P.C. Chau Š 2001
Table of Contents Preface 1. Introduction
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2. Mathematical Preliminaries .................................................................................................. 35 2.1 A simple differential equation model 2.2 Laplace transform 2.3 Laplace transforms common to control problems 2.4 Initial and final value theorems 2.5 Partial fraction expansion 2.5.1 Case 1: p(s) has distinct, real roots 2.5.2 Case 2: p(s) has complex roots 2.5.3 Case 3: p(s) has repeated roots 2.6 Transfer function, pole, and zero 2.7 Summary of pole characteristics 2.8 Two transient model examples 2.8.1 A Transient Response Example 2.8.2 A stirred tank heater 2.9 Linearization of nonlinear equations 2.10 Block diagram reduction Review Problems 3. Dynamic Response ............................................................................................................. 19 3.1 First order differential equation models 3.1.1 Step response of a first order model 3.1.2 Impulse response of a first order model 3.1.3 Integrating process 3.2 Second order differential equation models 3.2.1 Step response time domain solutions 3.2.2 Time-domain features of underdamped step response 3.3 Processes with dead time 3.4 Higher order processes and approximations 3.4.1 Simple tanks-in-series 3.4.2 Approximation with lower order functions with dead time 3.4.3 Interacting tanks-in-series 3.5 Effect of zeros in time response 3.5.1 Lead-lag element 3.5.2 Transfer functions in parallel Review Problems 4. State Space Representation ................................................................................................... 18 4.1 State space models 4.2 Relation with transfer function models 4.3 Properties of state space models 4.3.1 Time-domain solution 4.3.2 Controllable canonical form 4.3.3 Diagonal canonical form Review Problems 5.
Analysis of PID Control Systems ........................................................................................ 22 5.1 PID controllers 5.1.1 Proportional control 5.1.2 Proportional-Integral (PI) control 5.1.3 Proportional-Derivative (PD) control 5.1.4 Proportional-Integral-Derivative (PID) control 5.2 Closed-loop transfer functions