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Applications of Neural Networks to Control Systems View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Universidade do Algarve APPLICATIONS OF NEURAL NETWORKS TO CONTROL SYSTEMS by António Eduardo de Barros Ruano Thesis submitted to the UNIVERSITY OF WALES for the degree of DOCTOR OF PHILOSOPHY School of Electronic Engineering Science University of Wales, Bangor February, 1992 Statement of Originality The work presented in this thesis was carried out by the candidate. It has not been previously presented for any degree, nor is at present under consideration by any other degree awarding body. Candidate:- Antonio E. B. Ruano Directors of Studies:- Dr. Dewi I. Jones Prof. Peter J. Fleming ACKNOWLEDGMENTS I would like to express my sincere thanks and gratitude to Prof. Peter Fleming and Dr. Dewi Jones for their motivation, guidance and friendship throughout the course of this work. Thanks are due to all the students and staff of the School of Electronic Engineering Science. Special thanks to the Head of Department, Prof. J.J. O’Reilly, for his encouragement; Siân Hope, Tom Crummey, Keith France and David Whitehead for their advice on software; Andrew Grace, for fruitful discussions in optimization; and Fabian Garcia, for his advice in parallel processing. I am also very grateful to Prof. Anibal Duarte from the University of Aveiro, Portugal, whose advice was decisive to my coming to Bangor. I would like to acknowledge the University of Aveiro, University College of North Wales and the ‘Comissão Permanente Invotan’ for their financial support. I am also very grateful to all my friends in Bangor, who made my time here a most enjoyable one. Special thanks and love to my parents, António Delfim and Maria Celeste, for their life-time care and encouragement. To my parents-in-law, for their continuous support. Finally I thank my wife and colleague, Maria da Graça, for her love, patience and support and for the long hours of fruitful discussions; my daughter, Carina Alexandra, for cheering me up at those special moments. À Carina e à Graça ABSTRACT This work investigates the applicability of artificial neural networks to control systems. The following properties of neural networks are identified as of major interest to this field: their ability to implement nonlinear mappings, their massively parallel structure and their capacity to adapt. Exploiting the first feature, a new method is proposed for PID autotuning. Based on integral measures of the open or closed loop step response, multilayer perceptrons (MLPs) are used to supply PID parameter values to a standard PID controller. Before being used on-line, the MLPs are trained off- line, to provide PID parameter values based on integral performance criteria. Off-line simulations, where a plant with time-varying parameters and time varying transfer function is considered, show that well damped responses are obtained. The neural PID autotuner is subsequently implemented in real-time. Extensive experimentation confirms the good results obtained in the off-line simulations. To reduce the training time incurred when using the error back-propagation algorithm, three possibilities are investigated. A comparative study of higher- order methods of optimization identifies the Levenberg-Marquardt (LM) algorithm as the best method. When used for function approximation purposes, the neurons in the output layer of the MLPs have a linear activation function. Exploiting this linearity, the standard training criterion can be replaced by a new, yet equivalent, criterion. Using the LM algorithm to minimize this new criterion, together with an alternative form of Jacobian matrix, a new learning algorithm is obtained. This algorithm is subsequently parallelized. Its main blocks of computation are identified, separately parallelized, and finally connected together. The training time of MLPs is reduced by a factor greater than 70 executing the new learning algorithm on 7 Inmos transputers. Contents Contents 1 - Introduction 1 1.1 - General overview 1 1.2 - Outline of thesis and major achievements 3 2 - Artificial Neural Networks 7 2.1 - Introduction 7 2.2 - Artificial neural networks: a brief tutorial 8 2.2.1 - Biological neural networks 10 2.2.2 - Different types of artificial neural networks 12 2.2.2.1 - Hopfield networks 16 2.2.2.2 - CMAC networks 18 2.2.2.3 - Multilayer perceptrons 20 2.3 - Applications of neural networks to control systems: an overview 24 2.3.1 - Nonlinear identification 25 2.3.1.1 - Forward models 26 2.3.1.2 - Inverse models 28 2.3.2 - Control 31 2.3.2.1 - Model reference adaptive control 31 2.3.2.2 - Predictive control 34 2.4 - Conclusions 36 3 - A Connectionist Approach to PID Autotuning 38 3.1 - Introduction 38 3.2 - The PID controller 39 3.3 - An overview of existing methods of PID autotuning 40 3.3.1 - Methods based on the frequency response 41 3.3.2 - Methods based on the step response 42 3.3.3 - Methods based upon on-line parameter estimation 46 i Contents 3.3.4 - Methods based on expert and fuzzy logic systems 47 3.3.5 - Methods based on artificial neural networks 47 3.4 - A neural PID autotuner 49 3.4.1 - Inputs of the neural networks 49 3.4.2 - Outputs of the neural networks 53 3.4.3 - Training considerations 54 3.4.4 - On-line operation 57 3.5 - Simulation results 58 3.6 - Conclusions 65 4 - Training Multilayer Perceptrons 67 4.1 - Introduction 67 4.2 - Error back-propagation 68 4.2.1 - The error back-propagation algorithm 70 4.2.2 - Limitations of the error back-propagation algorithm 75 4.3 - Alternatives to the error back-propagation algorithm 84 4.3.1 - Quasi-Newton method 87 4.3.2 - Gauss-Newton method 88 4.3.3 - Levenberg-Marquardt method 89 4.4 - A new learning criterion 95 4.4.1 - Golub and Pereyra’s approach 100 4.4.2 - Kaufman’s approach 102 4.4.3 - A new approach 102 4.5 - Conclusions 104 5 - Parallelization of the Learning Algorithm 106 5.1 - Introduction 106 5.2 - Background 107 5.3 - First steps towards parallelization 110 5.4 - Least squares solution of overdetermined systems 111 5.4.1 - Sequential QR algorithms 113 5.4.2 - Parallelization of the selected algorithm 116 ii Contents 5.4.2.1 - Triangularization phase 116 5.4.2.2 - Solution phase 129 5.4.2.3 - Specializing the algorithm 131 5.5 - Recall operation 133 5.6 - Jacobian computation 139 5.7 - Connecting the blocks 142 5.8 - Conclusions 147 6 - Real-Time Implementation 150 6.1 - Introduction 150 6.2 - Preliminary remarks 150 6.3 - Operational modes and input/output devices 152 6.4 - System architecture 153 6.4.1 - The user interface 153 6.4.2 - The controller 154 6.4.3 - The plant 156 6.4.4 - The adaptation 157 6.4.5 - System overview 159 6.5 - Results 159 6.6 - Conclusions 165 7 - Conclusions 167 7.1 - General conclusions 167 7.2 - Future Work 170 References Derivation of the Identification Measures A-1 A.1 - Background A-1 A.2 - Open loop A-3 A.3 - Closed loop A-4 The Reformulated Criterion: Theoretical Proofs B-1 iii Contents B.1 - Background B-1 B.2 - Gradient proof B-2 B.3 - Jacobian proof B-3 iv Chapter 1 Introduction Chapter 1 Introduction 1.1 General overview In recent years there has been an increasing interest in the development and application of artificial neural networks technology. Neural network research has spread through almost every field of science, several journals [1][2][3] and major conferences [4][5] now being entirely devoted to this subject. Control systems form one area where artificial neural networks have found ready application. In every major conference in the field of control systems, sessions are now devoted to artificial neural networks applications. Special issues [6][7][8] of important publications on control systems have been dedicated to this new subject. The objectives of the work described in this thesis are to investigate the potential applications of neural networks to control systems, to identify suitable applications where neural network solutions are superior to conventional techniques, and to further develop the relevant approaches, with a view to practical implementation. When this PhD. programme started, in October 1988, applications of neural networks in control systems were in a embryonic state. From a literature survey conducted at that time [9], two important properties of artificial neural networks were identified as being of great potential interest to the area of control systems: their capacity to approximate nonlinear mappings, and their ability to learn and adapt. These properties could then be exploited for nonlinear systems identification, adaptive control of nonlinear systems and PID autotuning, among other areas. Clearly, this preliminary analysis was found to be correct, as confirmed by the number of publications, appeared during these last three years, where applications of neural networks on nonlinear systems identification and adaptive control of nonlinear systems have been proposed. Because of the practical importance of the problem, the ability of artificial neural networks to arbitrarily approximate nonlinear mappings is applied, in this thesis, to PID autotuning. Despite all the advances made in control theory, the majority of the regulators in industry are of the PID type. Large industrial plants may contain hundreds of these simple regulators. Manual tuning is an operation that, to be accurately performed, takes a considerable amount of time. Whether because of plant changes or because of component 1 Chapter 1 Introduction ageing, retuning needs to be performed regularly. Methods that can provide automatic tuning of PID controllers are, therefore, of a great practical importance. Several different methods have been proposed for tuning PID regulators, starting from the work of Ziegler-Nichols [10].
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