Modelling and Parameter Estimation of Dynamic Systems (IEE Control Engineering)

Parameter estimation is the process of using observations from a system to develop mathematical models that adequately represent the system dynamics. The assumed model consists of a finite set of parameters, the values of which are calculated using estimation techniques. Most of the techniques that exist are based on least-square minimization of error between the model response and actual system response. However, with the proliferation of high speed digital computers, elegant and innovative techniques like filter error method, H-infinity and Artificial Neural Networks are finding more and more use in parameter estimation problems. Modelling and Systems Parameter Estimation for Dynamic Systems presents a detailed examination of the estimation techniques and modeling problems. The theory is furnished with several illustrations and computer programs to promote better understanding of system modeling and parameter estimation. The material is presented in a way that makes for easy reading and enables the user to implement and execute the programs himself to gain first hand experience of the estimation process.Also available:Genetic Algorithms in Engineering Systems - ISBN 0852969023Deterministric Control of Uncertain Systems - ISBN 0863411703The Institution of Engineering and Technology is one of the world's leading professional societies for the engineering and technology community. The IET publishes more than 100 new titles every year; a rich mix of books, journals and magazines with a back catalogue of more than 350 books in 18 different subject areas including: -Power & Energy -Renewable Energy -Radar, Sonar & Navigation -Electromagnetics -Electrical Measurement -History of Technology -Technology Management Contents 8 Preface 14 Acknowledgements 16 1 Introduction 18 1.1 A brief summary 24 1.2 References 27 2 Least squares methods 30 2.1 Introduction 30 2.2 Principle of least squares 31 2.2.1 Properties of the least squares estimates 32 2.3 Generalised least squares 36 2.3.1 A probabilistic version of the LS 36 2.4 Nonlinear least squares 37 2.5 Equation error method 40 2.6 Gaussian least squares differential correction method 44 2.7 Epilogue 50 2.8 References 52 2.9 Exercises 52 3 Output error method 54 3.1 Introduction 54 3.2 Principle of maximum likelihood 55 3.3 Cramer-Rao lower bound 56 3.3.1 The maximum likelihood estimate is efficient 59 3.4 Maximum likelihood estimation for dynamic system 59 3.4.1 Derivation of the likelihood function 60 3.5 Accuracy aspects 62 3.6 Output error method 64 3.7 Features and numerical aspects 66 3.8 Epilogue 79 3.9 References 79 3.10 Exercises 80 4 Filtering methods 82 4.1 Introduction 82 4.2 Kalman filtering 83 4.2.1 Covariance matrix 84 4.2.2 Discrete-time filtering algorithm 85 4.2.3 Continuous-time Kalman filter 88 4.2.4 Interpretation and features of the Kalman filter 88 4.3 Kalman UD factorisation filtering algorithm 90 4.4 Extended Kalman filtering 94 4.5 Adaptive methods for process noise 101 4.5.1 Heuristic method 103 4.5.2 Optimal state estimate based method 104 4.5.3 Fuzzy logic based method 105 4.6 Sensor data fusion based on filtering algorithms 109 4.6.1 Kalman filter based fusion algorithm 110 4.6.2 Data sharing fusion algorithm 111 4.6.3 Square-root information sensor fusion 112 4.7 Epilogue 115 4.8 References 117 4.9 Exercise 119 5 Filter error method 122 5.1 Introduction 122 5.2 Process noise algorithms for linear systems 123 5.3 Process noise algorithms for nonlinear systems 128 5.3.1 Steady state filter 129 5.3.2 Time varying filter 131 5.4 Epilogue 138 5.5 References 138 5.6 Exercises 139 6 Determination of model order and structure 140 6.1 Introduction 140 6.2 Time-series models 140 6.2.1 Time-series model identification 144 6.2.2 Human-operator modelling 145 6.3 Model (order) selection criteria 147 6.3.1 Fit error criteria (FEC) 147 6.3.2 Criteria based on fit error and number of model parameters 149 6.3.3 Tests based on whiteness of residuals 151 6.3.4 F-ratio statistics 151 6.3.5 Tests based on process/parameter information 152 6.3.6 Bayesian approach 153 6.3.7 Complexity (COMP) 153 6.3.8 Pole-zero cancellation 154 6.4 Model selection procedures 154 6.5 Epilogue 161 6.6 References 162 6.7 Exercises 163 7 Estimation before modelling approach 166 7.1 Introduction 166 7.2 Two-step procedure 166 7.2.1 Extended Kalman filter/fixed interval smoother 167 7.2.2 Regression for parameter estimation 170 7.2.3 Model parameter selection procedure 170 7.3 Computation of dimensional force and moment using the Gauss-Markov process 178 7.4 Epilogue 180 7.5 References 180 7.6 Exercises 181 8 Approach based on the concept of model error 182 8.1 Introduction 182 8.2 Model error philosophy 183 8.2.1 Pontryagin’s conditions 184 8.3 Invariant embedding 186 8.4 Continuous-time algorithm 188 8.5 Discrete-time algorithm 190 8.6 Model fitting to the discrepancy or model error 192 8.7 Features of the model error algorithms 198 8.8 Epilogue 199 8.9 References 199 8.10 Exercises 200 9 Parameter estimation approaches for unstable/augmented systems 202 9.1 Introduction 202 9.2 Problems of unstable/closed loop identification 204 9.3 Extended UD factorisation based Kalman filter for unstable systems 206 9.4 Eigenvalue transformation method for unstable systems 208 9.5 Methods for detection of data collinearity 212 9.6 Methods for parameter estimation of unstable/augmented systems 216 9.6.1 Feedback-in-model method 216 9.6.2 Mixed estimation method 217 9.6.3 Recursive mixed estimation method 221 9.7 Stabilised output error methods (SOEMs) 224 9.7.1 Asymptotic theory of SOEM 226 9.8 Total least squares method and its generalisation 233 9.9 Controller information based methods 234 9.9.1 Equivalent parameter estimation/retrieval approach 235 9.9.2 Controller augmented modelling approach 235 9.9.3 Covariance analysis of system operating under feedback 236 9.9.4 Two-step bootstrap method 239 9.10 Filter error method for unstable/augmented aircraft 241 9.11 Parameter estimation methods for determining drag polars of an unstable/augmented aircraft 242 9.11.1 Model based approach for determination of drag polar 243 9.11.2 Non-model based approach for drag polar determination 244 9.11.3 Extended forgetting factor recursive least squares method 245 9.12 Epilogue 246 9.13 References 247 9.14 Exercises 248 10 Parameter estimation using artificial neural networks and genetic algorithms 250 10.1 Introduction 250 10.2 Feed forward neural networks 252 10.2.1 Back propagation algorithm for training 253 10.2.2 Back propagation recursive least squares filtering algorithms 254 10.3 Parameter estimation using feed forward neural network 256 10.4 Recurrent neural networks 266 10.4.1 Variants of recurrent neural networks 267 10.4.2 Parameter estimation with Hopfield neural networks 270 10.4.3 Relationship between various parameter estimation schemes 280 10.5 Genetic algorithms 283 10.5.1 Operations in a typical genetic algorithm 284 10.5.2 Simple genetic algorithm illustration 285 10.5.3 Parameter estimation using genetic algorithms 289 10.6 Epilogue 294 10.7 References 296 10.8 Exercises 297 11 Real-time parameter estimation 300 11.1 Introduction 300 11.2 UD filter 301 11.3 Recursive information processing scheme 301 11.4 Frequency domain technique 303 11.4.1 Technique based on the Fourier transform 304 11.4.2 Recursive Fourier transform 308 11.5 Implementation aspects of real-time estimation algorithms 310 11.6 Need for real-time parameter estimation for atmospheric vehicles 311 11.7 Epilogue 312 11.8 References 313 11.9 Exercises 313 Bibliography 316 Appendix A: Properties of signals, matrices, estimators and estimates 318 Appendix B: Aircraft models for parameter estimation 342 Appendix C: Solutions to exercises 370 Index 398

