Preface |
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xiii | |
To Instructors |
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xv | |
Authors |
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xix | |
1 Feedback and Sensitivity |
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1 | (34) |
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1.1 Feedback Control System |
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1 | (2) |
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1.2 Feedback: Positive and Negative |
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3 | (1) |
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4 | (2) |
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1.4 Loop Gain and Phase Frequency Responses |
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6 | (6) |
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1.4.1 Gain and Phase Responses |
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6 | (3) |
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9 | (2) |
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11 | (1) |
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1.5 Disturbance Rejection |
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12 | (1) |
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1.6 Example of System Analysis |
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13 | (4) |
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1.7 Effect of Feedback on the Actuator Nondynamic Nonlinearity |
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17 | (2) |
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19 | (2) |
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1.9 Effect of Finite Plant Parameter Variations |
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21 | (1) |
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1.10 Automatic Signal Level Control |
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21 | (1) |
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1.11 Lead and PID Compensators |
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22 | (1) |
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1.12 Conclusion and a Look Ahead |
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23 | (1) |
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23 | (10) |
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Answers to Selected Problems |
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33 | (2) |
2 Feedforward, Multi-Loop, and MIMO Systems |
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35 | (22) |
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35 | (3) |
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2.2 Prefilter and the Feedback Path Equivalent |
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38 | (1) |
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39 | (1) |
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39 | (2) |
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2.5 Multi-Loop Feedback Systems |
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41 | (1) |
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2.6 Local, Common, and Nested Loops |
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42 | (1) |
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2.7 Crossed Loops and Main/Vernier Loops |
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43 | (2) |
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2.8 Block Diagram Manipulations and Transfer Function Calculations |
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45 | (3) |
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2.9 MIMO Feedback Systems |
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48 | (3) |
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51 | (6) |
3 Frequency Response Methods |
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57 | (48) |
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3.1 Conversion of Time Domain Requirements to Frequency Domain |
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57 | (6) |
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3.1.1 Approximate Relations |
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57 | (4) |
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61 | (2) |
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3.2 Closed-Loop Transient Response |
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63 | (3) |
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66 | (1) |
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3.4 Nyquist Stability Criterion |
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67 | (3) |
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3.5 Robustness and Stability Margins |
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70 | (5) |
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3.6 Nyquist Criterion for Unstable Plants |
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75 | (2) |
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3.7 Successive Loop Closure Stability Criterion (Bode-Nyquist) |
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77 | (1) |
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3.8 Nyquist Diagrams for Loop Transfer Functions with Poles at the Origin |
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78 | (3) |
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3.9 Bode Phase-Gain Relation |
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81 | (4) |
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3.9.1 Minimum Phase Systems |
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81 | (1) |
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3.9.2 Phase-Gain Relation |
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82 | (3) |
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85 | (3) |
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3.11 From the Nyquist Diagram to the Bode Diagram |
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88 | (2) |
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3.12 More on Non-Minimum Phase Lag |
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90 | (1) |
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3.13 Ladder Networks and Parallel Connections of m.p. Links |
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91 | (2) |
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3.14 Other Bode Definite Integrals |
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93 | (4) |
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3.14.1 Integral of the Feedback |
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93 | (1) |
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3.14.2 Integral of the Imaginary Part |
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94 | (1) |
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3.14.3 Gain Integral over Finite Bandwidth |
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95 | (1) |
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3.14.4 Integral of the Resistance |
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95 | (2) |
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97 | (5) |
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Answers to Selected Problems |
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102 | (3) |
4 Shaping the Loop Frequency Response |
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105 | (42) |
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4.1 Optimality of the Compensator Design |
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105 | (2) |
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4.2 Feedback Maximization |
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107 | (17) |
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107 | (1) |
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108 | (3) |
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4.2.3 Example of a System Having a Loop Response with a Bode Step |
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111 | (8) |
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4.2.4 Reshaping the Feedback Response |
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119 | (1) |
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120 | (1) |
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121 | (1) |
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4.2.7 Nyquist-Stable Systems |
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122 | (2) |
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4.3 Feedback Bandwidth Limitations |
