PID Tuning : A Modern Approach via the Weighted Sensitivity Problem book cover
1st Edition

PID Tuning
A Modern Approach via the Weighted Sensitivity Problem

  • Available for pre-order. Item will ship after October 22, 2020
ISBN 9780367343729
October 22, 2020 Forthcoming by CRC Press
168 Pages - 74 B/W Illustrations

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Book Description

PID controller is the most common option in the realm of control applications and is dominant in the process control industry. Amongst the related analytical methods, Internal Model Control (IMC) has gained remarkable industrial acceptance due to their robust nature and good set-point responses, but they do result in poor load disturbance rejection for integrating/lag-dominant plants. This book presents an H∞ design which avoids some of the limitations of the IMC method, devised to work well for plants of modest complexity, for which analytical PID tuning is plausible. To alleviate the usual difficulties, plain H∞ weighted sensitivity problem has been described including chapters on Hinf and IMC control. Aimed at graduate students and researchers in control engineering, this book:

  • Considers PID controller tuning from a new perspective of use of modern control theory allowing the explicit handling of the servo/regulation and robustness trade-offs.
  • Gives a systematic optimization-based approach.
  • Help tune PID controllers in a unified way, encompassing stable, integrating, and unstable processes.
  • Pose the design problem analytically in terms of the weighted sensitivity problem.
  • Provide alternative, analytically based, derivations of existing tuning proposals.

Table of Contents

1.1 Servo, Regulation and Stability
1.2 Industrial (PID) Control
1.3 IMC and H-inf Control
1.3.1 Internal Model Control
1.3.2 H∞ control
1.3.3 Blending IMC and H∞ control
1.3.4 Vilanova’s (2008) design for robust PID tuning revisited
1.4 Outline of the book
I Model Matching approach to Robust PID design
2 Simple Model matching approach to Robust PID control
2.1 Problem statement
2.1.1 The control framework
2.1.2 The Model Matching Problem
2.1.3 The Model Matching problem within H∞ control
2.2 Analytical Solution
2.2.1 Initial formulation for set-point response
2.2.2 Alternative formulation
2.3 Stability analysis
2.3.1 Nominal stability
2.3.2 Robust stability
2.4 Automatic PID tuning derivation
2.4.1 Control effort constraints
2.5 Simulation examples
3 Alternative design for load disturbance improvement
3.1 Problem statement
3.1.1 The control framework
3.1.2 The Model Matching Problem formulation
3.2 Model matching solution for PID design
3.3 Trade-off tuning interval considering load disturbances
3.3.1 Nominal stability
3.4 Quantitative tuning guidelines
3.5 Simulation examples
3.5.1 Example 1
3.5.2 Example 2
4 Analysis of the smooth/tight - servo/regulation tradeoff
4.1 Revisiting the Model Matching designs
4.2 Smooth/Tight tuning analysis
4.3 Comparison of the servo and load disturbance based tuning approaches
4.4 Implementation aspects
4.5 Simulation examples
4.6 Summary
II Weight selection for Sensitivity Problem
5 H∞ design with application to PI tuning
5.1 Problem scenario
5.2 Analytical solution
5.3 Weight Selection
5.4 Stability and Robustness Analysis
5.5 Application to PI Tuning
5.5.1 Stable/unstable plants
5.5.2 Integrating plant case (τ → ∞)
5.6 Examples and comparisons
5.6.1 Example 1
5.6.2 Example 2
5.6.3 Example 3
5.6.4 Example 4
6 Generalized IMC design and H2 approach
6.1 Motivation for input/output disturbances tradeoff
6.2 IMC problem statement
6.3 Suitable weight selection for H2 control
6.4 Analytical solution
6.4.1 Analytical solution in terms of alternative IMC filters
6.4.2 Extension to plants with integrators or complex poles
6.5 Control system analysis: Performance and Robustness
6.5.1 General relations
6.6 Tuning guidelines
6.7 Examples and comparisons
III Weighted Sensitivity approach for Robust PID tuning
7 PID Design as a weighted sensitivity problem
7.1 Context, motivation and objective
7.2 Servo/Regulation and Robustness tradeoff
7.3 PID design problem. Statement and Unifying PID tuning
7.4 Special cases and tuning rule simplifications
7.4.1 First Order Cases (τ2 = 0)
7.4.2 Second Order Cases
7.5 Applicability: Normalized dead time range
8 PID tuning guidelines for a balanced (servo/regulation)-robust operation
8.1 Robustness and comparable designs
8.2 Performance (Servo/Regulation) evaluation
8.3 PI control using first order models
8.3.1 Stable and integrating cases Tuning based on Jmax Tuning based on Javg
8.3.2 Unstable case Tuning based on Jmax and Javg
8.4 PID control using second order models
8.4.1 Stable and integrating cases Tuning based on Jmax Tuning based on Javg
8.4.2 Unstable case Tuning based on Jmax and Javg
A Appendix 1

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Ramón Vilanova was born in Lérida, Spain, on September 10, 1968. He graduated in the Autonomous University of Barcelona (1991) obtaining the title of doctor through the same University (1996). At present he occupies the position of Lecturer at the School of Engineering of the Autonomous University of Barcelona where develops educational task teaching subjects of Signals and Systems, Automatic Control and Technology of Automated Systems. His research interests include methods of tuning of PID regulators, systems with uncertainty, analysis of control systems with several degrees of freedom, application to environmental systems and development of methodologies for design of machine-man interfaces. He is author of several book chapters and has more than 100 publications in international congresses/journals. He is a member of IEEE and SIAM. Salvador Alcántara received the B.S. in computer engineering in 2005, and the M.S. and PhD degrees in Systems Engineering and Automation in 2008 and 2011, respectively, all from the Autonomous University of Barcelona. Now, he holds a Post-Doc position at the Department of Telecommunications and Systems Engineering of the same university, where he also is (still) a mathematics undergraduate student. His primary research interests include simple analytical designs, PID tuning, robust and intelligent control, and time delay systems. Carles Pedret was born in Tarragona, Spain, on January 29, 1972. He received the B.Sc. degree in Electronic Engineering and the Ph.D. degree in System Engineering and Automation from the Autonomous University of Barcelona, in 1997 and 2003, respectively. He is Associate Professor at the department of Telecommunications and System Engineering of the Autonomous University of Barcelona. His research interest is in uncertain systems, time-delay systems and PID control.