Modern Control Design

Ashish Tewari is a Professor in the Department of Aerospace Engineering at the IIT-Kanpur. He specializes in flight mechanics and control, and his research areas include attitude dynamics and control, re-entry flight dynamics and control, non-linear optimal control and active control of flexible flight and structures.

• Preface xiii1. Introduction 1 1.1 What is Control? 11.2 Open-Loop and Closed-Loop Control Systems 21.3 Other Classifications of Control Systems 61.4 On the Road to Control System Analysis and Design 101.5 MATLAB, SIMULINK, and the Control System Toolbox 11References 122. Linear Systems and Classical Control 132.1 How Valid is the Assumption of Linearity? 132.2 Singularity Functions 222.3 Frequency Response 262.4 Laplace Transform and the Transfer Function 362.5 Response to Singularity Functions 512.6 Response to Arbitrary Inputs 582.7 Performance 622.8 Stability 712.9 Root-Locus Method 732.10 Nyquist Stability Criterion 772.11 Robustness 812.12 Closed-Loop Compensation Techniques for Single-Input, Single-Output Systems 872.12.1 Proportional-integral-derivative compensation 882.12.2 Lag, lead, and lead-lag compensation 962.13 Multivariable Systems 105Exercises 115References 1243. State-Space Representation 1253.1 The State-Space: Why Do I Need lt? 1253.2 Linear Transformation of State-Space Representations 1403.3 System Characteristics from State-Space Representation 1463.4 Special State-Space Representations: The Canonical Forms 1523.5 Block Building in Linear, Time-Invariant State-Space 160Exercises 168References 1704. Solving the State-Equations 1714.1 Solution of the Linear Time Invariant State Equations 1714.2 Calculation of the State-Transition Matrix 1764.3 Understanding the Stability Criteria through the State-Transition Matrix 1834.4 Numerical Solution of Linear Time-Invariant State-Equations 1844.5 Numerical Solution of Linear Time-Varying State-Equations 1964.6 Numerical Solution of Nonlinear State-Equations 2044.7 Simulating Control System Response with SIMULINK 213Exercises 216References 2185. Control System Design in State-Space 2195.1 Design: Classical vs. Modern 2195.2 Controllability 2225.3 Pole-Placement Design Using Full-State Feedback  2285.3.1 Pole-placement regulator design for single-input plants  2305.3.2 Pole-placement regulator design for multi-input plants  2455.3.3 Pole-placement regulator design for plants with noise  2475.3.4 Pole-placement design of tracking systems 2515.4 Observers, Observability, and Compensators 2565.4.1 Pole-placement design of full-order observers and compensators 2585.4.2 Pole-placement design of reduced-order observers and compensators 2695.4.3 Noise and robustness issues  276Exercises 277References 2826. Linear Optimal Control 2836.1 The Optimal Control Problem 2836.1.l The general optimal control formulation for regulators  2846.1.2 Optimal regulator gain matrix and the riccati equation  2866.2 Infinite-Time Linear Optimal Regulator Design  2886.3 Optimal Control of Tracking Systems 2986.4 Output Weighted Linear Optimal Control 3086.5 Terminal Time Weighting: Solving the Matrix Riccati Equation 312Exercises 318References 3217. Kalman Filters 3237.1 Stochastic Systems 3237.2 Filtering of Random Signals  3297.3 White Noise, and White Noise Filters  3347.4 The Kalman Filter 3397.5 Optimal (Linear, Quadratic, Gaussian) Compensators  3517.6 Robust Multivariable LQG Control: Loop Transfer Recovery  356Exercises 370References 3718. Digital Control Systems 3738. l What are Digital Systems?   3738.2 A/D Conversion and the z-Transform  3758.3 Pulse Transfer Functions of Single-Input, Single-Output Systems  3798.4 Frequency Response of Single-Input, Single-Output Digital Systems  3848.5 Stability of Single-Input, Single-Output Digital Systems   3868.6 Performance of Single-Input, Single-Output Digital Systems   3908.7  Closed-Loop Compensation Techniques for Single-Input, Single-Output  Digital Systems  3938.8 State-Space Modeling of Multivariable Digital Systems  3968.9 Solution of Linear Digital State-Equations 402 8.10 Design of Multivariable, Digital Control Systems Using Pole-Placement: Regulators, Observers, and Compensators 4068.11 Linear Optimal Control of Digital Systems 4158.12 Stochastic Digital Systems, Digital Kalman Filters, and Optimal Digital Compensators 424Exercises 432References 4369. Advanced Topics in Modern Control 4379.1 Introduction 4379.2 H∞ Robust, Optimal Control 4379.3 Structured Singular Value Synthesis for Robust Control 4429.4 Time-Optimal Control with Pre-shaped Inputs 4469.5 Output-Rate Weighted Linear Optimal Control 4539.6 Nonlinear Optimal Control 455Exercises 463References 465Appendix A: Introduction to MATLAB, SIMULINK and the Control System Toolbox 467Appendix B: Review of Matrices and Linear Algebra 481Appendix C: Mass, Stiffness, and Control Influence Matrices of the Flexible Spacecraft 487Answers to Selected, Exercises 489Index 495