presentation topic 3: simulation as part of control design ... · – operational and actuator...

Copyright 1998 DLMattern

PresentationPresentation

Topic 3: Simulation Topic 3: Simulation

as part of Control Design & Evaluationas part of Control Design & Evaluation


OutlineOutline

Simulation TerminologyPurpose of SimulationRevisit The Control Design ProcessSimulations Required for Control DesignModel Based RoutinesSoftware ToolsSummary


Simulation TerminologySimulation Terminology

Cycle Deck - Steady Flow Path Model of Engine CycleComponent Level Model (CLM)– Physical based model built from individual components

Piecewise Linear Model - scheduled linear modelsContinuous - requires numerical integrationDiscrete - integration implicit. Already transformed.Non-realtime - simulation time unrelated to “time”Realtime - simulation time a linear function of “time”– frame-time: simulation update period.


Purpose of SimulationPurpose of Simulation

Save Time and Money– Numerical Trial and Error Before Cutting Metal– Provide Platform for Spreadsheet type “what-if” analyzes– Control System Design and Validation

Verify Understanding of the Physics– Validate Model Against Observations

Starting Point for Model Based Approaches– An onboard model can be used for Controls, Diagnostics,

Engine & Fleet Maintenance


Revisit The Control Design ProcessRevisit The Control Design Process

Model Creation & Validation– Simplified cycle deck plus dynamics

Linearization– Generation of Design Point Linear Models

Linear Control Design at design pointsIncorporation of Nonlinearities:– Operational and actuator limits, scheduling, mode

logic, limit and integrator windup protection

Realtime Simulation: check timingRealtime I/O Checkout: hard & software

Modeling

Linearization

Control Design

Nonlinear Design

Timing

I/O Checkout

15%

45%

15%

15%

10%

given

percent time estimates assume you start with a validated dynamic model and experienced engineers working on all tasks


Simulations Required for Control DesignSimulations Required for Control Design

Cycle Deck Model for Schedule GenerationDynamic Nonlinear Model for Linear Model Creation and for the Design and Evaluation of Nonlinear Portions of the Control DesignDynamic Linear Models for Linear Control DesignReal-Time Dynamic Model (covered in another topic)– for Timing Evaluation– with Inputs and Outputs for Hardware-in-the-loop testing

» “wet bench” (hydraulic) testing of actuators.


Cycle Deck Model for Steady State Cycle Deck Model for Steady State PerformancePerformance

Once performance is obtained, the cycle deck can be used to define the engine steady state operating schedule.Historically these models have been written in FORTRAN because the tools used by component groups and performance people have typically been written in FORTRAN.– The main advantage that FORTRAN has over C for these types of

computations is multidimensional arrays and efficient compilers for vector, parallel, and multi-processing.


Cycle Deck Flow Path for a Turbofan EngineCycle Deck Flow Path for a Turbofan Engine

from Society of Automotive Engineering, SAE Aerospace Recommended Practice: ARP-1257A & ARP 755Assumptions: All flows are balanced, no volume dynamics.

Inle

t

Fan

Com

pres

sor M

ap

HP

C M

ap

Com

bust

or

LPT

Exh

aust

Duc

tFa

n D

uct

Mix

ing

Sec

tion

Afte

r bur

ner

Noz

zle

XM

Pamb

Tamb

W1

P1

T1

Inle

t Duc

t W2A

P2

T2

W25

P25

T25

W25

P25

T25

W3

P3

T3

W4

P4

T4 HP

T

W45

P45

T45

W5

P5

T5

W6

P6

T6

W16

P16

T16

W6

P6

T6

W7

P7

T7

F

W8

P8

T8

steady state control schedulefan-cvg cvg wf-fuel A8-area


Dynamic Nonlinear ModelDynamic Nonlinear Model

Rotor Dynamics added to Cycle Deck– Time Derivative of Steady State Energy Balance

