session 6 dynamic modeling and systems analysis · · 2015-01-13national aeronautics and space...

National Aeronautics and Space Administration

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Session 6 Dynamic Modeling and Systems Analysis

4th Propulsion Control and Diagnostics Workshop Ohio Aerospace Institute (OAI)

Cleveland, OH December 11-12, 2013

1

1:00 – 1:05p Overview – Jeffrey Csank

1:05 – 1:30p Dynamic Systems Analysis – Jeffrey Csank

1:30 – 1:55p T-MATS (Toolbox for the Modeling and Analysis of Thermodynamic Systems) – Jeffryes Chapman

1:55 – 2:20p Reducing Conservatism in Aircraft Engine Response Using Conditionally Active Min-Max Regulators – Ryan May

https://ntrs.nasa.gov/search.jsp?R=20140016527 2018-05-28T08:39:24+00:00Z


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Dynamic Systems Analysis

• Preliminary Engine Design – Systems Analysis (Steady state) – Lack of dynamic performance information

• Historical data (past experiences) • Additional conservatism in the design

• Dynamic Systems Analysis – Better predict/account for dynamic operation in PED – Allow for trade-offs between performance and operability margins

to meet future engine performance requirements – Enabled through the Tool for Turbine Engine Closed-loop Transient

Analysis (TTECTrA)

2


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T-MATS (Toolbox for the Modeling and Analysis of Thermodynamic Systems)

• Simulation System designed to give a user a library containing building blocks that may be used to create dynamic Thermodynamic systems. Includes:

- Iterative Solving capability - Generic Thermodynamic Component models

Turbomachinery components (compressor, turbine, burner, nozzle, etc.)

- Control system modeling (controller, actuator, sensor, etc.) • MATLAB/Simulink Based • Open Source (free of proprietary and export restrictions) • Development of T-MATS is being led by NASA Glenn Research

Center - NASA’s focus for this project is on the modeling of aerospace applications, however the T-MATS framework is extremely general and can be applied to any thermodynamic model.

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Reducing Conservatism in Aircraft Engine Response Using Conditionally Active Min-Max Limit Regulators

4

• Typical aircraft engine control is based on a Min-Max scheme

• Designed to keep the engine operating within prescribed mechanical and operational safety limits – Compares fuel flow to determine the limit that is closest to being

violated – Conservative

• Improve engine performance by allowing the limit regulators to only be active when a limit is in danger of being violated.


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Dynamic Systems Analysis



5

Jeffrey Csank NASA Glenn Research Center


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Team Members

• Jonathan Seidel, NASA Glenn Research Center/RTM • Jeffrey Chin, NASA Glenn Research Center/RTM • Alicia Zinnecker, N&R Engineering • Georgia Institute of Technology

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Outline

• Preliminary Engine Design • Systems Analysis • Tool for Turbine Engine Closed-loop Transient

Analysis (TTECTrA) • Dynamic Systems Analysis • Conclusion

7


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Preliminary Engine Design • Huge commitments are made

based on results • A completely new engine is

relatively rare • Most programs focus on

derivative engines

8

Weight

Performance

Scaling

Mission

Cycle

Configuration

Component Design

Component Test

Performance

Manufacture


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Systems Analysis

• Complex process that involves system-level simulations to evaluate system-level performance, weight, and cost (optimize system, compromise component)

• Focus on steady-state design cycle performance • Dynamic considerations

and issues are incorporated through the use of operating margins – Stall margin

9

Corrected Flow (Wc)

Pre

ssur

e R

atio

(PR

)


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Tool for Turbine Engine Closed-loop Transient Analysis (TTECTrA)

• Capable of automatically designing a controller • Easily integrates with users engine model in

MATLAB/Simulink environment • Provide an estimate of the closed-loop transient

performance/capability of a conceptual engine design • Requirements:

– MATLAB®/Simulink® (Release R2012b or later) • MATLAB® Version 8.0 (R2012b) • Simulink® Version 8.0 (R2012b) • Control Systems Toolbox® Version 9.4 (R2012b)

– Engine Model compatible with Simulink – State space linear model in MATLAB

10


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TTECTrA Architecture

• TTECTrA software automatically designs: – Set Point – Set Point Controller – Limit Controller

• Simulates different thrust profiles

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User Model Set Point Controller

Limit Controller

Engine

Sensors

Selector Logic

Desired Thrust

Set Point

Actuator

Feedback

Error Fuel Flow Engine

Outputs Set Point


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TTECTrA - Set Point Function

• Flight condition (altitude, Mach, temperature) • Define set point bounds and number of breakpoints

