereby increasing the airspeed but lowering the ground speed, the A/THR then commanded an in-crease of thrust since the ground speed was lowered. This is something that could be interesting totake into account for the Nx,est. It is although important in this case, and many other, to identify anddistinguish di�erent kinds of winds. He mentioned that a gust of wind usually has a zero mean butthat turbulence rarely has it. It might therefore be interesting to try to inject real recorded winds inthe simulations (or possibly a coloured Pilot agreed turbulence).Also in approach, it might be interesting for the wind detection to take into account the near groundwind reported by the tower. This is something that is taken into account by the pilot but not by theA/THR at this day. Moreover, in the case of strong gusts, it often does not do any good to react tomust with the throttles since there is usually a gust in the opposite direction not far behind. Howeverit is imperative to act when the speed approaches VLS or VMO (or VFE). Here's where the pilot usesthe speed trend as well. The problem with the application of the speed trend in the A/THR is thatit cannot be used directly. Jacques mentioned that he more or less integrates the speed trend andreacts accordingly. For example he may not react to a large speed trend that lasts for two seconds butvery well to a smaller speed trend that lasts for a longer period of time. A personal re�ection on theimplementation of this is whether to use the integrated value directly or if it should be con�rmed aswell before entering the controller.Regarding the control including the glide slope error, it can be directly implemented using the inputsto the G/S law. The question remains though if everything (GSDEV, DVTGT, SPDTREND) shouldbe baked together in the same fuzzy controller, which might be more complex to implement, or if itshould be implemented serially.Finally, Jacques reacted to the initial performance speci�cations given by Fabien GUIGNARD regard-ing the thrust derivative limits when approaching the borders of the �ight envelope. He mentionedthat it might not be very good to command a thrust derivative on a turbo reactor since it is so muchslower than the turbo prop which Fabien worked with. Instead he would suggest putting the limits onthe N1,TGT directly, since the slow engine response automatically evens the thrust curve. A commentby Matthieu was that this might also be better since the commanded thrust derivative might hit therate limit of the engine and it would therefore do no good.

56


C Modi�cation summary

Modi�cation Input Output Description Figure

Nx,est hybridisation TURBLVLDETcτ,ii = 1, 2, 3, 4

cτ,i = f(TURBLVLDET)0 ≤ cτ,i ≤ 1∑cτ,i = 1

Figure 15

ω modi�cation TURBLVLDET ω TURBLVLDET↗ ⇒ ω ↘ Figure 18

Limits: ∆V ∆V [kt] lim(N1,c)

∆V ≤ −5⇒ N1,c ≥ −2

∆V ≤ −10⇒ N1,c ≥ f(∆V )

∆V ≥ 10⇒ N1,c ≤ 2

∆V ≥ 15⇒ N1,c ≤ f(∆V )

Figure 26

Limits:∫

∆V dt∫

∆V dt lim(N1,c)

∫∆V dt > 20⇒ N1,c ≤ 2∫∆V dt < −10⇒ N1,c ≥ −2

Integ. reset to 0 if:sgn(∆V )6=sgn(V )

Figure 29

Limits: VLS , VMO VCAS , VMO, VLS lim(N1,c)Conf. during 2 seconds:VCAS − VLS ≤ 0⇒ N1,c > 0

VCAS − VMO ≥ 0⇒ N1,c < 0

Figure 27

Limits: Nz,c TURBLVLDET lim(|Nz,c|)

No turb: Nominal lim.Light turb: Tight lim.Med. turb: Loose lim.Sev. turb: Very loose lim.

Figure 35

Table 8: Summary of fuzzy A/THR modi�cations.

Switch Input Activation logicBFUZZYSWITCH

0 = Classic tuning1 = Fuzzy tuning

KWINGRADDET

BVTGTCHANGE

If KWINGRADDET ≤ 0.1and BVTGTCHANGE = 0then BFUZZYSWITCH = 1.

BLIMSWITCH

0 = No N1,c-limits1 = Fuzzy N1,c-limits

BFUZZYSWITCH

TURBLVLDET

If BFUZZYSWITCH = 1and TURBLVLDET > 0.3then BLIMSWITCH = 1.

Table 9: Summary of switching between classic and fuzzy A/THR tunings.

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References

[1] Bai, Y.; Zhuang, H.; Wang, D.,Advanced Fuzzy Logic Technologies in Industrial Applications,Springer, 2006, ISBN: 978-1-84628-468-7

[2] The MathWorksFuzzy Logic Toolbox User's GuideThe MathWorks, Inc., 1995

[3] McLauchlan, L.,Electr. Eng. & Comput. Sci. Dept., Texas A&M Univ. - Kingsville, Kingsville, TX, USAFuzzy logic controlled landing of a Boeing 747,Intelligent Robots and Systems, 2009. IEEE/RSJ International Conference, 2009

[4] Glad, T.; Ljung, L.Control theory - Multivariable and nonlinear methods,Studentlitteratur, Lund, 2003, ISBN-13: 978-0748408788

[5] Fabien Guignard, EYCDL,A/THR Memorandum,Airbus, Toulouse, 2014

[6] Clément Pontoizeau, EYCDL,Rapport de stage: Etude de l'automanette A380 - Problématique de l'ANTIAIO,Airbus, Toulouse, 2011

[7] EYCDL,Flight Control Laws Description - A380-800,Ref: L27RP0503707, Airbus, Toulouse, 2013

[8] Martin Delporte, EYCDA,A380 Stability and Control Handbook,Ref: L07D1-169.0167/2003, Airbus, Toulouse, 2008

[9] Stephance Marcy, EYCDR; Amy Wiggenhauser, Aéroconseil; Christelle Garcia, Aéroconseil,WIN SPECIFICATION,Ref: FM124 1089, Airbus, Toulouse, 2012

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