Preface |
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ix | |
Acknowledgments |
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xi | |
List of Commonly used Symbols |
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xiii | |
1 Introduction to Linear Feedback Controls |
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1 | (14) |
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1.1 What are Feedback Control Systems? |
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3 | (2) |
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5 | (2) |
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1.3 Design of Feedback Control Systems |
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7 | (2) |
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9 | (6) |
2 Systems and Signals |
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15 | (12) |
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2.1 Example First-Order System: The RC Lowpass |
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17 | (1) |
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2.2 Example Second-Order System: The Spring-Mass-Damper System |
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18 | (2) |
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2.3 Obtaining the System Response from a Step Input |
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20 | (2) |
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22 | (1) |
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2.5 Systems and Signals in Scilab |
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23 | (4) |
3 Solving Differential Equations in the Laplace Domain |
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27 | (30) |
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3.1 The Laplace Transform |
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27 | (4) |
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3.2 Fourier Series and the Fourier Transform |
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31 | (6) |
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3.3 Representation of the RC Lowpass and Spring-Mass-Damper Systems in the Laplace Domain |
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37 | (4) |
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3.4 Transient and Steady-State Response |
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41 | (3) |
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3.5 Partial Fraction Expansion |
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44 | (7) |
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3.5.1 Partial Fraction Expansion Examples |
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46 | (4) |
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3.5.2 Partial Fraction Expansion in Scilab |
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50 | (1) |
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3.6 Building Blocks of Linear Systems |
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51 | (6) |
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51 | (1) |
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51 | (1) |
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52 | (1) |
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3.6.4 Phase-Lag System, First-Order Lowpass |
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53 | (1) |
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3.6.5 First-Order Highpass |
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54 | (1) |
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3.6.6 PD System or Phase-Lead Compensator |
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54 | (1) |
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3.6.7 Allpass Compensator |
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55 | (1) |
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3.6.8 Second-Order System |
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55 | (1) |
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3.6.9 Dead-Time System (Time-Delay System) |
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56 | (1) |
4 Time-Discrete Systems |
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57 | (20) |
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4.1 Analog-to-Digital Conversion and the Zero-Order Hold |
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58 | (3) |
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61 | (4) |
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4.3 The Relationship between Laplace- and z-domains |
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65 | (5) |
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70 | (1) |
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4.5 Building Blocks for Digital Controllers |
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70 | (7) |
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71 | (1) |
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72 | (1) |
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72 | (1) |
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73 | (1) |
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74 | (1) |
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74 | (1) |
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4.5.7 Lead-Lag Compensator |
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75 | (2) |
5 First Comprehensive Example: The Temperature-Controlled Waterbath |
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77 | (12) |
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5.1 Mathematical Model of the Process |
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78 | (1) |
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5.2 Determination of the System Coefficients |
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79 | (3) |
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5.3 Determining the Transfer Function-General Remarks |
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82 | (2) |
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5.4 Introducing Feedback Control |
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84 | (1) |
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5.5 Comparison of the Open-Loop and Closed-Loop Systems |
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85 | (4) |
6 Laplace- and z-Domain Description of the Waterbath Example |
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89 | (14) |
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6.1 Laplace-Domain Description of the Process |
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89 | (2) |
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6.2 The Closed-Loop System |
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91 | (2) |
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6.3 Sensitivity and Tracking Error |
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93 | (2) |
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6.4 Using a P1 Controller |
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95 | (4) |
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6.5 Time-Discrete Control |
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99 | (4) |
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6.5.1 Time-Discrete Control with the Bilinear Transform |
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100 | (3) |
7 Block Diagrams: Formal Graphical Description of Linear Systems |
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103 | (10) |
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7.1 Symbols of a Block Diagram |
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103 | (1) |
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7.2 Block Diagram Manipulation |
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104 | (2) |
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7.3 Block Diagram Simplification Examples |
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106 | (5) |
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111 | (2) |
8 Linearization of Nonlinear Components |
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113 | (8) |
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8.1 Linearization of Components with Analytical Description |
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114 | (2) |
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8.2 Linearization of Tabular Data |
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116 | (1) |
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8.3 Linearization of Components with Graphical Data |
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117 | (1) |
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118 | (3) |
9 A Tale of Two Poles: The Positioner Example and the Significance of the Poles in the s-Plane |
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121 | (18) |
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9.1 A Head-Positioning System |
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122 | (1) |
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9.2 Introducing Feedback Control |
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123 | (2) |
