Feedback Control Systems

1 INTRODUCTION 1.1 The Control Problem 1.2 Examples of Control Systems 1.3 Short History of Control References 2 MODELS OF PHYSICAL SYSTEMS 2.1 System Modeling 2.2 Electrical Circuits 2.3 Block Diagrams and Signal Flow Graphs 2.4 Masonis Gain Formula 2.5 Mechanical Translational Systems 2.6 Mechanical Rotational Systems 2.7 Electromechanical Systems 2.8 Sensors 2.9 Temperature-control System 2.10 Analogous Systems 2.11 Transformers and Gears 2.12 Robotic Control System 2.13 System Identification 2.14 Linearization 2.15 Summary References Problems 3 STATE-VARIABLE MODELS 3.1 State-Variable Modeling 3.2 Simulation Diagrams 3.3 Solution of State Equations 3.4 Transfer Functions 3.5 Similarity Transformations 3.6 Digital Simulation 3.7 Controls Software 3.8 Analog Simulation 3.9 Summary References Problems 4 SYSTEM RESPONSES 4.1 Time Response of First-Order Systems 4.2 Time Response of Second-order Systems 4.3 Time Response Specifications in Design 4.4 Frequency Response of Systems 4.5 Time and Frequency Scaling 4.6 Response of Higher-order Systems 4.7 Reduced-order Models 4.8 Summary References Problems 5 CONTROL SYSTEM CHARACTERISTICS 5.1 Closed-loop Control System 5.2 Stability 5.3 Sensitivity 5.4 Disturbance Rejection 5.5 Steady-state Accuracy 5.6 Transient Response 5.7 Closed-loop Frequency Response 5.8 Summary References Problems 6 STABILITY ANALYSIS 6.1 Routh-Hurwitz Stability Criterion 6.2 Roots of the Characteristic Equation 6.3 Stability by Simulation 6.4 Summary Problems 7 ROOT-LOCUS ANALYSIS AND DESIGN 7.1 Root-Locus Principles 7.2 Some Root-Locus Techniques 7.3 Additional Root-Locus Techniques 7.4 Additional Properties of the Root Locus 7.5 Other Configurations 7.6 Root-Locus Design 7.7 Phase-lead Design 7.8 Analytical Phase-Lead Design 7.9 Phase-Lag Design 7.10 PID Design 7.11 Analytical PID Design 7.12 Complementary Root Locus 7.13 Compensator Realization 7.14 Summary References Problems 8 FREQUENCY-RESPONSE ANALYSIS 8.1 Frequency Responses 8.2 Bode Diagrams 8.3 Additional Terms 8.4 Nyquist Criterion 8.5 Application of the Nyquist Criterion 8.6 Relative Stability and the Bode Diagram 8.7 Closed-Loop Frequency Response 8.8 Summary References Problems 9 FREQUENCY-RESPONSE DESIGN 9.1 Control System Specifications 9.2 Compensation 9.3 Gain Compensation 9.4 Phase-Lag Compensation 9.5 Phase-Lead Compensation 9.6 Analytical Design 9.7 Lag-Lead Compensation 9.8 PID Controller Design 9.9 Analytical PID Controller Design 9.10 PID Controller Implementation 9.11 Frequency-Response Software 9.12 Summary References Problems 10 MODERN CONTROL DESIGN 10.1 Pole-Placement Design 10.2 Ackermannis Formula 10.3 State Estimation 10.4 Closed-Loop System Characteristics 10.5 Reduced-Order Estimators 10.6 Controllability and Observability 10.7 Systems with Inputs 10.8 Summary References Problems 11 DISCRETE-TIME SYSTEMS 11.1 Discrete-Time System 11.2 Transform Methods 11.3 Theorems of the z-Transform 11.4 Solution of Difference Equations 11.5 Inverse z-Transform 11.6 Simulation Diagrams and Flow Graphs 11.7 State Variables 11.8 Solution of State Equations 11.9 Summary References Problems 12 SAMPLED-DATA SYSTEMS 12.1 Sampled Data 12.2 Ideal Sampler 12.3 Properties of the Starred Transform 12.4 Data Reconstruction 12.5 Pulse Transfer Function 12.6 Open-Loop Systems Containing Digital Filters 12.7 Closed-Loop Discrete-Time Systems 12.8 Transfer Functions for Closed-Loop Systems 12.9 State Variables for Sampled-Data Systems 12.10 Summary References Problems 13 ANALYSIS AND DESIGN OF DIGITAL CONTROL SYSTEMS 13.1 Two Examples 13.2 Discrete System Stability 13.3 Juryis Test 13.4 Mapping the s-Plane into the z-Plane 13.5 Root Locus 13.6 Nyquist Criterion 13.7 Bilinear Transformation 13.8 RouthnHurwitz Criterion 13.9 Bode Diagram 13.10 Steady-State Accuracy 13.11 Design of Digital Control Systems 13.12 Phase-Lag Design 13.13 Phase-Lead Design 13.14 Digital PID Controllers 13.15 Root-Locus Design 13.16 Summary References Problems 14 DISCRETE-TIME POLE-ASSIGNMENT AND STATE ESTIMATION 14.1 Introduction 14.2 Pole Assignment 14.3 State Estimtion 14.4 Reduced-Order Observers 14.5 Current Observers 14.6 Controllability and Observability 14.7 Systems and Inputs 14.8 Summary References Problems 15 NONLINEAR SYSTEM ANALYSIS 15.1 Nonlinear System Definitions and Properties 15.2 Review of the Nyquist Criterion 15.3 Describing Function 15.4 Derivations of Describing Functions 15.5 Use of the Describing Function 15.6 Stability of Limit Cycles 15.7 Design 15.8 Application to Other Systems 15.9 Linearization 15.10 Equilibrium States and Lyapunov Stability 15.11 State Plane Analysis 15.12 Linear-System Response 15.13 Summary References Problems APPENDICES A Matrices B Laplace Transform C Laplace Transform and z-Transform Tables D MATLAB Commands Used in This Text E Answers to Selected Problems INDEX