PID Trajectory Tracking Control for Mechanical Systems

Przednia okładka
Springer Science & Business Media, 23 sty 2004 - 112
Though PID control has a long history as much as its life force since Ziegler and Nichols published the empirical tuning rules in 1942, surprisingly, it has never been changed in the structure itself. The strength of PID control lies in the simplicity, lucid meaning, and clear e?ect. Though it must be a widely - cepted controller for mechanical control systems, it is still short of theoretical bases,e.g., optimality, performance tuning rules, automatic performance t- ing method, and output feedback PID control have not been clearly presented formechanicalcontrolsystems.Thesesubjectswillbethoroughlydiscussedin this book. There are many books of PID controller for the purpose of process control, but it is hard to ?nd a book on the characteristics of PID control for mechanical systems. In the ?rst place, when nonlinear optimal control theory is applied to mechanical systems, a class of Hamilton-Jacobi (HJ) equations is derived as a result of optimization. There are two methods to solve a class of HJ eq- tions: a direct method using an approximation and inverse method ?nding the performance index from a class of HJ equations. Also, there are two control methods according to the objective: the set-point regulation control and t- jectory tracking control. The trajectory tracking control is basically di?erent from set-point regulation one in that the desired con?guration, velocity and acceleration pro?les according to time progress are added to the motion of mechanical system. This book is focusing on an inverse optimization method and the trajectory tracking control system.
 

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Spis treści

Introduction
3
12 Historic PD and PID
4
13 Book Preview
5
14 Notations
7
Robust and Optimal Control for Mechanical Systems
9
22 Nonlinear Mechanical Control Systems
10
221 Lagrangian System
11
222 Hamiltonian System
12
43 Compound Performance Tuning
56
431 Performance Limitation for Composite Error
57
432 Compound Rule
59
433 Illustrative Example
60
44 Experimental Results
61
Square and Linear Rules
62
Performance Estimation by Optimality
66
Compound Rule
67

23 SetPoint Regulation Control
13
232 Direct
15
24 Trajectory Tracking Control
18
242 𝓗₀₀ Control of a ModifiedCTC Park and Chung
22
25 Notes
26
Full State Feedback PID Control
27
𝓗₀₀ Optimality of PID Control
29
32 StateSpace Description of Lagrangian Systems
30
33 ISS and 𝓗₀₀ Optimality of PID Control
32
332 Hoo Optimality of PID Control Law
35
34 Inverse Optimal PID Control
38
341 Selection Guidelines for Gains
40
342 Performance Estimation by Optimality
42
343 Illustrative Example
43
35 Summary
46
Performance Limitation and Tuning
47
42 Square and Linear Performance Tunings
48
422 Square and Linear Rules
53
423 Illustrative Example
54
45 Summary
69
Automatic Performance Tuning
70
52 Quasiequilibrium Region
71
53 Automatic Performance Tuning
74
531 Autotuning Law
75
532 Criterion for Autotuning
77
533 Performance Enhanced by Autotuning Law
78
54 Model Adaptation
80
55 Experimental Results
82
56 Summary
84
62 Normal Form of Lagrangian Systems
89
63 PID State Observer
90
632 Stability
92
633 ReducedOrder ID State Observer
97
64 Notes
99
Concluding Remarks
100
References
102
Index
106
Prawa autorskie

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