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9.3 Dynamic Response of the Closed-Loop System |
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125 | (2) |
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9.4 Dynamic Response Performance Metrics |
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127 | (4) |
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9.5 Time-Integrated Performance Metrics |
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131 | (2) |
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9.6 Feedback Control with a Time-Discrete Controller |
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133 | (6) |
10 Stability Analysis for Linear Systems |
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139 | (10) |
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10.1 The Routh-Hurwitz Scheme |
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140 | (2) |
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10.2 Routh Arrays for Low-Order Systems |
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142 | (1) |
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10.3 Stability of Time-Discrete Systems with the w-Transform |
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143 | (1) |
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144 | (1) |
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10.5 Jury Arrays for Low-Order Systems |
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145 | (1) |
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10.6 Example Applications |
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146 | (3) |
11 Frequency-Domain Analysis and Design Methods |
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149 | (26) |
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11.1 Frequency Response of LTI Systems |
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149 | (3) |
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11.2 Frequency Response and Stability |
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152 | (1) |
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152 | (2) |
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11.4 Definition of Phase and Gain Margin |
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154 | (1) |
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11.5 Construction of Bode Diagrams |
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155 | (2) |
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11.6 Frequency Response of a Second-Order System |
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157 | (4) |
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11.7 Frequency Response of Digital Filters |
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161 | (3) |
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11.8 The Nyquist Stability Criterion |
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164 | (11) |
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11.8.1 The Nyquist Stability Criterion for Time-Discrete Systems |
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169 | (2) |
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11.8.2 Nyquist Stability in Scilab |
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171 | (4) |
12 The Root Locus Method |
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175 | (18) |
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12.1 Graphical Construction of Root Locus Plots |
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176 | (5) |
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12.1.1 Prepare the Characteristic Equation in Root Locus Form |
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176 | (2) |
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12.1.2 Open-Loop Poles and Zeros and Asymptotes |
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178 | (1) |
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12.1.3 Branches of the Root Locus on the Real Axis |
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178 | (1) |
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179 | (1) |
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12.1.5 Departure Angles for Complex Poles |
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180 | (1) |
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12.2 Root Locus Diagrams in Scilab |
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181 | (1) |
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12.3 Design Example: Positioner with PI Control |
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182 | (4) |
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12.4 Design Example: Resonance Reduction |
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186 | (3) |
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12.5 The Root Locus Method for Time-Discrete Systems |
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189 | (4) |
13 The PID Controller |
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193 | (16) |
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13.1 Intuitive Introduction |
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193 | (1) |
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13.2 Transfer Functions with PID Control |
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194 | (4) |
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13.2.1 PID Control of a First-Order Process |
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195 | (1) |
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13.2.2 PID Control of a Second-Order Process |
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196 | (2) |
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13.3 Frequency-Domain Aspects of PID Control |
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198 | (1) |
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13.4 Time-Discrete PID Controllers |
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199 | (4) |
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13.5 PID Controller Tuning |
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203 | (3) |
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13.5.1 Iterative Adjustment with an Oscilloscope |
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204 | (1) |
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13.5.2 Ziegler-Nichols Tuning Method |
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205 | (1) |
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13.5.3 Cohen-Coon Tuning Method |
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206 | (1) |
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13.6 Variations and Alternatives of PID Control |
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206 | (2) |
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206 | (1) |
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13.6.2 Nonlinear Processes |
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207 | (1) |
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207 | (1) |
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208 | (1) |
14 Design Examples |
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209 | (40) |
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14.1 Precision Temperature Control |
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209 | (3) |
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14.2 Fast-Tracking Temperature Control |
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212 | (2) |
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14.3 Motor Speed and Position Control |
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214 | (8) |
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14.3.1 Open-Loop Control with Step Motors |
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215 | (3) |
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14.3.2 Closed-Loop Control with DC Motors |
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218 | (4) |
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14.4 Resonant Sine Oscillator |
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222 | (8) |
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14.5 Low-Distortion (Hi-Fi) Amplifiers with Feedback |
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230 | (5) |
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14.6 Phase-Locked Loop Systems |
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235 | (5) |
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14.7 Stabilizing an Unstable System |
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240 | (9) |
Appendix A Laplace Correspondence Tables |
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249 | (4) |
Appendix B Z-Transform Correspondence Tables |
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253 | (2) |
Appendix C Introduction to Operational Amplifiers |
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255 | (4) |
Appendix D Relevant Scilab Commands |
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259 | (2) |
References and Further Reading |
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261 | (2) |
Glossary |
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263 | |