Introduction to Feedback Control using Design Studies

This textbook provides a unique introduction to Feedback Control. It differs from typical control books by presenting principles in the context of three specific design examples: a one link robot arm, a pendulum on a cart, and a satellite attitude problem. These three design examples illustrate the full process of implementing control strategies on mechanical systems. The book begins by introducing the Euler Lagrange method for modeling mechanical systems and discusses computer simulation of these models. Linear design models are developed, specifically transfer function and state space models, that capture the behavior of the system around equilibria. The book then presents three different design strategies for output feedback control: PID control, observer based design, and loopshaping design methods based on the frequency response of the system. Extensive examples show how the controllers are implemented in Simulink, Matlab object oriented code, and Python. 1 Introduction 9 Design Study A: Single Link Robot Arm 13 Design Study B: Pendulum on a Cart 14 Design Study C: Satellite Attitude Control 15 I Simulation Models 16 2 Kinetic Energy 19 3 Euler-Lagrange 41 II Design Models 57 4 Linearization 59 5 Transfer Functions 69 6 State Space Models 81 III PID Control Design 94 7 Second Order Systems 99 8 Second Order Design 107 9 Integrators 135 10 Digital PID 153 IV Observer Based Control Design 166 11 Full State Feedback 169 12 Full State with Integrators 193 13 Observers 213 14 Disturbance Observers 243 V Loopshaping Control Design 266 15 Frequency Response 267 16 Frequency Specifications 289 17 Stability and Robustness Margins 309 18 Compensator Design 329 VI Homework Problems 383 D Design Study: Mass Spring Damper 385 E Design Study: Ball on Beam 393 F Design Study: Planar VTOL 401 Appendices 409 P.1 Simulating Control Systems in Python 415 P.2 Simulating Control Systems in Matlab 429 P.3 Simulating Control Systems in Simulink 443 P.4 Numerical ODE Solvers 455 P.5 Differential Equations 467 P.6 Root Locus 475 P.7 Linear Algebra 485 Bibliography 491 Index 491