PID Tuning

A Modern Approach via the Weighted Sensitivity Problem

Salvador Alcántara Cano, Ramon Vilanova Arbós, Carles Pedret i Ferré

• Publisher: CRC Press
• Year: 2020
• eBook ISBN: 9781000208528
• Edition: 1
• Topic: Scienze fisiche
• Subtopic: Ingegneria elettronica e telecomunicazioni

The PID controller is the most common option in the realm of control applications and is dominant in the process control industry. Among the related analytical methods, Internal Model Control (IMC) has gained remarkable industrial acceptance due to its robust nature and good set-point responses. However, the traditional application of IMC results in poor load disturbance rejection for lag-dominant and integrating plants. This book presents an IMC-like design method which avoids this common pitfall and is devised to work well for plants of modest complexity, for which analytical PID tuning is plausible. For simplicity, the design only focuses on the closed-loop sensitivity function, including formulations for the H? and H2 norms. Aimed at graduate students and researchers in control engineering, this book:

• Considers both the robustness/performance and the servo/regulation trade-offs
• Presents a systematic, optimization-based approach, ultimately leading to well-motivated, model-based, and analytically derived tuning rules
• Shows how to tune PID controllers in a unified way, encompassing stable, integrating, and unstable processes
• Finds in the Weighted Sensitivity Problem the sweet spot of robust, optimal, and PID control
• Provides a common analytical framework that generalizes existing tuning proposals

1

Introduction

The aim of this introduction is to guide the reader through the content of subsequent chapters, offering a high-level presentation of the underlying concepts and ideas that appear all throught the book. The discussion that follows is based on the unity feedback, linear time invariant (LTI), and single-input-single-output (SISO) continuous-time system of Figure 1.1, where P is the plant and K the feedback controller to be designed. The output signals y, u represent, respectively, the plant output and the control action. Two exogenous inputs to the system are considered: d and r. Here, d represents a disturbance affecting the plant input, and the term regulator mode refers to the case when this is the main exogenous input.

Figure 1.1
Conventional feedback configuration.

1.1Servo, regulation, and stability

The term servo mode refers to the case when the set-point change r is the main concern. Although the reference tracking can be improved by using a two-degree-of-freedom (2DOF) controller [72, 20], there will always be some unmeasured disturbance directly affecting the plant output, which may be represented as an unmeasured signal r (in this case, the plant output would be the control error e = r − y). In summary, there is a fundamental trade-off between the regulator (input disturbance) and servo (output disturbance) modes. The closed-loop mapping for the system in Figure 1.1 is given by

[yu]=[TSPKSS][rd]≐H(P,K)[rd]	(1.1)

where S≐11+PK and T≐PK1+PK denote the sensitivity and complementary sensitivity functions [72], respectively (note that S + T = 1). In terms of the performance for the regulator and servo modes, the closed-loop effect of disturbance and set-point changes on the outpu...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Contents
• Foreword
• Preface
• Authors
• 1. Introduction
• I. Model-Matching Approach to Robust PID Design
• II. WEIGHT SELECTION FOR SENSITIVITY SHAPING
• III. WEIGHTED SENSITIVITY APPROACH FOR ROBUST PID TUNING
• Appendix A
• Bibliography
• Index