– Fuel flow – Thrust

12

0 1 2 3 4 5

x 104

1000

1500

2000

2500

3000

3500

4000

4500

Close figure to accept setpointsLeave figure open and use GUI to recalculate

Corrected Thrust (lbf)

Con

trol V

aria

ble


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TTECTrA – Set Point Controller

• Bandwidth (Hz) • Phase Margin • Feedback filter (Hz) • Throttle Filter (Hz)

13

-50

0

50

100

150

Mag

nitu

de (

dB)

100

-180

-135

-90

-45

0

Pha

se (d

eg)

Bode Diagram

Frequency (rad/s)

PlantLoop Gain

-10 0 10 20 30 40-10

-5

0

5

10Root Locus

Real Axis (seconds -1)Im

agin

ary

Axi

s (s

econ

ds-1

)

0 2 4 60

0.5

1

1.5

Time, s

Con

trol

Var

iabl

e

LMPre-Filter


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TTECTrA – Limit Controller

• Acceleration Minimum Surge Margin (HPC) – Ncdot vs NcR25

• Deceleration Minimum Surge Margin (LPC) – Wf/Ps3

14

7000 8000 9000 10000 11000 120000

200

400

600

800

1000

1200

1400

Corrected core speed (rpm)

Cor

e ac

cele

ratio

n (r

pm/s

ec)


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User Model

TTECTrA - Selector Logic / Actuator

• Selector Logic (Min/Max scheme) – Min (Set Point, Acceleration) – Max (Min, Deceleration)

• Actuators – Currently only models fuel flow – First order filter

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Engine

Sensors

Selector Logic

Desired Thrust

Set Point

Actuator

Feedback

Error Fuel Flow Engine

Outputs

Set Point Set Point Controller

Limit Controller

Actuator


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Commercial Modular Aero Propulsion System Simulator 40,000 (C-MAPSS40k)

• 40,000 Lb Thrust Class High Bypass Turbofan Engine Simulation

• Matlab/Simulink Environment

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• Publically available

• Realistic controller • Realistic surge

margin calculations


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Burst and Chop Thrust Profile

• Idle (14% of max thrust) to Take-off thrust profile to test the TTECTrA controller

• Compare the thrust response to the Federal Aviation Administrations (FAA) Federal Aviation Regulation (FAR) Part 33, Section 33.73(b)

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0 10 20 30 40 500

2

4

6x 10

4

Time, s

Thru

st

0 10 20 30 40 501

1.5

2

Time, s

Con

trol V

aria

ble

DmdFdbk

10 12 14 16 180

1

2

3

4

5x 10

4

Time, s

Thr

ust

DmdFdbk95% Max5 s


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Burst and Chop Thrust Profile

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0 10 20 30 40 5010

20

30

40

50

HPC

SM

, %

Time, s

6000 8000 10000 12000-1000

-500

0

500

1000

1500

2000

Nc do

t

NcR25

0 10 20 30 40 5010

20

30

40

50

60

LPC

SM

, %

Time, s

0 10 20 30 40 500

0.002

0.004

0.006

0.008

0.01

0.012

Wf/P

s3

Time, s


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Engine Deterioration

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0 20 40 6010

20

30

40

50

Time, s

HPC

SM

, %

0 20 40 6010

20

30

40

50

60

Time, s

LPC

SM

0 20 40 601

1.2

1.4

1.6

1.8

Time, s

Con

trol V

aria

ble

0 20 40 600

1

2

3

4

5x 10

4

Time, s

Thru

st, l

bf

NewEOL


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The Benefit of TTECTrA

Stack % Uncertainty 11

Reynolds Number 2

Distortion 4

Tip Clearances 1.5

Deterioration 1.5

Random 2

Transient Allowance 12

Total 23

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Do we have enough margin? Too much margin?

Corrected Flow (Wc)

Pre

ssur

e R

atio

(PR

)

UncertaintySADSA


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The Benefit of TTECTrA • Combustor Stability

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• Turbine life

• Low Pressure Compressor

NcR25, rpm

Ps3

R, p

si

SADSA

Corrected Flow (Wc)

Pre

ssur

e R

atio

(PR

)

SADSA

Nc, rpm

T40,

�R

SADSA


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Future Work

• NPSS Model in Simulink – Georgia Institute of Technology

• Integrate TTECTrA with the NPSS Simulink model – NASA/RHC

• Integrate TTECTrA/NPSS Simulink with a larger

systems analysis optimization algorithm – NASA/RHC and NASA/RTM

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Conclusion

• Dynamic systems analysis: – Enables engine transient performance to be accounted for in

the optimization of the engine design and early in the preliminary design of turbine engines.

