Structure and Synthesis of Pid Controllers

by Datta, Aniruddha; Ho, Ming-Tzu; Bhattacharyya, Shankar P.

• ISBN13: 9781852336141
• ISBN10: 1852336145
• Format: Hardcover
• Copyright: 1999-10-01
• Publisher: Springer Verlag

Summary

In many industrial applications, the existing constraints mandate the use of controllers of low and fixed order while, typically, modern methods of optimal control produce high order controllers. Structure and Synthesis of PID Controllersseeks to start to bridge the resultant gap and presents a novel methodology for the design of low-order controllers such as those of the P, PI and PID types. Written in a self-contained and tutorial fashion, this research monograph first develops a fundamental result, generalizing a classical stability theorem - the Hermite-Biehler Theorem - and then applies it to designing controllers that are widely used in industry. It contains material on: current techniques for PID controller design, generalization of the Hermite-Biehler theorem, stabilization of linear time-invariant plants using PID controllers, optimal design with PID controllers, robust and non-fragile PID controller design, stabilization of first-order systems with time delay, constant-gain stabilization with desired damping, constant-gain stabilization of discrete-time plants. Practitioners, researchers and graduate students should find this book a valuable source of information on cutting-edge research in the field of control.

Table of Contents

Overview of Control Systems	1	(14)
Introduction to Control	1	(2)
The Magic of Integral Control	3	(3)
PID Controllers	6	(2)
Feedback Stabilization of Linear Systems	8	(3)
The Characteristic Polynomial	8	(1)
Stabilization by observer based state feedback	9	(1)
Pole placement compensators	10	(1)
YJBK Parametrization	11	(1)
Optimal Control	11	(3)
Linear Quadratic Regulator (LQR)	11	(2)
H∞ Optimal Control	13	(1)
Notes and References	14	(1)
Some Current Techniques for PID Controller Design	15	(10)
The Ziegler-Nichols Step Response Method	15	(1)
The Ziegler-Nichols Frequency Response Method	16	(3)
PID Settings using the Internal Model Controller Design Technique	19	(3)
Dominant Pole Design: The Cohen-Coon Method	22	(1)
New Tuning Approaches	22	(2)
Time Domain Optimization Methods	23	(1)
Frequency Domain Shaping	23	(1)
Optimal Control Methods	23	(1)
Contribution of this Book	24	(1)
The Hermite-Biehler Theorem and Its Generalization	25	(26)
Introduction	25	(1)
The Hermite-Biehler Theorem for Hurwitz Polynomials	26	(7)
Root Distribution and Net Accumulated Phase	33	(1)
Imaginary and Real Signatures Associated with a Real Polynomial	34	(1)
Generalizations of the Hermite-Biehler Theorem	35	(10)
No Imaginary Axis Roots	35	(3)
No Roots at the Origin	38	(4)
No Restriction on Root Locations	42	(3)
An Elementary Derivation of the Routh-Hurwitz Criterion	45	(4)
Singular Cases	48	(1)
Notes and References	49	(2)
Stabilization of Linear Time-invariant Plants Using PID Controllers	51	(42)
Introduction	51	(1)
A Characterization of All Stabilizing Feedback Gains	52	(12)
A Characterization of All Stabilizing PI Controllers	64	(7)
A Characterization of All Stabilizing PID Controllers	71	(10)
PID Controllers Without Pure Derivative Action	81	(3)
Some Applications of the Stabilizing PID Characterization	84	(7)
Assessing the Stability of a Ziegler-Nichols Design	84	(4)
A Possible Approach for Redesigning the PID Parameters	88	(3)
Notes and References	91	(2)
Optimal Design Using PID Controllers	93	(32)
Introduction	93	(1)
Unconstrained Order Optimal Designs	94	(2)
H∞ Robust Controller Design Using the YJBK Parametrization	94	(1)
H2 Optimal Controller Design using the YJBK Parametrization	95	(1)
Design Using a Constant Gain	96	(1)
Design Using a PI Controller	97	(9)
Design Using a PID Controller	106	(18)
Notes and References	124	(1)
Robust and Non-fragile PID Controller Design	125	(16)
Introudction	125	(1)
Kharitonov's Theorem and Its Generalization	126	(2)
Robust Stabilization Using a Constant Gain	128	(2)
Robust Stabilization Using a PI Controller	130	(4)
Robust Stabilization Using a PID Controller	134	(3)
Design of Robust and Non-Fragile PID Settings	137	(2)
Notes and References	139	(2)
Stabilization of First-order Systems with Time Delay	141	(36)
Introduction	141	(1)
Extension of the Hermite-Biehler Theorem	142	(1)
Stabilization using a Constant Gain	143	(11)
Open-loop Stable Plant	145	(4)
Open-loop Unstable Plant	149	(5)
Stabilization using a Pure Integrator	154	(5)
Stabilization using a PI Controller	159	(14)
Open-loop Stable Plant	161	(11)
Open-loop Unstable Plant	172	(1)
Notes and References	173	(4)
Constant Gain Stabilization with Desired Damping	177	(28)
Introduction	177	(1)
Problem Formulation	178	(4)
Generalized Hermite-Biehler Theorem: Complex Polynomials	182	(11)
Root Distribution and Net Accumulated Phase	182	(1)
Generalizations of the Hermite-Biehler Theorem	183	(10)
Stabilization with Damping Margin Using a Constant Gain	193	(7)
Example	200	(3)
Notes and References	203	(2)
Constant Gain Stabilization of Discrete-time Plants	205	(22)
Introduction	205	(1)
The Hermite-Biehler Theorem for Schur Polynomials	206	(7)
Poles and Zeros in the Unit Disc and Net Accumulated Phase	213	(1)
Discrete-time Versions of the Generalized Hermite-Biehler Theorem	214	(2)
Stabilization Using a Constant Gain	216	(9)
Notes and References	225	(2)
Appendix A. Root Locus Ideas for Narrowing the Sweeping Range for kp	227	(4)
References	231	(4)
Index	235