Active Disturbance Rejection Control for Nonlinear Systems

Bao-Zhu Guo, Chinese Academy of Sciences, China; University of the Witwatersrand, South Africahas been working on control theory since his PhD studies in the Chinese university of Hong Kong from 1987-1991. His main expertise is in control theory for systems described by partial differential equations or infinite-dimensional systems. In this area, he has published over 160 articles in international journals and three books. In 1999, Prof. Guo was awarded the One Hundred Talent Program from the Chinese Academy of Sciences. Other honours include the National Science Fund for Distinguished Young Scholars (2003) from the National Natural Science Foundation of China and the One Hundred Talent Program from Shanxi Province, China (2009).Zhi-Liang Zhao, Shaanxi Normal University, China is currently an associate professor in the Department of Mathematics. His research expertise is the convergence of active disturbance rejection control and is working on extending its application to more general nonlinear systems.

• Preface ix1 Introduction 11.1 Problem Statement 11.2 Overview of Engineering Applications 61.3 Preliminaries 91.3.1 Canonical Form of ADRC 91.3.2 Stability for Nonlinear Systems 181.3.3 Stability of Linear Systems 241.3.4 Finite-Time Stability of Continuous System 271.3.5 Stability of Discontinuous Systems 321.3.6 Proof of Theorem 1.3.11 341.4 Remarks and Bibliographical Notes 502 The Tracking Differentiator (TD) 532.1 Linear Tracking Differentiator 552.2 Nonlinear Tracking Differentiator 592.2.1 Second-Order Nonlinear Tracking Differentiator 602.2.2 High-Order Nonlinear Tracking Differentiator 642.3 Finite-Time Stable System-Based Tracking Differentiator 692.3.1 Convergence of Finite-Time Stable System-Based TD 702.3.2 A Second-Order Finite-Time Stable Tracking Differentiator 752.4 Illustrative Examples and Applications 772.4.1 Comparison of Three Differentiators 772.4.2 Applications to Frequency Online Estimation 812.4.3 Application to the Boundary Stabilization of Wave Equation 852.5 Summary and Open Problems 882.6 Remarks and Bibliographical Notes 893 Extended State Observer 933.1 Linear Extended State Observer for SISO Systems 943.2 Nonlinear Extended State Observer for SISO Systems 1003.2.1 Nonlinear ESO for SISO Systems 1013.2.2 Some Special ESO 1093.3 The ESO for SISO Systems with Time-Varying Gain 1193.4 The ESO for MIMO Systems with Uncertainty 1333.4.1 ESO for Systems with Total Disturbance 1333.4.2 ESO for Systems with External Disturbance Only 1413.4.3 Examples and Numerical Simulations 1443.5 Summary and Open Problems 1503.6 Remarks and Bibliographical Notes 1534 The Active Disturbance Rejection Control 1554.1 Linear ADRC for SISO Systems 1574.1.1 Global Convergence of Linear ADRC for SISO Systems 1574.1.2 Global Convergence for Systems with External Disturbance Only 1674.1.3 Semi-Global Convergence of LADRC 1764.1.4 Numerical Simulations 1834.2 Nonlinear ADRC for SISO Systems 1874.2.1 Global ADRC for SISO Systems with Total Disturbance 1874.2.2 Global ADRC for SISO System with External Disturbance Only 1954.2.3 Semi-global ADRC for SISO System with Vast Uncertainty 2034.2.4 Examples and Numerical Simulations 2044.3 ADRC with Time-Varying Tuning Parameter 2064.4 Nonlinear ADRC for MIMO Systems with Vast Uncertainty 2284.4.1 Semi-Global ADRC for MIMO Systems with Uncertainty 2314.4.2 Global ADRC for MIMO Systems with Uncertainty 2384.4.3 Global ADRC for MIMO Systems with External Disturbance Only 2454.4.4 Numerical Simulations 2504.5 IMP Versus ADRC 2524.6 HGC and SMC Versus ADRC 2634.7 Applications to PMSMs 2674.8 Application to Wave Equation with Uncertainty 2704.8.1 Control Design 2714.8.2 Proof of Theorem 4.8.1 2794.9 Summary and Open Problems 2874.10 Remarks and Bibliographical Notes 2895 ADRC for Lower Triangular Nonlinear Systems 2915.1 ESO for Lower Triangular Systems 2915.1.1 Constant High-Gain ESO 2925.1.2 Time-Varying Gain ESO 3015.1.3 Numerical Simulation 3065.2 Stabilization of Lower Triangular Systems by ADRC 3125.2.1 ADRC with Constant Gain ESO 3135.2.2 ADRC with Time-Varying Gain ESO 3275.3 Numerical Simulations 3315.4 Summary and Open Problems 3365.5 Remarks and Bibliographical Notes 338References 341Index 349