– Allows trading of overly conservative surge margin for better performance through system redesign (or opline).

• Developed the Tool for Turbine Engine Closed-loop

Transient Analysis (TTECTrA) – Capable of automatically designing a controller at a single

flight condition. – Easily integrates with users engine model in

MATLAB/Simulink environment. – Open source

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Questions?

24

Thank you


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Toolbox for the Modeling and Analysis of Thermodynamic Systems

(T-MATS)

Jeffryes W. Chapman Vantage Partners, LLC.

25




www.nasa.gov 26

Team

• Jeffryes W. Chapman

Vantage Partners, LLC. Cleveland, OH 44135

• Thomas M. Lavelle

NASA Glenn Research Center, Cleveland, OH 44135

• Ryan D. May

Vantage Partners, LLC. Cleveland, OH 44135

• Jonathan S. Litt


• Ten-Huei Guo



www.nasa.gov 27

Outline

• T-MATS Description

• Background

• Framework

• Block Sets

• Examples

• Conclusion

• Future work


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T-MATS Description

• Toolbox for the Modeling and Analysis of Thermodynamic systems, T-MATS – Modular thermodynamic modeling framework – Designed for easy creation of custom Component Level Models

(CLM) – Built in MATLAB®/Simulink®

• Package highlights – General thermodynamic simulation design framework – Variable input system solvers – Advanced turbo-machinery block sets – Control system block sets

• Development being led by NASA Glenn Research Center – Non-proprietary, free of export restrictions, and open source

• Open collaboration environment


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Background

• Thermodynamic simulation examples Model Type Examples

Steady-State (system convergence may be required)

Gas turbine cycle model • e.g., performance models

Dynamic with Quasi-steady-state variables (multi-iteration simulation; time and system convergence)

Gas turbine model with spool dynamics only. (real time running capability) • e.g., control models

Fully Defined Dynamic Simulation (iteration over time)

Dynamic gas turbine model with spool and volume dynamics (typically runs more slowly) • e.g., near stall performance models


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Background: Industry Study

Package User Friendly*

Flexibility* Export Restricted

Source code available

Dynamic Control System

Cost

C-MAPSS40k, NASA

High Low Yes Yes

Yes Yes MATLAB

Matlab: Thermlib toolbox, Eutech

High Medium No No Yes

No MATLAB + $4900

Cantera, Open source

Low High No Yes No No None

Gas Turbine Simulation Program (GSP), NRL

Medium Medium No No Yes Yes $4,000

GasTurb, Nrec Medium Low No No Yes Yes $1340

T-MATS, NASA High High No Yes Yes Yes MATLAB

Definitions: 1* User Friendly, Controls Perspective Low : Code based Med: Model based High: Model based with package implemented in a platform that is an industry standard

2* Flexibility Low : Plant configuration set Med: Object oriented, objects difficult to update High: Object oriented, objects easily adaptable by user


www.nasa.gov 31

T-MATS Framework

• T-MATS is a plug-in for a MATLAB/Simulink platform – additional blocks in the Simulink Library Browser:

– additional diagram tools for model development in Simulink:

Faster and easier model creation

Added Simulink Thermodynamic modeling and numerical solving functionality


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T-MATS Framework • Dynamic Simulation Example:

– Multi-loop structure • The “outer” loop (green) iterates in the time domain

– Not required for steady-state models

• The “inner” loop (blue) solves for plant convergence during each time step


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Blocks: Numerical Solver • Many Thermodynamic models are partially defined and require a solver to

ensure model conservation (e.g., mass, energy, etc.). – In many gas turbine simulations, component flow will typically be solved by an

independent solver.

• T-MATS contains solvers that perform in two main steps: – Automated Jacobian (system gradient) Calculation

• Each plant input is perturbed to find the effect on each plant output. – Newton-Raphson method is used to “converge” the system.

where,

33


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Blocks: Turbo-machinery

– Models based on common industry practices • Energy balance modeling approach • R-line compressor maps in Compressor model • Pressure Ratio maps in Turbine model • Single fuel assumption • Flow errors generated by comparing component

calculated flow with component input flow

– Includes blocks such as; compressor, turbine, nozzle, flow splitter, and valves among others.

– Built with S-functions, utilizing compiled MEX functions

34

• T-MATS contains component blocks necessary for creation of turbo-machinery systems


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Blocks: Controls

– Sensors:

– Actuators:

– PI controllers:

35

• T-MATS contains component blocks designed for fast control systems creation


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Blocks: Settings

36

• The T-MATS Simulation System is a highly tunable and flexible framework for Thermodynamic modeling.

