Internal Model Control Design Based on Equal Order Fractional Butterworth Filter for Multivariable Systems

An internal model control with inverted decoupling (ID-IMC) controller design method based on equal fractional Butterworth (EFBW) filter is proposed for Multiple Input-Multiple Output (MIMO) systems with multiple time delays and Right Half Plane (RHP) zeros. There has been finite memory and limited flexibility for multivariable processes developed using a direct ID-IMC method. This paper presents a novel procedure to approximate Butterworth (BW) filters using fractional-order (FO) theories, so that the degree-of-freedom for tunable parameters is increased. The proposed ID-IMC controller cascaded with EFBW filter combines the computational simplicity of the ID-IMC structure with the greater flexibility of the EFBW filter, in conjunction with a better set-point tracking and disturbance rejection performance. Further, the stability analysis of the designed controller is given to ensure the stability of the closed-loop system. Dynamic performance indicators and sensitivity functions are carried out for the time domain and robustness analysis. Two illustrative examples are presented to show the merits of the proposed method.