PID Trajectory Tracking Control for Mechanical Systems (Lecture Notes in Control and Information Sciences Vol.298) (2004. XVI, 111 p. w. 22 figs.)

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PID Trajectory Tracking Control for Mechanical Systems (Lecture Notes in Control and Information Sciences Vol.298) (2004. XVI, 111 p. w. 22 figs.)

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Description


(Text)
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.
(Table of content)
1 Introduction.- 2 Robust and Optimal Control for Mechanical Systems.- 3 Optimality of PID Control.- 4 Performance Limitation and Tuning.- 5 Automatic Performance Tuning.- 6 Output Feedback PID Control.- 7 Concluding Remarks.

Table of Contents

Part I Preliminaries
1 Introduction 3 (6)
1.1 Motivation 3 (1)
1.2 Historic PD and PID 4 (1)
1.3 Book Preview 5 (2)
1.4 Notations 7 (2)
2 Robust and Optimal Control for Mechanical 9 (20)
Systems
2.1 Introduction 9 (1)
2.2 Nonlinear Mechanical Control Systems 10 (3)
2.2.1 Lagrangian System 11 (1)
2.2.2 Hamiltonian System 12 (1)
2.3 Set-Point Regulation Control 13 (5)
2.3.1 Global Asymptotic Stability 13 (2)
[Arimoto et al.]
2.3.2 Direct Ηinfinity Control [Choi 15 (3)
et al.]
2.4 Trajectory Tracking Control 18 (8)
2.4.1 Optimal Control of a Modified-CTC 18 (4)
[Dawson et al.]
2.4.2 Ηinfinity Control of a 22 (4)
Modified-CTC [Park and Chung]
2.5 Notes 26 (3)
Part II Full State Feedback PID Control
3 Ηinfinity Optimality of PID Control 29 (18)
3.1 Introduction 29 (1)
3.2 State-Space Description of Lagrangian 30 (2)
Systems
3.3 ISS and Ηinfinity Optimality of PID 32 (6)
Control
3.3.1 ISS-CLF for Lagrangian Systems 32 (3)
3.3.2 Ηinfinity Optimality of PID 35 (3)
Control Law
3.4 Inverse Optimal PID Control 38 (8)
3.4.1 Selection Guidelines for Gains 40 (2)
3.4.2 Performance Estimation by Optimality 42 (1)
3.4.3 Illustrative Example 43 (3)
3.5 Summary 46 (1)
4 Performance Limitation and Tuning 47 (24)
4.1 Introduction 47 (1)
4.2 Square and Linear Performance Tunings 48 (8)
4.2.1 Performance Limitation for State 48 (5)
Vector
4.2.2 Square and Linear Rules 53 (1)
4.2.3 Illustrative Example 54 (2)
4.3 Compound Performance Tuning 56 (5)
4.3.1 Performance Limitation for 57 (2)
Composite Error
4.3.2 Compound Rule 59 (1)
4.3.3 Illustrative Example 60 (1)
4.4 Experimental Results 61 (8)
4.4.1 Experiment: Square and Linear Rules 62 (4)
4.4.2 Experiment: Performance Estimation 66 (1)
by Optimality
4.4.3 Experiment: Compound Rule 67 (2)
4.5 Summary 69 (2)
5 Automatic Performance Tuning 71 (18)
5.1 Introduction 71 (1)
5.2 Quasi-equilibrium Region 72 (3)
5.3 Automatic Performance Tuning 75 (6)
5.3.1 Auto-tuning Law 76 (2)
5.3.2 Criterion for Auto-tuning 78 (1)
5.3.3 Performance Enhanced by Auto-tuning 79 (2)
Law
5.4 Model Adaptation 81 (2)
5.5 Experimental Results 83 (2)
5.6 Summary 85 (4)
Part III Output Feedback PID Control
6 Output Feedback PID Control 89 (12)
6.1 Introduction 89 (1)
6.2 Normal Form of Lagrangian Systems 90 (1)
6.3 PID State Observer 91 (9)
6.3.1 Observer Gain 91 (2)
6.3.2 Stability 93 (5)
6.3.3 Reduced-Order ID State Observer 98 (2)
6.4 Notes 100(1)
7 Concluding Remarks 101(2)
References 103(4)
Index 107