Fractional Order IMC Controller Design for Two-input-two-output Fractional Order System

• Published in: International journal of control, automation, and systems Vol. 17; no. 4; pp. 936 - 947
• Main Authors: Li, Dazi, He, Xingyu, Song, Tianheng, Jin, Qibing
• Format: Journal Article
• Language: English
• Published: Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01-04-2019; Springer Nature B.V; 제어·로봇·시스템학회
• Subjects: Automation; Calculus; Control; Control methods; Control stability; Control systems design; Controllers; Decoupling method; Engineering; Mathematical functions; Mathematical models; Mechatronics; Methods; Parameter sensitivity; Process controls; Regular Papers; Robotics; Robustness (mathematics); Systems stability; Time lag; 제어계측공학; two-input-two-output process; Fractional order system; time delay; maximum sensitivity function; internal model control; Lyapunov stability theory; inverted decoupling
• ISSN: 1598-6446; 2005-4092
• DOI: 10.1007/s12555-018-0129-3

Research on the fractional order system is becoming more and more popular. Most of the fractional order controller design methods focus on single-input-single-output processes. In this paper, a fractional order internal model controller with inverted decoupling is proposed to handle non-integer order two-input-two-output systems with time delay. The fractional order two-input-two-output (FO-TITO) process is decoupled by inverted decoupling method. The fractional order internal model control (IMC) is then used to simplify the tuning process. Because of the complexity of multiple time delay, the condition of FO-TITO process with time delay is discussed. In order to ensure the robustness of the system, a Maximum sensitivity function is used to tune the parameters. Then Lyapunov stability theory is applied to verify the stability of the system. The proposed controller provides ideal performance for both set point-tracking and disturbance rejection and is robust to process gain variations. Numerical results show the performance of the proposed method.