» d/dt{ Kinetic Energy } = d/dt { Net Energy Into System }

» d/dt { 1/2 J ω2 } = Shaft Power in - Shaft Power out

» ωdot * J ω = (Turbine Power - Compressor Power)» ωdot = (Net Shaft Power)/(Jω) (Note: no one is currently measuring net

shaft torque online and using this measurement for control or diagnostics )

Temperature Heat Soaks - first order mass capacitance– Metal temperatures and how they affect clearances

Pressure Dynamics: (for high bandwidth model)– Engine Pressure Ratio (EPR), fan bypass duct pressure ratio


Dynamic Nonlinear ModelsDynamic Nonlinear Models

To validate your model with test data, you will need an appropriate set of sensors and actuators.

SensorRotor Speeds: N1, N2Pressures: Pamb, PT2,

P25, PS3, PS16, PS56Temperatures: Tamb, T2,

T25, T3, T4, T56

ActuatorsFuel Flow: WF36, W6Nozzle Area, A8Inlet Guide Vanes, IGVCore Variable Stator Vanes, VSVHPC Bleed Flow, WB3Variable Area Bypass Injector, VABI(door to bypass duct)

EstimatesEPR: P6/PT2OPR: PS3/PT2DP/P: (P21-PS14)/P14Gross Thrust: FG9Mass flows, w2, w12, w21, w6

Fan IGV

PambTamb

VABI-A14 VABI-A16

A8 A9

WF6- Afterburner

PS14P25T25

T4 PS16 PS56T56

PS3T3

PT2T2 N1 N2

WF36

VSVWB 3

MIXING

PLANE


Dynamic Linear ModelsDynamic Linear Models

Once the Dynamic Nonlinear Model has been validated and frozen, you can generate linear models.– Linearization tools using perturbation are magnitude dependent

and may require trial end error to obtain an appropriate “delta”.– MATLAB [A,B,C,D] = LINMOD( 'SYS', X, U, PARAM, XPERT, UPERT )

» set the perturbation levels for all of the elements of X and U» NOTE: LINMOD only does positive perturbations.

Better method does positive and negative and averages the two.

Only important if operating point is highly nonlinear.

» Many of the Simulink Blocks don’t linearize properly.Example: Continuous Time Delay.

– ISI’s SystemBuild actually provides a PADE’ approximation duringlinearization of their continuous time delay.


Dynamic Linear ModelsDynamic Linear Models

Linearization: A family of linear models– Determine domain (size) of linear model. (avoid limits)– Determine uncertainty in linear model.

» Customer bleed can cause an unknown disturbance

– Prepare Structure for Schedule if used.

Mach No.

alt

0

∆WF

∆A8

Temp.

linear models are symmetric about each axis (+/-)

models requiredover the flight envelope, altitude, temperature. Mach number, power (PLA).


Dynamic Linear Models: ReferencesDynamic Linear Models: References

Linearization, see– Sugiyama N., “Derivation of ABCD System Matrices from

Nonlinear Dynamic Simulation of Jet Engine”, National Aerospace Lab, Tokyo, Japan, AIAA 92-3319, 28th Joint Propulsion Conf., 1992.

Schedule of Linear Controller Gains– Use a neural network to provide the scheduling of the gains.

» Lin Shih-Tin, Lee Chun-Mo, “Multivariable Control of the J-85 Turbojet Engine for Full Flight Envelope Operation”, AIAA Journal of Guidance, Control, & Dynamics, Vol 19, #4, July-Aug. 1996, p 913

Shih-Tin - National Chung-Hsing University, Taichung, Taiwan

Chun-Mo Lee - China Motor Corporation, Taiwan.


Dynamic Linear Models: Design ModelDynamic Linear Models: Design Model

Linear Design Plant Model– Scaled plant, actuators, sensors, weights– Weighted inputs, sensitivity, complementary sensitivity

ScaledLinear Plant

u yucmd ActuatorModels

SensorModels

MeasurementNoise

Exogenouscommands

Wc(s)

WT(s)

WS(s)

Z

Y

U

W

NoiseFilter

CmdFilter e

FrequencyWeights

Mixed Sensitivity, H-inf Model StructureMay not need all this complexity for simple systems

u y

zw

K

G


Dynamic Linear Models: ScalingDynamic Linear Models: Scaling

Scaling for a linear design, relative to operating point– Consider operational and actuator limit– Goal is a symmetric linear design– Don’t typically use the nominal operating point value to scale.

