Dynamic Modelling of Gas Turbines

Identification, Simulation, Condition Monitoring and Optimal Control

By: Haydn A. Thompson, Gennady G. Kulikov (Editor)

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Hardcover | 3 June 2004

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342 Pages

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Gas turbines play an important role in power generation and aeroengines. An extended survey of methods associated with the control and systems identification in these engines, Dynamic Modelling of Gas Turbines reviews current methods and presents a number of new perspectives.- Describes a total modelling and identification program for various classes of aeroengine, allowing you to deal with the engine's behaviour over its complete life cycle- Shows how the above regime can be applied to a real engine balancing the theory with practical use- Follows a comparative approach to the study of existing and newly derived techniques thus offering an informed choice of controllers and models from the tied-and trusted to the most up-to-date evolutionary optimisation models- Presents entirely novel work in modelling, optimal control and systems identification to help you get the most from your engine designsDynamic Modelling of Gas Turbines represents the latest research of three groups of internationally recognised experts in gas turbine studies. It will be of interest to academics working in aeroengine control and to industrial practitioners in companies concerned with their design. The work presented here is easily extendible to be relevant in other areas in which gas turbines play a role such as power engineering.

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Paperback

Published: 21st October 2010

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Series Editors' Foreword	p. vii
Preface	p. ix
Introduction	p. xi
Notation	p. xxiii
Introduction to Gas Turbine Engine Control	p. 1
Introduction	p. 1
Calculation of Effective Thrust	p. 2
Military Engine Example	p. 3
Engine Control Programs	p. 5
On-Line Optimization	p. 8
Example of Maximum Distance Calculation at Cruise Flight	p. 9
Power Plant Efficiency	p. 10
Limitations of Current Controllers	p. 11
Design of Optimizing Control	p. 12
Concluding Remarks	p. 13
Gas Turbine Models
Models and the Control System Design Cycle	p. 17
Introduction	p. 17
Mathematical Models and Controller Life Cycle	p. 17
Design Stage Models	p. 19
Experimental Demonstration and Production Stage Models	p. 19
In-Service Use Models	p. 19
Dynamic Modelling Techniques	p. 20
Dynamic Modelling for Control Systems Development	p. 21
Dynamic Characteristic	p. 22
Adaptation of Controller Structure and Parameters at the Design Stage	p. 23
Linear Dynamic Models	p. 24
Real-time Piecewise Linear Dynamic Models	p. 24
Control System Testing	p. 25
Concluding Remarks	p. 26
Off-line Models	p. 27
Introduction	p. 27
Detailed Nonlinear Static Modelling	p. 28
Detailed Nonlinear Dynamic Modelling	p. 30
Relationship Between Static and Dynamic Models	p. 31
Dynamic Characteristic Models	p. 33
Deriving the Dynamic Characteristic Model	p. 33
Graphical Representation	p. 35
Dynamic Characteristic in Reduced Parameters	p. 35
Interpolation Between Operating Points	p. 37
Linear Dynamic Models	p. 39
Obtaining Linear Dynamic Models	p. 40
Estimation of LDM Parameters Using Detailed Static Model	p. 40
Accounting for Additional Gas Flow Dynamics	p. 43
Twin-shaft Turbo Jet Example	p. 44
Concluding Remarks	p. 46
On-line Models	p. 47
Introduction	p. 47
Conflicting Requirements of Simplicity, Speed and Accuracy	p. 47
Stages of Building RPLDM	p. 49