parameter Estimation Is The Process Of Using Observations From A System To Develop Mathematical Models That Adequately Represent The System Dynamics. The Assumed Model Consists Of A Finite Set Of Parameters, The Values Of Which Are Calculated Using Estimation Techniques. Most Of The Techniques That Exist Are Based On Least-square Minimization Of Error Between The Model Response And Actual System Response. However, With The Proliferation Of High Speed Digital Computers, Elegant And Innovative Techniques Like Filter Error Method, H-infinity And Artificial Neural Networks Are Finding More And More Use In Parameter Estimation Problems. Modelling And Systems Parameter Estimation For Dynamic Systems Presents A Detailed Examination Of The Estimation Techniques And Modeling Problems. The Theory Is Furnished With Several Illustrations And Computer Programs To Promote Better Understanding Of System Modeling And Parameter Estimation. The Material Is Presented In A Way That Makes For Easy Reading And Enables The User To Implement And Execute The Programs Himself To Gain First Hand Experience Of The Estimation Process.

"Parameter estimation is the process of using observations from a system to develop mathematical models that adequately represent the system dynamics. The assumed model consists of a finite set of parameters, the values of which are calculated using estimation techniques. Most of the techniques that exist are based on least-square minimisation of error between the model response and actual system response. However, with the proliferation of high-speed digital computers, elegant and innovative techniques like filter error method, genetic algorithms and artificial neural networks are finding more and more use in parameter estimation problems. Modelling and Parameter Estimation of Dynamic Systems presents a detailed examination of many estimation techniques and modelling problems."--BOOK JACKET This book comprises ten invited expert contributions on the theory and applications of genetic algorithms in a variety of engineering systems. In addition to addressing the simple formulation of GAs, the chapters include original material on the design of evolutionary algorithms for particular engineering applications. Includes sections on: Sliding mode control with switching command devices. Hyperplane design and CAD of variable structure control systems. Variable structure controllers for robots. The hyperstability approach to VSCS design. Nonlinear continuous feedback for robust tracking. Control of infinite dimensional plants. This volume covers both the historical and current state of variable structure control, with theory illustrated by practical examples. Among the topics examined are switching command devices, hyperplane design and CAD of variable structure control systems, subspace attractivity and invariance A broad survey of the current trends and techniques in genetic algorithms (GAs), which are general purpose search and optimisation methods applicable to a wide variety of problems. Theoretical innovations and practical applications in engineering systems are then discussed in the text.