Session 6 Dynamic Modeling and Systems Analysis
Transcript of Session 6 Dynamic Modeling and Systems Analysis
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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
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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)
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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
4th Propulsion Control and Diagnostics Workshop Ohio Aerospace Institute (OAI)
Cleveland, OH December 11-12, 2013
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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
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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
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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
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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
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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)
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-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
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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
20
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?
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Thank you
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Toolbox for the Modeling and Analysis of Thermodynamic Systems
(T-MATS)
Jeffryes W. Chapman Vantage Partners, LLC.
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4th Propulsion Control and Diagnostics Workshop Ohio Aerospace Institute (OAI)
Cleveland, OH December 11-12, 2013
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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
NASA Glenn Research Center, Cleveland, OH 44135
• Ten-Huei Guo
NASA Glenn Research Center, Cleveland, OH 44135
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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
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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,
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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
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• T-MATS contains component blocks necessary for creation of turbo-machinery systems
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Blocks: Controls
– Sensors:
– Actuators:
– PI controllers:
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• T-MATS contains component blocks designed for fast control systems creation
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Blocks: Settings
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• 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
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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
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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
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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
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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
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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
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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
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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
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Overview
• Introduction • Baseline Control Architecture • Conditionally Active Limit Regulator Approach • Simulation Examples • Conclusions & Future Work
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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
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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
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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
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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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Conditionally Active Limit Regulators
• 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
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max111 )1( yy ����
max1111 yTydtdy �����
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Conditionally Active Limit Regulators
• Criteria 1 is satisfied at tA
• Criteria 2 is satisfied at tB
• Therefore the limit regulator is enabled at tB
NASA GRC Propulsion Control and Diagnostics Workshop 56
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
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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
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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
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HP
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urge
Mar
gin
time [s]
BaselineLimitCA Accel
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Simulation Results• Case when a limit (Nc) is reached
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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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