Combination of Static Line and Set of Linear Models	p. 49
LDM at the Nearest Static Point	p. 50
Piecewise Linear Approximation of the Static Line	p. 51
Operating Parameter and Perpendicular to Static Line	p. 53
Piecewise Linear Approximation of LDM Parameters	p. 55
Example of Turbo Jet Modelling	p. 59
Accounting for Atmospheric Conditions of Engine Operation	p. 60
Concluding Remarks	p. 62
Gas Turbine System Identification
Linear System Identification	p. 65
Introduction	p. 65
Linear Models	p. 65
Model Estimation	p. 68
Time-Domain	p. 68
Frequency-Domain	p. 71
Model Order Selection and Validation	p. 76
Comparison of Models and Approaches	p. 78
Experiment Design	p. 79
Input Signals	p. 81
Analysing Periodic Data	p. 85
Concluding Remarks	p. 88
Linear Gas Turbine Modelling	p. 89
Introduction	p. 89
Gas Turbine Testing	p. 89
Test Signal Designs	p. 91
Nonparametric Analysis	p. 91
Synchronisation	p. 91
Drift and Repeatability	p. 92
Noise and Nonlinearities	p. 93
Frequency Response Functions	p. 96
Frequency-Domain Estimation	p. 97
High-Pressure Shaft	p. 100
Low-Pressure Shaft	p. 101
Models at Different Operating Points	p. 104
Low-Frequency Mode	p. 105
Influence of Engine Nonlinearity	p. 105
Time-Domain Estimation	p. 108
High-Pressure Shaft	p. 108
Low-Pressure Shaft	p. 109
Time- Versus Frequency-Domain	p. 112
Comparison with Thermodynamic Models	p. 115
Concluding Remarks	p. 116
Closed-Loop Control and System Identification	p. 117
Introduction	p. 117
Concept of Closed-Loop Identifiability	p. 117
Existing Approaches to Closed-Loop Identifiability	p. 119
Parametric Identifiability	p. 120
Nonparametric Identifiability	p. 121
Common Features of Parametric and Nonparametric Identifiability	p. 122
Summary of Identifiability Concepts	p. 123
Example of Closed-Loop Identifiability Analysis	p. 123
Relationship Between Identifiability and Distribution Function	p. 126
Identifiability Monitoring via Asymmetry and Excess Analysis	p. 127
Identifiability Monitoring via Comparison of a priori Models with Estimates	p. 128
Identifiability and Instrumental Variable Method	p. 128
Concluding Remarks	p. 130
Nonlinear Gas Turbine Modelling	p. 131
Introduction	p. 131
Nonlinear System Representation	p. 131
Functional Representations	p. 132
Block-Structured Systems	p. 133
The Polynomial NARMAX Approach	p. 134
Feedforward Neural Network Models	p. 136
Local Approximations	p. 136
Nonlinear System Identification	p. 137
Nonlinear Gas Turbine Modeling Using NARMAX Structures	p. 139
Parameter Estimation	p. 139
Structure Selection	p. 143
Model Validation	p. 146
A Proposed Identification Scheme	p. 148
Gas Turbine Modelling	p. 149
Nonlinear Gas Turbine Modeling Using Neural Network Models	p. 151
Multilayer Perceptron Neural Networks	p. 151
Gas Turbine Modelling Using Multilayer Perceptron Neural Networks	p. 153
Concluding Remarks	p. 155
New Perspectives in Modelling, Identification, Condition Monitoring and Control
Nonlinear Model Structure Selection Using Evolutionary Optimisation Methods	p. 159
Introduction	p. 159
Genetic Algorithms and Genetic Programming	p. 159
Genetic Algorithms	p. 160
Genetic Algorithm Operators	p. 161
Genetic Programming	p. 162
Genetic Programming Operators	p. 163
Multiobjective Optimisation	p. 165
Pareto-ranking Method	p. 166
Example of Engine Model Structure Selection Using Genetic Programming	p. 167
Description of the Engine System	p. 168
Result Analysis	p. 168
Concluding Remarks	p. 176
System Identification Using Frequency Response Techniques with Optimal Spectral Resolution	p. 177
Introduction	p. 177
Problem Formulation	p. 178
Spectral Estimation	p. 179
Spectral Analysis Calculations	p. 181
Mean Value	p. 181