– T-MATS block Function Block Parameters • fast table and variable updates

– Open source code

• flexibility in component composition, as equations can be updated to meet system design

– MATLAB/Simulink development

environment • user-friendly, powerful, and versatile

operation platform for model design


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Dynamic Gas Turbine Example: Objective System

37

Simple Turbojet


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Dynamic Gas Turbine Example: Creating the Inner Loop


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Dynamic Gas Turbine Example: Inner Loop Plant

39

Turbojet plant model architecture made simple by T-MATS vectored I/O and block labeling

Input

Compressor

Burner

Turbine Nozzle

Shaft


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Dynamic Gas Turbine Example: Creating the Solver


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Dynamic Gas Turbine Example: Solver

41

Plant flow errors driven to zero by iterative solver block in parallel with While Iterator

Simulink While Iterator block

Iterative Solver

Inner Loop Plant from previous slide


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Outer Loop Effectors

Outer Loop Plant

X_ol(t+dt)

Outputs

Iteration over time, t

Outer Loop Effectors

Outer Loop Plant

X_ol(t+dt)

Outputs

Iteration over time, t

42

Dynamic Gas Turbine Example: Creating the Outer Loop

Inner Loop Plant

Iterative Solver

f(x(n))

X_il(n+1)

Iteration to ensure convergence, n

y(t)

Do While Iterations

Simulink Block

Iteration Condition

T-MATS Block


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Dynamic Gas Turbine Example: Outer Loop Plant

43

Shaft speed integration

Environmental conditions

Simple Control System

Shaft integrator and other Outer Loop effectors added to create full system simulation


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Verification and Release

• Verification was performed by matching T-MATS simulation data with other established simulations. – Models chosen for verification

• NPSS steady-state turbojet model • C-MAPSS – High bypass turbofan engine model

– In all cases differences in simulation performance were within acceptable limits.

• Expected Release: Q4,2013 or Q1,2014. – Pre-built examples will include:

• Newton-Raphson equation solver • Steady state turbojet simulation • Dynamic turbojet simulation

44


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Conclusions

• T-MATS offers a comprehensive thermodynamic simulation system – Thermodynamic system modeling framework – Automated system “convergence” – Advanced turbo-machinery modeling capability – Fast controller creation block set

45


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Future Work

• Increase thermodynamic modeling capability – Introduce Cantera to T-MATS

• “Cantera is a suite of object-oriented software tools for problems involving chemical kinetics, thermodynamics, and/or transport processes”

• Open source • Increases thermodynamic modeling capability to include:

– Non-fuel specific gas turbine modeling – Fuel cells – Combustion – Chemical Equilibriums

46

O + CH �H + CO


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Reducing Conservatism in Aircraft Engine Response Using Conditionally Active Min-Max

Limit Regulators

Ryan D. May Vantage Partners, LLC

Sanjay Garg NASA Glenn Research Center

4th Propulsion Control and Diagnostics Workshop

Ohio Aerospace Institute (OAI) Cleveland , OH

December 11-12th, 2013


www.nasa.gov


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Overview

• Introduction • Baseline Control Architecture • Conditionally Active Limit Regulator Approach • Simulation Examples • Conclusions & Future Work

NASA GRC Propulsion Control and Diagnostics Workshop 48


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Introduction

• The primary task of an engine control system is to deliver the guaranteed performance while ensuring safe operation throughout operating envelope over the life of the engine

• Guaranteed performance is defined as meeting the FAA certification requirements for engine responsiveness – maximum allowed 95% rise time for idle to max thrust command



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Baseline Control Architecture

• Typical aircraft engine control is based on a Min-Max scheme

• Designed to keep the engine operating within prescribed mechanical and operational safety limits


n


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Engine Response with Baseline Control • C-MAPSS40k Full throttle burst at sea-level static

conditions with an end-of-life engine


14 15 16 17 18 19 20

1.1

1.2

1.3

1.4

1.5

EP

R

14 15 16 17 18 19 200

1

2

3

4x 10

4

time [s]

F net [l

bf]

EPR SetpointBaseline

14 15 16 17 18 19 20

0

1

time [s]

Acc

el L

imit

Act

ive

0.9 0.95 1 1.05 1.1 1.15 1.2

x 104

0

500

1000

1500

dNc/

dt [r

pm/s

]

Nc [rpm]

14 15 16 17 18 19 200

10

20

30

40

HP

C S

urge

Mar

gin

time [s]

BaselineLimit

• Acceleration limit regulator is active immediately even though it is far from the limit - Conservative Response


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Is the Conservative Response an issue? • No:

• Not during normal flight as long as it meets the FAA response requirements

• Yes: • On aircraft where primary flight control surfaces are damaged

(e.g. UAL 232, Bagdad DHL, AA 587) • On aircraft with integrated flight/propulsion control

• Can we improve the engine response while maintaining the current architecture?



