| Foreword |
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xi | |
| Preface |
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xiii | |
| Acknowledgement |
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xxi | |
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xxiii | |
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xxix | |
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xxxi | |
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1 Mathematical Models of Physical Systems |
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1 | (30) |
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1.1 Modeling of Physical Systems |
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2 | (13) |
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1.1.1 Model Variables and Element Types |
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3 | (1) |
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1.1.1 First-Order ODE Models |
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4 | (4) |
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1.1.1 Solving First-Order ODE Models with Step Input |
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8 | (2) |
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1.1.1 Second-Order ODE Models |
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10 | (2) |
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1.1.1 Solving Second-Order ODE Models |
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12 | (3) |
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1.2 Transfer Function Models |
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15 | (6) |
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16 | (4) |
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1.2.2 Industrial Process Models |
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20 | (1) |
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1.3 State Variable Models |
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21 | (3) |
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1.4 Linearization of Nonlinear Models |
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24 | (5) |
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1.4.4 Linearization About an Operating Point |
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25 | (2) |
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1.4.4 Linearization of a General Nonlinear Model |
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27 | (2) |
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Skill Assessment Questions |
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29 | (2) |
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2 Analysis of Transfer Function Models |
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31 | (32) |
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2.1 Characterization of Transfer Function Models |
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32 | (4) |
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2.1.1 System Poles and Zeros |
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32 | (2) |
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2.1.1 System Natural Response |
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34 | (2) |
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2.2 System Response to Inputs |
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36 | (13) |
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2.2.2 The Impulse Response |
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36 | (2) |
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38 | (6) |
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2.2.2 Characterizing the System Transient Response |
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44 | (2) |
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46 | (3) |
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2.3 Sinusoidal Response of a System |
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49 | (10) |
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2.3.3 Sinusoidal Response of Low-Order Systems |
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50 | (2) |
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2.3.3 Visualizing the Frequency Response |
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52 | (7) |
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Skill Assessment Questions |
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59 | (4) |
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3 Analysis of State Variable Models |
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63 | (30) |
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3.1 State Variable Models |
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64 | (13) |
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3.1.1 Solution to the State Equations |
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65 | (1) |
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3.1.1 Laplace Transform Solution and Transfer Function |
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66 | (2) |
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3.1.1 The State-Transition Matrix |
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68 | (2) |
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3.1.1 Homogenous State Equation and Asymptotic Stability |
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70 | (4) |
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3.1.1 System Response for State Variable Models |
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74 | (3) |
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3.2 State Variable Realization of Transfer Function Models |
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77 | (9) |
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3.2.2 Simulation Diagrams |
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78 | (2) |
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3.2.2 Controller Form Realization |
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80 | (3) |
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3.2.2 Dual (Observer Form) Realization |
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83 | (1) |
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83 | (2) |
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3.2.2 Diagonalization and Decoupling |
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85 | (1) |
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3.3 Linear Transformation of State Variables |
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86 | (4) |
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3.3.3 Transformation into Controller Form |
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86 | (2) |
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3.3.3 Transformation into Modal Form |
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88 | (2) |
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Skill Assessment Questions |
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90 | (3) |
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4 Feedback Control Systems |
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93 | (18) |
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4.1 Static Gain Controller |
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95 | (1) |
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96 | (12) |
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4.2.2 First-Order Phase-Lead and Phase-Lag Controllers |
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97 | (2) |
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99 | (4) |
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4.2.2 Rate Feedback Controllers |
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103 | (5) |
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Skill Assessment Questions |
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108 | (3) |
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5 Control System Design Objectives |
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111 | (22) |
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5.1 Stability of the Closed-Loop System |
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112 | (5) |
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5.1.1 Closed-Loop Characteristic Polynomial |
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112 | (2) |
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5.1.1 Stability Determination by Algebraic Methods |
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114 | (2) |
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5.1.1 Stability Determination from the Bode Plot |
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116 | (1) |
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5.2 Transient Response Improvement |
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117 | (7) |
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5.2.2 System Design Specifications |
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119 | (2) |
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5.2.2 The Desired Characteristic Polynomial |
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121 | (2) |
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5.2.2 Optimal Performance Indices |
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123 | (1) |
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5.3 Steady-State Error Improvement |
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124 | (4) |
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5.3.3 The Steady-State Error |
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124 | (1) |
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5.3.3 System Error Constants |
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125 | (1) |
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5.3.3 Steady-State Error to Ramp Input |
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126 | (2) |
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5.4 Disturbance Rejection |
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128 | (2) |
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5.5 Sensitivity and Robustness |
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130 | (2) |
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Skill Assessment Questions |
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132 | (1) |
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6 Control System Design with Root Locus |
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133 | (34) |
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135 | (8) |
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6.1.1 Roots of the Characteristic Polynomial |
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135 | (1) |
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136 | (2) |
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6.1.1 Obtaining Root Locus Plot in MATLAB |
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138 | (1) |