Correlation Functions	p. 182
Spectral Density	p. 183
Spectral Windowing	p. 183
Frequency Response and Coherence	p. 186
Errors of FRF Estimation by Spectral Methods	p. 186
Spectral Estimation Bias	p. 187
Spectral Estimation Variance	p. 188
Optimal Spectral Resolution	p. 192
Graphical Interpretation	p. 193
Optimum Spectral Resolution And Wavelets	p. 194
Concluding Remarks	p. 195
Turbo Prop Fan Engine Identification: Practical Issues	p. 197
Introduction	p. 197
Turbo Prop Fan Identification	p. 197
Description of Experiment	p. 197
Plant Decomposition	p. 199
Identification of Fuel Metering System	p. 199
Identification of Shaft Speed Dynamics	p. 203
Identification of Compressor Pressure Dynamics	p. 204
Identification of Turbine Temperature Dynamic Model	p. 206
Identification of VSV Actuators in LP And HP Compressors	p. 207
Identification of Step Drives in Prop Fan Controller	p. 211
Identification of Prop Fan Dynamics	p. 212
Closed-Loop Identifiability Analysis	p. 214
Concluding Remarks	p. 215
Stochastic Gas Turbine Engine Models	p. 217
Introduction	p. 217
Disturbances Affecting Control Systems of Aero Engines	p. 217
Applications of Stochastic Modelling in Aero Engine Control	p. 218
Signal Filtering	p. 218
Identification for Control Systems Design and Condition Monitoring	p. 219
Optimal Control of Power Plant	p. 220
Stochastic Simulation in Control Systems Design and Testing	p. 221
Markov Modelling of Dynamic Systems	p. 222
Basic Definitions	p. 222
Markov Chain Representation of Dynamic Systems	p. 223
Basic Descriptive Properties	p. 226
Probability Density Function	p. 226
Mean Value	p. 227
Correlation Function	p. 227
Parameters of Autoregression Model	p. 227
Identification of Markov Chains	p. 228
Fuzzy Markov Chains	p. 229
Concluding Remarks	p. 232
Markov Modelling of Turbo Prop Fan	p. 233
Introduction	p. 233
Experimentation with Turbo Prop Fan	p. 233
Identification of Gas Turbine Dynamics	p. 234
Simulation of Random Environment in HIL Tests of Digital Controllers	p. 238
Markov Simulation Technique	p. 239
Modelling of Inlet Pressure and Temperature with Markov Chains	p. 240
Hardware-in-the-Loop Simulation Using Stochastic Models	p. 241
Markov Modelling in Condition Monitoring of Aero Engines	p. 244
Model-Based Approach to Condition Monitoring	p. 245
Condition Monitoring in Dual-Lane Control	p. 245
Simulation Results	p. 249
Concluding Remarks	p. 249
Optimal Control of Gas Turbine Engines Using Mathematical Programming	p. 251
Introduction	p. 251
Optimization of Engine Performance Through Optimal Control	p. 251
Problem Formulation	p. 253
Algorithm for Real-Time Resolution of a Quadratic Programming Problem	p. 256
Example of Turbo Jet Control, Optimal by Speed	p. 259
Example of Turbo Jet Control, Optimal by Specific Fuel Consumption	p. 261
Concluding Remarks	p. 270
Dynamic Model Identification of a Turbo Jet Engine	p. 271
Introduction	p. 271
Static Modelling Techniques	p. 271
Parametric Dynamic Modelling Techniques	p. 273
Static Model Identification	p. 275
Mean Values	p. 275
"Three-Level" Test	p. 275
Comparison with Previous Series of Tests	p. 277
Notes Regarding Fuel Feed System	p. 278
Dynamic Model Identification	p. 279
Multisine Test	p. 279
Open-Loop Identification with No Test Signal	p. 281
Closed-Loop Identification with No Test Signal	p. 286
Concluding Remarks	p. 292
References	p. 293
Index	p. 305
Table of Contents provided by Publisher. All Rights Reserved.

Dynamic Modelling of Gas Turbines

Identification, Simulation, Condition Monitoring and Optimal Control

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Hardcover

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