» Use size of operating range

∆N1

∆EPR

G(s)

FromLinearization

Process

Wf

A8

N1

EPRSu1

Su2

Sy1

Sy2

Wfs

A8s

N1s

EPRs


Other Applications for these ModelsOther Applications for these Models

You spent all the time and effort developing these models. What else can you use them for.– Object Oriented Programming: reuse of the functions:

compressor and turbine maps, combustor model, dynamic equations.

– Model Based Control Design– Model Based Diagnostics & Maintenance

» Everything is compared against a fleet baseline modelComparison can be used for component life estimates.


Object Oriented Approach to ModelingObject Oriented Approach to Modeling

Engine Components are true “Objects”.Coded properly, you have a family of reusable objects

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Pamb

Tamb

W1

P1

T1

Inle

t Duc

t W2A

P2

T2

W25

P25

T25

W25

P25

T25

W3

P3

T3

W4

P4

T4 HP

T

W45

P45

T45

W5

P5

T5

W6

P6

T6

W16

P16

T16

W6

P6

T6

W7

P7

T7

F

W8

P8

T8

steady state control schedulefan-cvg cvg wf-fuel A8-area


Model Based ControlModel Based Control

Error between engine and model used in controller– Internal Model Control (IMC), Robust Process Control, Morari,

M., Zafiriouu E., 1989– Alternative approach to handle limits– Technique to measure model uncertainty, “online”

Engine

Model

Controller-

+

Cmds

Auxilliary Model outputs could also be use as analytical redundant sensors and measurements in dual redundancy sensor fault detection voting schemes.

estimates: -fuel flow- stall margin- thrustOnline model could also be used

in steady state optimization. Performance Seeking Control, NASA Dryden


Model Based Diagnostics & MaintenanceModel Based Diagnostics & Maintenance

Baseline model for comparison– error classifier can be used for various applications.

» fault detection and identification. Component life estimate» “onrequest” maintenance instead of periodic maintenance

Baseline is never modified. Basis of comparison.

Engine

Model

Controller-

+Error

Classifier

Cmds

Neural Network Error Classifier- fault detection- component life estimates


Software ToolsSoftware Tools

Object Oriented Tools for the Control Design Process:– The MathWorks: Matlab, Simulink, Realtime Workshop– Integrated Systems, Inc.: Xmath, SystemBuild, AC100– Visual Solutions: Vissim– others lesser packages, Maple, Mathmatica, …etc.

Rapid Prototyping tools help to tie together the nonreal-time and the real-time development.– ISI’s AC100– MathWorks RealTime Workshop

» 3rd party hardware


Software ToolsSoftware Tools

NOTE: ISI’s SystemBuild is a superior simulation environment compared to the MathWorks Simulink. However, while ISI’s Xmath is powerful, has a steep learning curve. It is not the same as MatrixX.– Xmath uses Parameter-Dependent-Matrices (PDM) in ALL

functions. This requires a reformulation of the way you think about systems. (3D matrices)

SystemBuild has a one step process from continuous to discrete and back. Simulink has no such path, but theMathWorks RealTime Workshop will run continuous systems.


SummarySummary

Simulation can save you time and moneyThere are a number of different design models:– Cycle Deck, Nonlinear Dynamic Model, Linear Dynamic Model

from Linearization, and Real-Time Models (to be discussed next)

Models must be validated.– Critical to understanding the system physics– Useful in Model Based Techniques, controls & diagnostics

Software tools available for Simulation– Icon based programming environments so you don’t have to

develop your own tools and can concentrate on your application.

presentation topic 3: simulation as part of control design ... · – operational and actuator...

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