Digital Control of Dynamic Systems

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1 Second Edition Digital Control of Dynamic Systems Gene F. Franklin Stanford University J. David Powell Stanford University Michael L. Workman IBM Corporation TT ADDISON-WESLEY PUBLISHING COMPANY Reading, Massachusetts Menlo Park, California New York Don Mills, Ontario Wokingham, England Amsterdam Bonn Sydney Singapore Tokyo Madrid San Juan

2 Contents CHAPTER1 Introduction Problem Definition Example Systems for Study Overviewof Design Approach Computer-Aided Design Summary Suggestions for Further Reading 10 Problems and Exercises 11 CHAPTER2 Linear, Discrete, Dynamic-Systems Analysis: The 2-Transform Introduction Linear Difference Equations The Discrete Transfer Function The2-Transform The Transfer Function Block Diagrams and State-Variable Descriptions Relation of Transfer Function to Pulse Response External Stability and Jury's Test Discrete Models of Sampled-Data Systems Using the 2-Transform Continuous Time Delay State-Space Form State-Space Models for Systems with Delay Numerical Considerations in Computing <I> and F 61

3 xvi CONTENTS 2.5 Signal Analysis and Dynamic Response The Unit Pulse The Unit Step Exponential General Sinusoid Correspondence with Continuous Signals Step Response Frequency Response Properties of the z-transform z-transform Properties Another Derivation of the Transfer Function Summary 95 Problems and Exercises 95 CHAPTER 3 Sampled-Data Systems Introduction Analysis ofthe Sample and Hold Spectrum ofa Sampled Signal and Aliasing Data Extrapolation and Impostors Block-Diagram Analysis Summary 130 Problems and Exercises 130 CHAPTER4 Discrete Equivalents to Continuous Transfer Functions: The Digital Filter Introduction Design of Discrete Equivalents by Numericai Integration Zero-Pole Mapping Equivalents Hold Equivalents Zero-Order Hold Equivalent Triangle Hold Equivalent Summary 155 Problems and Exercises 156 CHAPTER 5 Design of Digital Control Systems Using Transform Techniques Introduction Control System Specifications Design Using Emulation 174

4 CONTENTS xvii Plane Design Using Root Locus Frequency-Response Methods with the ^-Transform Cain and Phase Plotting Nyquist Stability Low-Frequency Gains and Error Coefficients Compensator Design Frequency-Response Methods with the ü'-transform Direct Design Methodof Ragazzini PID Control Proportional Control Derivative Control Integral Control PID Control Ziegler-Nichols PID Tuning Summary 229 Problems and Exercises 230 CHAPTER 6 Design of Digital Control Systems Using State-Space Methods Introduction Control-Law Design Pole Placement Controllability Ackermann's Formula Estimator Design Prediction Estimators Observability Ackermann's Formula Current Estimators Reduced-Order Estimators Regulator Design: Combined Control Law and Estimator The Separation Principle Guidelines for Pole Placement Introduction of the Reference Input Reference Inputs for Full-State Feedback Reference Inputs with Estimators: The State-Command Structure Effect of Reference Input on System Zeros Output Error Command A Comparison of the Estimator Structure and Classical Methods Integral Contro! Integral Control by State Augmentation Bias Estimation 292

5 xvüi CONTENTS 6.7 Pole Placement using Polynomials Integral Control Controllability and Observability Summary 308 Appendix to Cbapter Problems and Exercises 315 CHAPTER7 Quantization Effects 7.1 Introduction Analysis of Round-Off Error Effects of Roundoff of Parameters Limit Cycles and Dither Summary 345 Problems and Exercises 345 CHAPTER 8 System Identification 8.1 Introduction and Problem Definition Identification of Nonparametric Models Models for Parametric Identification Least Squares Recursive Least Squares Stochastic Least Squares Maximum Likelihood Numerical Searcb for the Maximum-Likelihood Estimate 8.9 Summary 413 Problems and Exercises 413 CHAPTER 9 Multivariable and Optimal Control 9.1 Introduction Decoupiing Time-Varying Optimal Control LQR Steady-State Optimal Control Reciprocal Root Properties Symmetrie Rool Locus Eigenvector Decomposition Cost Equivalents Emulation by Equivalent Cost 441

6 CONTENTS 9.5 Optimal Estimation The Kaiman Filter Steady-State Optimal Estimation ;? Noise Matrices and Discrete Equivalents Multivariable Control Design SelectionofWeighting Matrices Q, and Q, Pincer Procedure Paper-Machine Design Example Magnetic-Tape-Drive Design Example Summary 480 Problems and Exercises 480 CHAPTER10 Sample Rate Selection Introduction The Sampling Theorem's Limit Time Response and Smoothness Error.s Due to Random Plant Di.sturbances Sensitivity to Parameter Variations Mea.surement Noise and Antialiasing Filters Multirate Sampling Summary 511 Problems and Exercises 513 CHAPTER 11 Nonlinear Control Introduction Analysis Techniques Simulation Linearization Describing Functions Equivalent Gains Circle Criterion Lyapunov Functions Nonlinear Control Structures: Design Large-Signai Linearization: Inverse Nonlinearities Time-Optimal Servomechanisms Extended PTOS for Flexible Structures Introduction to Adaptive Control Controller versus Regulator Adaptive Nonlinear Control Design with Nonlinear Cost Functions Random Neighborhood Search 625

7 CONTENTS 11.5 Summary 633 Problems and Exercises 635 CHAPTER12 Application and Practice of Digital Control 12.1 Introduction Digital Control System Hardware Processors Support Hardware Error Detection and Correction Hardware D/As, A/D's, and Sample and Hold's Saturating Components Sensors Software or Firmware Development More than Control Equations Microcode Versions Reprogramming versus Changing Hardware Processor Microcode Development Tools Error Detection and Correction Microcode Control Wind-Up Fixed-and Floating-Point Arithmetic Fixed-Point Arithmetic Scaling Floating-Point Arithmetic Scaling System Integration Hardware Simulators Frequency Response and Modal Analysis Manufacturing Digital Control Systems Communication Interface Robust Design Design Specifications Self-Test Adjustments Program Structure Minimizing Control Delay Sample Rate Selection Revisited Case Design: Disk-Drive Servo Disk Drives Goals and Objectives Design Implementation Summary Problems and Exercises 747 Appendix A to Chapter Appendix B to Chapter

8 CONTENTS APPENDIX A Examples 777 A.l Single-Axis Satellite Attitüde Control 777 A.2 A Servomechanism für Antenna Azimuth Control 779 A.3 Temperature Control of Fluid in a Tank 783 A.4 Control through a Flexible Structure 785 A.5 Control ofa Pressurized Flow Box 788 APPENDIX B Tables 790 B.l Properties of^-tfansforms 791 B.2 Table o^-transforms 792 ß.3 w-plane Transfer Functions 794 APPENDIX C A Few Results from Matrix Analvsis 796 C.l Determinants and the Matrix Inverse 796 C.2 Eigenvalues and Etgenvectors 798 C.3 Similarity Transformations 800 C.4 The Caley-Hamilton Theorem 803 APPENDIX D Summary of Facts from the Theory of Probability and Stochastic Processes 805 D.l Random Variables 805 D.2 Expectation 807 D.3 More than One Random Variable 810 D.4 Stochastic Processes 812 APPENDIXE CAD Routines 817 References 819 Index 833

System analysis and signal processing

System analysis and signal processing with emphasis on the use of MATLAB PHILIP DENBIGH University of Sussex ADDISON-WESLEY Harlow, England Reading, Massachusetts Menlow Park, California New York Don Mills,