Page 9 - Practical Control Engineering a Guide for Engineers, Managers, and Practitioners

Contents ix

4-5 A First-Order with Dead-Tune (FOWDT)
Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4-5-1 The Concept of Minimum Phase 109
4-5-2 Proportional-Dnly Control . . . . . . . . 109
4-5-3 Proportional-Integral Control of the
FOWDT Process . . . . . . . . . . . . . . . . . 111
4-6 A Few Comments about Simulating
Processes with Variable Dead Tunes . . . . . . . 114
4-7 Partial Summary and a Slight Modification
of the Rule of Thumb . . . . . . . . . . . . . . . . . . . 116
4-8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

5 Matrices and Higher-Order Process Models 121
5-1 Third-Order Process without
Backflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5-2 Third-Order Process with
Backflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5-3 Control of Three-Tank System with No
Backflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5-4 Critical Values and Finding the Poles 139
5-5 Multitank Processes . . . . . . . . . . . . . . . . . . . . 140
5-6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

6 An Underdamped Process . . . . . . . . . . . . . . . . . . . • . 145
6-1 The Dynamics of the Mass/Spring/
Dashpot Process . . . . . . . . . . . . . . . . . . . . . . . . 145
6-2 Solutions in Four Domains . . . . . . . . . . . . . . 149
6-2-1 Tune Domain . . . . . . . . . . . . . . . . . . . . 149
6-2-2 Laplace Domain Solution . . . . . . . . . 149
6-2-3 Frequency Domain . . . . . . . . . . . . . . . 150
6-2-4 State-Space Representation . . . . . . . . 151
6-2-5 Scaling and Round-Off Error 152
6-3 PI Control of the Mass/Spring/Dashpot
Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6-4 Derivative Control (PID) . . . . . . . . . . . . . . . . 156
6-4-1 Complete Cancellation . . . . . . . . . . . . 161
6-4-2 Adding Sensor Noise . . . . . . . . . . . . . 161
6-4-3 Filtering the Derivative . . . . . . . . . . . 163
6-5 Compensation before Control-The Transfer
Function Approach . . . . . . . . . . . . . . . . . . . . . 165
6-6 Compensation before Control-The State-Space
Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
6-7 An Electrical Analog to the Mass/Dashpot/
Spring Process . . . . . . . . . . . . . . . . . . . . . . . . . 174
6-8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176