True Digital Control

True Digital Control: Statistical Modelling and Non Minimal State Space Designdevelops a true digital control design philosophy that encompasses data based model identification, through to control algorithm design, robustness evaluation and implementation. With a heritage from both classical and modern control system synthesis, this book is supported by detailed practical examples based on the authors research into environmental, mechatronic and robotic systems. Treatment of both statistical modelling and control design under one cover is unusual and highlights the important connections between these disciplines. Starting from the ubiquitous proportional integral controller, and with essential concepts such as pole assignment introduced using straightforward algebra and block diagrams, this book addresses the needs of those students, researchers and engineers, who would like to advance their knowledge of control theory and practice into the state space domain; and academics who are interested to learn more about non minimal state variable feedback control systems. Such non minimal state feedback is utilised as a unifying framework for generalised digital control system design. This approach provides a gentle learning curve, from which potentially difficult topics, such as optimal, stochastic and multivariable control, can be introduced and assimilated in an interesting and straightforward manner. Key features: Covers both system identification and control system design in a unified manner Includes practical design case studies and simulation examples Considers recent research into time variable and state dependent parameter modelling and control, essential elements of adaptive and nonlinear control system design, and the delta operator (the discrete time equivalent of the differential operator) systems Accompanied by a website hosting MATLAB examples True Digital Control: Statistical Modelling and Non Minimal State Space Design is a comprehensive and practical guide for students and professionals who wish to further their knowledge in the areas of modern control and system identification.

True Digital Control: Statistical Modelling andNon-Minimal State Space Designdevelops a true digitalcontrol design philosophy that encompasses data-basedmodel identification, through to control algorithm designrobustness evaluation and implementation. With a heritage from bothclassical and modern control system synthesis, this book issupported by detailed practical examples based on theauthors' research into environmental, mechatronic and roboticsystems. Treatment of both statistical modelling and control designunder one cover is unusual and highlights the important connectionsbetween these disciplines.Starting from the ubiquitous proportional-integralcontroller, and with essential concepts such as pole assignmentintroduced using straightforward algebra and block diagrams, thisbook addresses the needs of those students, researchers andengineers, who would like to advance their knowledge of controltheory and practice into the state space domain; and academics whoare interested to learn more about non-minimal state variablefeedback control systems. Such non-minimal state feedback isutilised as a unifying framework for generalised digital controlsystem design. This approach provides a gentle learning curve, fromwhich potentially difficult topics, such as optimal, stochastic andmultivariable control, can be introduced and assimilated in aninteresting and straightforward manner.Key features:* Covers both system identification and control systemdesign in a unified manner* Includes practical design case studies and simulationexamples* Considers recent research into time-variable andstate-dependent parameter modelling and control, essentialelements of adaptive and nonlinear control system design, and thedelta-operator (the discrete-time equivalent of thedifferential operator) systems* Accompanied by a website hosting MATLAB examplesTrue Digital Control: Statistical Modelling andNon-Minimal State Space Design is a comprehensive andpractical guide for students and professionals who wish to furthertheir knowledge in the areas of modern control and systemidentification.

Preface xiiiList of Acronyms xv1 Introduction 11.1 Control Engineering and Control Theory 21.2 Classical and Modern Control 51.3 The Evolution of the NMSS Model Form 81.4 True Digital Control 111.5 Book Outline 121.6 Concluding Remarks 13References 142 Discrete-Time Transfer Functions 172.1 Discrete-Time TF Models 182.2 Stability and the Unit Circle 242.3 Block Diagram Analysis 262.4 Discrete-Time Control 282.5 Continuous to Discrete-Time TF Model Conversion 362.6 Concluding Remarks 38References 383 Minimal State Variable Feedback 413.1 Controllable Canonical Form 443.2 Observable Canonical Form 503.3 General State Space Form 533.4 Controllability and Observability 583.5 Concluding Remarks 61References 624 Non-Minimal State Variable Feedback 634.1 The NMSS Form 644.2 Controllability of the NMSS Model 684.3 The Unity Gain NMSS Regulator 694.4 Constrained NMSS Control and Transformations 774.5 Worked Example with Model Mismatch 814.6 Concluding Remarks 85References 865 True Digital Control for Univariate Systems 895.1 The NMSS Servomechanism Representation 935.2 Proportional-Integral-Plus Control 985.3 Pole Assignment for PIP Control 1015.4 Optimal Design for PIP Control 1105.5 Case Studies 1165.6 Concluding Remarks 119References 1206 Control Structures and Interpretations 1236.1 Feedback and Forward Path PIP Control Structures 1236.2 Incremental Forms for Practical Implementation 1316.3 The Smith Predictor and its Relationship with PIP Design1376.4 Stochastic Optimal PIP Design 1426.5 Generalised NMSS Design 1536.6 Model Predictive Control 1576.7 Concluding Remarks 163References 1647 True Digital Control for Multivariable Systems 1677.1 The Multivariable NMSS (Servomechanism) Representation1687.2 Multivariable PIP Control 1757.3 Optimal Design for Multivariable PIP Control 1777.4 Multi-Objective Optimisation for PIP Control 1867.5 Proportional-Integral-Plus Decoupling Control by AlgebraicPole Assignment 1927.6 Concluding Remarks 195References 1968 Data-Based Identification and Estimation of Transfer FunctionModels 1998.1 Linear Least Squares, ARX and Finite Impulse Response Models2008.2 General TF Models 2118.3 Optimal RIV Estimation 2188.4 Model Structure Identification and Statistical Diagnosis2318.5 Multivariable Models 2438.6 Continuous-Time Models 2488.7 Identification and Estimation in the Closed-Loop 2538.8 Concluding Remarks 260References 2619 Additional Topics 2659.1 The delta-Operator Model and PIP Control 2669.2 Time Variable Parameter Estimation 2799.3 State-Dependent Parameter Modelling and PIP Control 2909.4 Concluding Remarks 298References 298A Matrices and Matrix Algebra 301References 310B The Time Constant 311Reference 311C Proof of Theorem 4.1 313References 314D Derivative Action Form of the Controller 315E Block Diagram Derivation of PIP Pole Placement Algorithm317F Proof of Theorem 6.1 321Reference 322G The CAPTAIN Toolbox 323References 325H The Theorem of D.A. Pierce (1972) 327References 328Index 329