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Tables of Contents for System Modelling and Control
Chapter/Section Title
Page #
Page Count
Preface
iii
List of principal symbols
xi
1 Introduction
1
9
1.1 What is a system?
1
2
1.2 System control
3
1
1.3 The need for analysis
4
1
1.4 Methods of system representation
4
2
1.5 Methods of analysis and design
6
4
2 Mathematical Description of System Components
10
21
2.1 Linearity of systems
10
4
2.2 Laplace transforms and their significance
14
2
2.3 Transfer functions and the characteristic equation
16
2
2.4 Transfer functions for some simple elements
18
8
2.5 Effect of secondary factors on transfer functions
26
3
2.6 State equations
29
2
3 Transient Response of Systems
31
19
3.1 Response of first order system to step, ramp, or impulse function
32
3
3.2 Response of second order system to step, ramp, or impulse function
35
3
3.3 Transient response of third and higher order systems
38
2
3.4 Performance characteristics (time domain)
40
3
3.5 Step response testing of practical systems
43
4
3.6 Comparison of transient forcing functions
47
1
3.7 The convolution integral
48
2
4 System Simulation
50
16
4.1 Analogue simulation
50
3
4.2 Digital continuous system simulation
53
5
4.3 Simulation languages
58
8
5 State Space Representation and Analysis
66
21
5.1 State variable diagrams
67
5
5.2 Generalized state equations
72
2
5.3 State relations in the s-domain
74
2
5.4 Solution of the state vector differential equation
76
4
5.5 Discrete-time model
80
7
6 Frequency Response of Systems
87
19
6.1 The transfer function in the frequency domain
88
1
6.2 Polar plots
89
5
6.3 Bode plots
94
9
6.4 Frequency response testing of practical systems
103
1
6.5 Frequency domain performance criteria
104
2
7 Statistical Methods for System Identification
106
32
7.1 Correlation functions
107
6
7.2 Dynamic testing using correlation techniques
113
3
7.3 Power spectral density
116
4
7.4 System identification using spectral density functions
120
2
7.5 Digital evaluation of correlation functions and power spectral density
122
6
7.6 Pseudo random binary sequences (PRBS)
128
4
7.7 Illustrative example
132
6
8 Feedback Systems-Accuracy and Stability
138
18
8.1 Closed loop or feedback control
138
3
8.2 Steady state error
141
2
8.3 Routh-Hurwitz stability criterion
143
4
8.4 Nyquist stability criterion
147
1
8.5 Gain margin and phase margin
148
3
8.6 Loci of constant closed loop magnitude and phase
151
5
9 The Root Locus Method
156
23
9.1 Rootlocus.plots
157
4
9.2 Construction of root loci
161
2
9.3 Aids to construction of root locus diagram
163
5
9.4 Interpretation of the root locus diagram
168
6
9.5 Root contours
174
5
10 The Sampled-Data Process
179
29
10.1 Mathematical description of sampling process
180
1
10.2 Transfer function of sampled-data element
181
1
10.3 Closed-loop transfer function
182
2
10.4 Polar plots
184
2
10.5 Pulse transfer function
186
3
10.6 Block diagrams
189
2
10.7 Inverse operation
191
1
10.8 Data reconstruction
192
6
10.9 Relationship between z-transforms and difference equations
198
1
10.10 The z-plane
199
1
10.11 Routh-Hurwitz stability test
200
4
10.12 Frequency response of sampled-data system
204
4
11 Design of Closed Loop Systems
208
46
11.1 The general approach to design
208
3
11.2 Proportional control
211
1
11.3 Integral and derivative action
212
6
11.4 Selecting controller settings on existing process plant
218
2
11.5 System compensation
220
1
11.6 Phase lead series compensation
221
1
11.7 Phase lag, and lag-lead series compensation
222
11
11.8 Pole cancellation, and feedforward compensation
233
1
11.9 State vector feedback control
234
9
11.10 Digital control with (P + I) controller
243
4
11.11 Phase compensation of sampled-data system
247
7
12 Nonlinearities and Dead Time
254
25
12.1 Typical nonlinearities
254
2
12.2 The general approach to analysis
256
1
12.3 Phase plane technique
256
8
12.4 Describing function technique
264
5
12.5 Liapunov stability criterion
269
3
12.6 Dead time
272
7
13 Case Studies
279
19
13.1 Electrohydraulic servomechanism
279
12
13.2 Design of discrete controller for a space vehicle
291
7
Appendix
A Problems
298
20
B Bibliography
318
3
C Introduction to matrix algebra
321
5
D Answers to problems
326
12
Index
338