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124 | (11) |
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124 | (1) |
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4.3.2 Sensor Noise at the System Output |
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125 | (2) |
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4.3.3 Sensor Noise at the Actuator Input |
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127 | (1) |
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4.3.4 Non-Minimum Phase Shift |
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128 | (1) |
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129 | (2) |
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4.3.6 Lightly Damped Flexible Plants: Collocated and Non-Collocated Control |
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131 | (3) |
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134 | (1) |
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4.4 Coupling in MIMO Systems |
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135 | (2) |
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4.5 Shaping Parallel Channel Responses |
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137 | (4) |
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141 | (3) |
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Answers to Selected Problems |
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144 | (3) |
5 Compensator Design |
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147 | (46) |
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5.1 Loop Shaping Accuracy |
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147 | (1) |
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5.2 Asymptotic Bode Diagram |
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148 | (3) |
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5.3 Approximation of Constant Slope Gain Response |
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151 | (1) |
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152 | (3) |
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155 | (1) |
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156 | (4) |
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5.7 Parallel Connection of Links |
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160 | (1) |
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5.8 Simulation of a PID Controller |
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161 | (3) |
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5.9 Analog and Digital Controllers |
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164 | (1) |
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5.10 Digital Compensator Design |
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165 | (14) |
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5.10.1 Discrete Trapezoidal Integrator |
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165 | (2) |
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5.10.2 Laplace and Tustin Transforms |
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167 | (3) |
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170 | (1) |
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5.10.4 Block Diagrams, Equations, and Computer Code |
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170 | (2) |
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5.10.5 Compensator Design Example |
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172 | (3) |
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5.10.6 Aliasing and Noise |
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175 | (2) |
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5.10.7 Transfer Function for the Fundamental |
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177 | (2) |
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179 | (5) |
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Answers to Selected Problems |
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184 | (9) |
6 Analog Controller Implementation |
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193 | (42) |
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193 | (11) |
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6.1.1 Operational Amplifier |
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193 | (2) |
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6.1.2 Integrator and Differentiator |
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195 | (1) |
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6.1.3 Noninverting Configuration |
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196 | (1) |
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6.1.4 Op-Amp Dynamic Range, Noise, and Packaging |
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197 | (1) |
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6.1.5 Transfer Functions with Multiple Poles and Zeros |
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198 | (2) |
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200 | (2) |
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202 | (2) |
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6.2 Design and Iterations in the Element Value Domain |
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204 | (5) |
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6.2.1 Cauer and Foster RC Two-Poles |
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204 | (3) |
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207 | (2) |
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6.3 Analog Compensator, Analog or Digitally Controlled |
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209 | (1) |
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6.4 Switched-Capacitor Filters |
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210 | (2) |
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6.4.1 Switched-Capacitor Circuits |
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210 | (1) |
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6.4.2 Example of Compensator Design |
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210 | (2) |
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6.5 Miscellaneous Hardware Issues |
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212 | (4) |
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212 | (1) |
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6.5.2 Signal Transmission |
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213 | (2) |
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6.5.3 Stability and Testing Issues |
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215 | (1) |
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6.6 PID Tunable Controller |
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216 | (4) |
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216 | (2) |
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218 | (2) |
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6.7 Tunable Compensator with One Variable Parameter |
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220 | (4) |
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6.7.1 Linear Fractional Transfer Function |
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220 | (1) |
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6.7.2 Symmetrical Regulator |
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221 | (2) |
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6.7.3 Hardware Implementation |
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223 | (1) |
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6.8 Loop Response Measurements |
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224 | (4) |
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228 | (4) |
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Answers to Selected Problems |
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232 | (3) |
7 Linear Links and System Simulation |
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235 | (42) |
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7.1 Mathematical Analogies |
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235 | (6) |
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7.1.1 Electromechanical Analogies |
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235 | (3) |
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7.1.2 Electrical Analogy to Heat Transfer |
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238 | (1) |
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239 | (2) |
