Road Map for Sliding Mode Control Design (SpringerBriefs in Mathematics)

✍ Scribed by Vadim Utkin, Alex Poznyak, Yury V. Orlov, Andrey Polyakov

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 134
• Category: Library

✦ Synopsis

This book is devoted to control of finite and infinite dimensional processes with continuous-time and discrete time control, focusing on suppression problems and new methods of adaptation applicable for systems with sliding motions only. Special mathematical methods are needed for all the listed control tasks. These methods are addressed in the initial chapters, with coverage of the definition of the multidimensional sliding modes, the derivation of the differential equations of those motions, and the existence conditions. Subsequent chapters discusses various areas of further research. The book reflects the consensus view of the authors regarding the current status of SMC theory. It is addressed to a broad spectrum of engineers and theoreticians working in diverse areas of control theory and applications. It is well suited for use in graduate and postgraduate courses in such university programs as Electrical Engineering, Control of Nonlinear Systems, and Mechanical Engineering.

✦ Table of Contents

Preface
Contents
About the Authors
1 Introduction
References
2 Mathematical Methods
2.1 Definition of Sliding Mode
2.2 Solution Existence and Uniqueness Problem
2.3 Filippov Solution
2.4 Equivalent Control Method
2.5 Sliding Mode Equations in Control Affine Systems
2.6 Regularization
References
3 Design Principles
3.1 Sketch of the Design Procedure
3.2 Regular Form
3.3 Reaching and Existence Conditions
3.4 Decoupling
3.5 Invariance
3.6 Output Sliding Mode Control
3.7 Integral SMC
3.7.1 Main Idea
3.7.2 Design Method
3.8 Unit Control
3.9 Second-Order Sliding Mode Control
3.9.1 Twisting Algorithm
3.9.2 Super-Twisting Algorithm
3.10 Suboptimal Control
References
4 Lyapunov Stability Tools for Sliding Modes
4.1 Finite-Time Stabilization: What is This?
4.2 Strict Lyapunov Functions
4.3 Finite-Time Stability and Homogeneity
4.4 Fixed-Time Stability
References
5 SM Observers
5.1 Observers for Linear Time-Invariant Systems
5.2 Observers for Uncertain Systems
5.2.1 Second-Order System
5.2.2 Uncertain System of an Arbitrary Order
5.2.3 Analysis of the State Estimation Error Convergence for Matched Disturbances
5.2.4 Differentiators
References
6 Chattering Problem
6.1 What is Chattering? Basic Ideas
6.2 Power Converters
References
7 High-Order Sliding Mode Control
7.1 HOSM Definition and Its Properties
7.2 Simple Examples of Systems with HOSM Control
7.3 HOSM in SISO Affine Systems in Regulation and Tracking Problems
7.3.1 Uncertain Plant
7.3.2 Lyapunov Function for HOSM Controllers' Analysis
7.3.3 HOSM Controllers
7.3.4 Discontinuous and Quasi-Continuous HOSM Controllers for SISO Systems
References
8 Discrete-Time Systems
8.1 Discretization of Continuous-Time Models
8.2 Definition of SM for Discrete-Time Systems
8.3 Behavior Under Uncertainties
References
9 Adaptive SMC
9.1 The σ-Adaptation Method
9.2 The Dynamic Adaptation Based on the Equivalent Control Method
9.2.1 The Simple Motivating Example
9.2.2 Multidimensional Case
9.3 Super-Twisting Control with Adaptation
References
10 SMC in Infinite-Dimensional Systems
10.1 Infinite-Dimensional Setting
10.2 Unit Control for Infinite-Dimensional Systems
References
11 Open Problems in SMC
11.1 Stability Problem of the System =Asign( x)
11.2 SMC in the Presence of Noise in Measurements
11.3 Finite-Time Stability of SMs in Infinite-Dimensional Systems
11.4 A Little Fantasy: SMC for Systems Governed by Shift Operators
11.5 On Stochastic SM
References
12 Conclusions