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

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.