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7.2 Junctions of Unilateral Links |
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241 | (3) |
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241 | (1) |
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241 | (2) |
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243 | (1) |
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7.3 Effect of the Plant and Actuator Impedances on the Plant Transfer Function Uncertainty |
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244 | (1) |
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7.4 Effect of Feedback on the Impedance (Mobility) |
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245 | (4) |
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7.4.1 Large Feedback with Velocity and Force Sensors |
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245 | (1) |
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246 | (1) |
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247 | (1) |
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248 | (1) |
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248 | (1) |
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7.5 Effect of Load Impedance on Feedback |
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249 | (1) |
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7.6 Flowchart for Chain Connection of Bidirectional Two-Ports |
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250 | (8) |
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7.6.1 Chain Connection of Two-Ports |
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250 | (3) |
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253 | (1) |
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7.6.3 Motor Output Mobility |
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254 | (1) |
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255 | (1) |
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7.6.5 Drivers, Transformers, and Gears |
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255 | (2) |
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257 | (1) |
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7.7 Examples of System Modeling |
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258 | (3) |
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261 | (4) |
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7.8.1 Impedance (Mobility) of a Lossless System |
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261 | (1) |
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7.8.2 Lossless Distributed Structures |
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262 | (1) |
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263 | (1) |
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7.8.4 Non-Collocated Control |
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264 | (1) |
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265 | (3) |
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265 | (2) |
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7.9.1.1 Position and Angle Sensors |
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265 | (1) |
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266 | (1) |
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266 | (1) |
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266 | (1) |
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7.9.2 Effect of Feedback on the Signal-to-Noise Ratio |
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267 | (1) |
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7.10 Mathematical Analogies to the Feedback System |
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268 | (1) |
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7.10.1 Feedback-to-Parallel-Channel Analogy |
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268 | (1) |
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7.10.2 Feedback-to-Two-Pole-Connection Analogy |
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269 | (1) |
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7.11 Linear Time-Variable Systems |
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269 | (2) |
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271 | (4) |
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Answers to Selected Problems |
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275 | (2) |
8 Introduction to Alternative Methods of Controller Design |
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277 | (14) |
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277 | (3) |
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8.2 Root Locus and Pole Placement Methods |
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280 | (1) |
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8.3 State-Space Methods and Full-State Feedback |
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281 | (5) |
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8.3.1 Comments on Example 8.3 |
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284 | (2) |
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286 | (1) |
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8.5 Hinfinity, µ-Synthesis, and Linear Matrix Inequalities |
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287 | (4) |
9 Adaptive Systems |
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291 | (10) |
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9.1 Benefits of Adaptation to the Plant Parameter Variations |
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291 | (2) |
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9.2 Static and Dynamic Adaptation |
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293 | (1) |
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9.3 Plant Transfer Function Identification |
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294 | (1) |
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9.4 Flexible and N.P. Plants |
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294 | (1) |
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9.5 Disturbance and Noise Rejection |
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295 | (2) |
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9.6 Pilot Signals and Dithering Systems |
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297 | (2) |
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299 | (2) |
10 Provision of Global Stability |
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301 | (26) |
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10.1 Nonlinearities of the Actuator, Feedback Path, and Plant |
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301 | (2) |
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10.2 Types of Self-Oscillation |
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303 | (1) |
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10.3 Stability Analysis of Nonlinear Systems |
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304 | (2) |
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10.3.1 Local Linearization |
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304 | (1) |
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305 | (1) |
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306 | (1) |
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307 | (4) |
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10.5.1 Analogy to Passive Two-Poles' Connection |
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307 | (3) |
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10.5.2 Different Forms of the Popov Criterion |
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310 | (1) |
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10.6 Applications of Popov Criterion |
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311 | (1) |
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10.6.1 Low-Pass System with Maximum Feedback |
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311 | (1) |
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10.6.2 Band-Pass System with Maximum Feedback |
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311 | (1) |
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10.7 Absolutely Stable Systems with Nonlinear Dynamic Compensation |
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312 | (11) |
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10.7.1 Nonlinear Dynamic Compensator |
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312 | (1) |
