Chemical Process Control: A First Course with MATLAB

chap10.pdf......Page 0
1. Introduction......Page 6
2.1 A simple differential equation model......Page 9
2.2 Laplace transform......Page 11
2.3 Laplace transforms common to control problems......Page 14
2.4 Initial and final value theorems......Page 16
2.5.1 Case 1: p(s) has distinct, real roots......Page 18
2.5.2 Case 2: p(s) has complex roots......Page 20
2.5.3 Case 3: p(s) has repeated roots......Page 21
2.6 Transfer function, pole, and zero......Page 23
2.7 Summary of pole characteristics......Page 25
2.8.1 A Transient Response Example......Page 28
2.8.2 A stirred tank heater......Page 31
2.9 Linearization of nonlinear equations......Page 34
2.10 Block diagram reduction......Page 38
3. Dynamic Response......Page 45
3.1 First order differential equation models......Page 46
3.1.3 Integrating process......Page 47
3.2 Second order differential equation models......Page 49
3.2.1 Step response time domain solutions......Page 50
3.2.2 Time-domain features of underdamped step response......Page 51
3.3 Processes with dead time......Page 53
3.4.1 Simple tanks-in-series......Page 55
3.4.2 Approximation with lower order functions with dead time......Page 56
3.4.3 Interacting tanks-in-series......Page 58
3.5.1 Lead-lag element......Page 59
3.5.2 Transfer functions in parallel......Page 60
4.1 State space models......Page 64
4.2 Relation with transfer function models......Page 70
4.3.1 Time-domain solution......Page 77
4.3.2 Controllable canonical form......Page 78
4.3.3 Diagonal canonical form......Page 79
5.1 PID controllers......Page 82
5.1.1 Proportional control......Page 83
5.1.2 Proportional-Integral (PI) control......Page 85
5.1.3 Proportional-Derivative (PD) control......Page 86
5.1.4 Proportional-Integral-Derivative (PID) control......Page 87
5.2.1 Closed-loop transfer functions and characteristic polynomials......Page 88
5.2.2 How do we choose the controlled and manipulated variables?......Page 90
5.2.3 Synthesis of a single-loop feedback system......Page 91
5.3 Closed-loop system response......Page 93
5.4 Selection and action of controllers......Page 100
5.4.1 A few comments on the choice of controllers......Page 101
6.1 Tuning controllers with empirical relations......Page 104
6.1.1 Controller settings based on process reaction curve......Page 105
6.1.2 Minimum error integral criteria......Page 106
6.1.3 Ziegler-Nichols ultimate-cycle method......Page 107
6.2.1 Direct synthesis......Page 112
6.2.2 Pole-zero cancellation......Page 115
6.2.3 Internal model control (IMC)......Page 117
7.1 Definition of Stability......Page 125
7.2 The Routh-Hurwitz Criterion......Page 126
7.3 Direct Substitution Analysis......Page 130
7.4 Root Locus Analysis......Page 133
7.5 Root Locus Design......Page 139
8.1 Magnitude and Phase Lag......Page 142
8.1.2 Some important properties......Page 144
8.2.2 Polar Coordinate Plots......Page 146
8.2.3 Magnitude vs Phase Plot......Page 147
8.3.1 Nyquist Stability criterion......Page 155
8.3.2 Gain and Phase Margins......Page 156
8.4.1 How do we calculate proportional gain without trial-and-error?......Page 162
8.4.2 A final word: Can frequency response methods replace root locus?......Page 169
9.1.1 Controllability.......Page 171
9.1.2 Observability......Page 172
9.2.1 Pole placement and Ackermann's formula.......Page 175
9.2.3 Servo systems with integral control.......Page 177
9.3.1. State estimator.......Page 181
9.3.3. Estimator design......Page 182
9.3.4. Reduced-order estimator......Page 184
10.1 Cascade control......Page 189
10.2 Feedforward control......Page 194
10.3 Feedforward-feedback control......Page 197
10.4 Ratio control......Page 198
10.5 Time delay compensation—the Smith predictor......Page 199
10.6 Multiple-input Multiple-output Control......Page 201
10.6.1 MIMO Transfer functions......Page 202
10.6.2 Process gain matrix......Page 203
10.6.3 Relative gain array......Page 205
10.7.1 Alternate definition of manipulated variables......Page 207
10.7.2 Decoupler functions......Page 208
10.7.3 Feedforward decoupling functions......Page 210