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6.1.1 Stability from the Root Locus Plot |
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139 | (2) |
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6.1.1 Analytic Root Locus Conditions |
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141 | (2) |
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6.2 Static Controller Design |
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143 | (1) |
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6.3 Dynamic Controller Design |
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144 | (19) |
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6.3.3 Transient Response Improvement |
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145 | (6) |
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6.3.3 Steady-State Error Improvement |
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151 | (1) |
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6.3.3 Lead-Lag and PID Designs |
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152 | (4) |
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6.3.3 Rate Feedback Compensation |
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156 | (5) |
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6.3.3 Controller Designs Compared |
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161 | (2) |
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6.4 Controller Realization |
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163 | (2) |
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6.4.4 Phase-Lead/Phase-Lag Controllers |
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164 | (1) |
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6.4.4 PD, PI, PID Controllers |
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164 | (1) |
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Skill Assessment Questions |
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165 | (2) |
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7 Design of Sampled-Data Systems |
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167 | (44) |
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7.1 Models of Sampled-Data Systems |
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169 | (6) |
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169 | (2) |
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171 | (1) |
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7.1.1 Pulse Transfer Function |
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172 | (3) |
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7.2 Sampled-Data System Response |
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175 | (9) |
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7.2.2 Difference Equation Solution by Iteration |
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175 | (1) |
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7.2.2 Unit-Pulse Response |
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176 | (3) |
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179 | (4) |
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7.2.2 Response to Arbitrary Inputs |
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183 | (1) |
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7.3 Stability in the Case of Sampled-Data Systems |
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184 | (2) |
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7.3.3 Jury's Stability Test |
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184 | (1) |
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7.3.3 Stability Through Bilinear Transform |
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185 | (1) |
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7.4 Closed-Loop Sampled-Data Systems |
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186 | (6) |
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7.4.4 Closed-Loop System Stability |
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186 | (1) |
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187 | (3) |
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7.4.4 Steady-State Tracking Error |
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190 | (2) |
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7.5 Controllers for Sampled-Data Systems |
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192 | (14) |
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7.5.5 Root Locus Design of Digital Controllers |
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193 | (3) |
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7.5.5 Analog and Digital Controller Design Compared |
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196 | (4) |
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7.5.5 Digital Controller Design by Emulation |
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200 | (3) |
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7.5.5 Emulation of Analog PID Controller |
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203 | (3) |
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Skill Assessment Questions |
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206 | (5) |
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8 Controller Design for State Variable Models |
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211 | (36) |
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8.1 State Feedback Controller Design |
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212 | (10) |
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8.1.1 Pole Placement with State Feedback |
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213 | (2) |
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8.1.1 Pole Placement in the Controller Form |
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215 | (2) |
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8.1.1 Pole Placement using Bass-Gura Formula |
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217 | (1) |
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8.1.1 Pole Placement using Ackermann's Formula |
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218 | (2) |
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8.1.1 Pole Placement using Sylvester's Equation |
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220 | (2) |
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8.2 Tracking System Design |
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222 | (8) |
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8.2.2 Tracking System Design with Feedforward Gain |
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222 | (3) |
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8.2.2 Tracking PI Controller Design |
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225 | (5) |
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8.3 State Variable Models of Sampled-Data Systems |
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230 | (5) |
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8.3.3 Discretizing the State Equations |
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230 | (2) |
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8.3.3 Solution to the Discrete State Equations |
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232 | (2) |
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8.3.3 Pulse Transfer Function from State Equations |
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234 | (1) |
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8.4 Controllers for Discrete State Variable Models |
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235 | (9) |
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8.4.4 Emulating an Analog Controller |
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235 | (1) |
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8.4.4 Pole Placement Design of Digital Controller |
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236 | (2) |
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8.4.4 Deadbeat Controller Design |
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238 | (3) |
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8.4.4 Tracking PI Controller Design |
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241 | (3) |
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Skill Assessment Questions |
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244 | (3) |
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9 Frequency Response Design of Compensators |
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247 | (34) |
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9.1 Frequency Response Representation |
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248 | (6) |
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248 | (2) |
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250 | (4) |
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9.2 Measures of Performance |
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254 | (7) |
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254 | (2) |
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9.2.2 Phase Margin and the Transient Response |
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256 | (3) |
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9.2.2 Error Constants and System Type |
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259 | (1) |
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260 | (1) |
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9.3 Frequency Response Design |
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261 | (15) |
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261 | (1) |
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9.3.3 Phase-Lag Compensation |
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262 | (2) |
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9.3.3 Phase-Lead Compensation |
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264 | (3) |
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9.3.3 Lead-Lag Compensation |
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267 | (2) |
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269 | (2) |
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271 | (2) |
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273 | (2) |
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9.3.3 Compensator Designs Compared |
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275 | (1) |
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9.4 Closed-Loop Frequency Response |
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276 | (4) |
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Skill Assessment Questions |
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280 | (1) |
| Appendix |
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281 | (4) |
| Index |
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285 | (4) |
| About the Author |
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289 | |