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10.7.2 Reduction to Equivalent System |
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313 | (1) |
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314 | (9) |
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323 | (2) |
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Answers to Selected Problems |
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325 | (2) |
11 Describing Functions |
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327 | (36) |
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327 | (2) |
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11.1.1 Harmonic Balance Analysis |
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327 | (1) |
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11.1.2 Harmonic Balance Accuracy |
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328 | (1) |
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329 | (2) |
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11.3 Describing Functions for Symmetrical Piece-Linear Characteristics |
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331 | (4) |
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331 | (3) |
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11.3.2 Approximate Formulas |
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334 | (1) |
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335 | (3) |
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11.5 Nonlinear Links Yielding Phase Advance for Large-Amplitude Signals |
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338 | (2) |
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11.6 Two Nonlinear Links in the Feedback Loop |
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340 | (1) |
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11.7 NDC with a Single Nonlinear Nondynamic Link |
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341 | (3) |
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11.8 NDC with Parallel Channels |
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344 | (2) |
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11.9 NDC Made with Local Feedback |
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346 | (3) |
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11.10 Negative Hysteresis and Clegg Integrator |
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349 | (2) |
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11.11 Nonlinear Interaction between the Local and the Common Feedback Loops |
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351 | (1) |
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11.12 NDC in Multi-Loop Systems |
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352 | (1) |
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11.13 Harmonics and Intermodulation |
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353 | (3) |
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353 | (2) |
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355 | (1) |
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11.14 Verification of Global Stability |
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356 | (2) |
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358 | (3) |
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Answers to Selected Problems |
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361 | (2) |
12 Process Instability |
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363 | (12) |
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363 | (1) |
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12.2 Absolute Stability of the Output Process |
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364 | (2) |
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366 | (4) |
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370 | (2) |
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370 | (1) |
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12.4.2 Second Subharmonic |
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371 | (1) |
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12.5 Nonlinear Dynamic Compensation |
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372 | (1) |
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372 | (3) |
13 Multiwindow Controllers |
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375 | (20) |
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13.1 Composite Nonlinear Controllers |
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375 | (2) |
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377 | (2) |
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13.3 Switching from a Hot Controller to a Cold Controller |
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379 | (2) |
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13.4 Wind-Up and Anti-Wind-Up Controllers |
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381 | (3) |
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384 | (1) |
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13.6 Acquisition and Tracking |
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385 | (2) |
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13.7 Time-Optimal Control |
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387 | (1) |
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388 | (4) |
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392 | (3) |
14 Nonlinear Multi-Loop Systems with Uncertainty |
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395 | (10) |
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14.1 Systems with High-Frequency Plant Uncertainty |
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395 | (2) |
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14.2 Stability and Multi-Frequency Oscillations in Band-Pass Systems |
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397 | (1) |
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14.3 Bode Single-Loop System |
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398 | (1) |
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14.4 Multi-Input Multi-Output Systems |
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399 | (1) |
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14.5 Nonlinear Multi-Loop Feedback |
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399 | (3) |
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14.6 Design of the Internal Loops |
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402 | (1) |
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14.7 Input Signal Reconstruction |
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402 | (3) |
Appendix 1: Feedback Control, Elementary Treatment |
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405 | (14) |
Appendix 2: Frequency Responses |
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419 | (14) |
Appendix 3: Causal Systems, Passive Systems and Positive Real Functions, and Collocated Control |
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433 | (2) |
Appendix 4: Derivation of Bode Integrals |
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435 | (8) |
Appendix 5: Program for Phase Calculation |
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443 | (4) |
Appendix 6: Generic Single-Loop Feedback System |
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447 | (4) |
Appendix 7: Effect of Feedback on Mobility |
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451 | (2) |
Appendix 8: Regulation |
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453 | (4) |
Appendix 9: Balanced Bridge Feedback |
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457 | (2) |
Appendix 10: Phase-Gain Relation for Describing Functions |
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459 | (2) |
Appendix 11: Discussions |
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461 | (14) |
Appendix 12: Design Sequence |
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475 | (2) |
Appendix 13: Examples |
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477 | (46) |
Appendix 14: Bode Step Toolbox |
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523 | (24) |
Appendix 15: Nonlinear Multi-Loop Feedback Control (Patent Application) |
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547 | (10) |
Bibliography |
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557 | (4) |
Notation |
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561 | (4) |
Index |
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565 | |