Page 6 - Servo Motors and Industrial Control Theory

Contents

1 Feedback Control Theory ......................................................................... 1
1.1 Linear System ...................................................................................... 1
1.2 Nonlinear Systems .............................................................................. 2
1.3 Linearization Technique ...................................................................... 3
1.4 Laplace Transform .............................................................................. 4
1.5 Transfer Function ................................................................................ 7
1.6 First Order Transfer Function .............................................................. 7
1.7 Frequency Response ............................................................................ 10
1.8 Second Order Transfer Function ......................................................... 11
1.9 Block Diagram Representation ........................................................... 13
1.10 Frequency Response ............................................................................ 14
1.11 Conclusion ........................................................................................... 16

2 Feedback Control Theory Continued ...................................................... 17
2.1 Introduction ......................................................................................... 17
2.2 Routh–Hurwitz Stability Criteria ........................................................ 17
2.3 Root Locus Method ............................................................................. 19
2.4 Important Features of Root Locus ....................................................... 23
2.5 Proof of Nyquist Stability Criterion .................................................... 29
2.6 Nyquist Plot ......................................................................................... 31
2.7 Bode Diagram ..................................................................................... 36
2.8 Steady State Error ............................................................................... 46

3 State Variable Feedback Control Theory ................................................ 49
3.1 Introduction ......................................................................................... 49
3.2 State Variables ..................................................................................... 50
3.3 Eigenvalues, Eigenvectors, and Characteristic Equation .................... 53
3.4 State Variable Feedback Control Theory ............................................ 56
3.5 Dynamic Observer .............................................................................. 60
3.6 Controllability and Observability ........................................................ 61
3.7 Conclusion........................................................................................... 63

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