P.C. Chau © 2001
Table of Contents
Preface
1. Introduction
............................................................ [Number of 10-point single-space pages -->] 3
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 ..............................................................