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The Case for Conditionally Active Limit Regulators

• The baseline Min-Max selection control approach is inherently conservative

• Every limit regulator is capable of limiting fuel flow to engine – regardless of proximity to current limit

• Depending on how the individual PI regulators are tuned, the regulator may intervene when there is no danger of a limit being violated

• To reduce conservatism, limit regulators should become active only when a limit is in “danger” of being violated.



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Conditionally Active Limit Regulators

• For operation with reduced conservatism while still ensuring safety, following two criteria must both be satisfied to enable a limit regulator: 1) The regulated variable must be “close” to the specified limit 2) The rate of change of the regulated variable is such that the

regulated variable will reach the limit within a specified number of control update time steps



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• The conditions for the limit regulator to be active can be stated as:

For a maximum limit variable y1 with limit y1max:

–where α1 and β1 are positive design parameters

• Similar equations can be developed for minimum limit variables


max111 )1( yy ��

max1111 yTydtdy ��


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• Criteria 1 is satisfied at tA

• Criteria 2 is satisfied at tB

• Therefore the limit regulator is enabled at tB


y1

t

(1-α1)y

1max

y1max

A

B

tA

tB

tA+β

1*ΔT

tB+β

1*ΔTt

A'

tB'

Graphical interpretation:


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CA Architecture Modification Uses the existing Min-Max architecture, but each regulator’s output is only considered if the associated criteria are satisfied


sssssssssssssssssssssssssssssssssssssssss


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Choice of CA Design Parameters

• We currently do not have an analytical approach to selecting the CA limit regulator design parameters α and β

• The CA parameters are tuned empirically – - � value selected first to ensure limit is not

violated for operation under worst case conditions

- With a fixed �, the β value is selected to provide fastest possible response without violating limit

• Numerical optimization algorithm has been developed



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• Reduced conservatism resulting in much faster response

Simulation Results• Full throttle burst at sea-level static conditions with an

end-of-life engine


14 15 16 17 18 19 20

1.1

1.2

1.3

1.4

1.5

EP

R

14 15 16 17 18 19 200

1

2

3

4x 10

4

time [s]

F net [l

bf]

CommandBaselineCA Accel

14 15 16 17 18 19 200

1

time [s]

Acc

el L

imit

Act

ive

NominalCA Accel

0.9 0.95 1 1.05 1.1 1.15 1.2

x 104

0

500

1000

1500

dNc/

dt [r

pm/s

]

Nc [rpm]

14 15 16 17 18 19 200

10

20

30

40

HP

C S

urge

Mar

gin

time [s]

BaselineLimitCA Accel


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Simulation Results• Case when a limit (Nc) is reached


14 16 18 20 22 241

1.05

1.1

1.15

1.2

1.25x 10

4

time [s]

Nc

[rpm

]

BaselineNc LimitCA

14 16 18 20 22 240

1

0

1

0

1

time [s]Li

mite

r Sta

tes

BaselineCA

Nc max limiter

EPR Setpoint

Accel limiter

14 16 18 20 22 240.8

1

1.2

EP

R

CommandBaselineCA

14 16 18 20 22 240

0.5

1

1.5

2x 10

4

time [s]

Fne

t [lbf

]


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Conclusions

• The use of properly tuned Conditionally Active limit regulators can improve the engine response without compromising safety

• This approach should simplify the tuning and validation of the limit regulator gains as the regulators are only active in a small number of possible cases

• The CA limit regulator does not require modifications to any other aspect of the well established control architecture



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Future Work

• Formulate the CA limit regulator approach in a proper mathematical framework

• Investigate development of analytical approach to determining the CA design parameters so as to satisfy performance and safety requirements



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References

• May, R.D., Garg, S., "Reducing Conservatism in Aircraft Engine Response Using Conditionally Active Min-Max Limit Regulators," ASME-GT2012-70017, ASME Turbo Expo 2012, Copenhagen, Denmark, June, 2012.

• Nassirharand, A., “Optimization of conditionally active MIN-MAX limit regulators for reducing conservatism in aircraft engines,” Part of 2013 NASA Glenn Faculty Fellowship Program Final Report.



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session 6 dynamic modeling and systems analysis · · 2015-01-13national aeronautics and space...

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