Fractional Order PID and ADR Controls

This book explores the design and analysis of fractional-order and active disturbance rejection control, examining both the theoretical foundations and their practical applications. It covers fractional-order proportional-integral-derivative (PID) control, fractional-order active disturbance rejection (ADR) control, and the combined fractional-order PID-ADR control. The book begins with an analysis of the three-parameter fractional-order PID controller, demonstrating its application to the permanent magnet synchronous motor (PMSM) speed servo system, due to its comprehensive inclusion of proportional, integral, and differential elements. It then delves into active disturbance rejection control and periodic disturbance compensation, comparing the performance of each controller based on various parameters. This comparison enables readers to critically evaluate the advantages and limitations of each approach before implementation. Offering a thorough guide to fractional-order and active disturbance rejection control, the book also includes numerical methods for assessing and developing these systems. The book will be of particular interest to professionals working with numerical methods, fractional-order systems and control, PID controller, active disturbance rejection, control design, and production and is especially relevant to those in mechanical, industrial, and electrical engineering.

Pengchong Chen earned a PhD in mechanical science and engineering at Huazhong University of Science and Technology, Wuhan, China, in 2022. He is currently an Associate Professor in the School of Electrical and Information Engineering at Zhengzhou University, Zhengzhou, China. Dr. Chen's research interests include mechatronics, robotic control, fractional order, and active disturbance rejection controls. Ying Luo earned a PhD in control theory and engineering with a joint-PhD program at South China University of Technology (China) and Utah State University (USA) in 2009. He was an Assistant Research Professor at the Center for Self-Organizing and Intelligent Systems in the Department of Electrical and Engineering at Utah State University from 2009 to 2010. Dr. Luo is currently a Professor at the School of Automation Science and Engineering at the South China University of Technology, Guangzhou, China. His research interests include applied fractional calculus in modeling and controls, mechatronics and robotics, active disturbance rejection controls, and smart control engineering.

Section I: Fundamentals of Fractional Order PID and ADR Controls. 1. Introduction. Section II: Fractional Order PID Control. 2. Robust Three-Parameter FOPID Control. 3. Optimal Four-Parameter FOPI- D Control. 4. Five-Parameter FO-PI-Dµ Control. 5. Fractional Order PI-Dµ Control Design with Bode's Ideal Cutoff Filter. Section III: Fractional Order ADR Control. 6. FO-ADRC with the Idea of a Cascaded FO Integrator. 7. Quasi-Fractional-Resonant-NESO Design for PMSM Servo Current Measurement Error. 8. Resonant-Model-Based ADRC Compensation with Future Work on FO-ADRC. Section IV: Fractional Order PID and ADR Control. 9. Optimal Fractional Order PD and ADR Control. 10. A Two-Degree-of-Freedom Controller Design Satisfying Separation Principle with FOPD and Generalized ESO.