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

Abstract

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.

Extended Approach to Analytical Triangular Decoupling Internal Model Control of Square Stable Multivariable Systems With Delays and Right-Half-Plane Zeros

“…For square MIMO systems with delays and without RHP transmission zeros, the process of design of controllers using DIMC involves approximate transfer function matrix inversion, with appropriate elements of the resulting controller matrix approximated to rational transfer functions with delays [11,12,14]. Because of the intuitive appeal of dynamic decoupling [16], many multivariable control formulations have been developed over the years using the dynamic decoupling concept, with IMC either used directly or together with such concepts such as Simplified Decoupling and Inverted Decoupling achieve control using an IMC structure or a conventional feedback structure ( [15], [17][18][19][20][21][22][23][24]).…”

Fractional PID controller based on biggest log modulus tuning method with MOPSO optimization for distillation column

“…In literature, there are many works in fractional domain in many fields and the control system is one of them. It was applied for monovariable system [9], [10], multivariable systems [11]- [14] and for fractional multivariable systems [15], [16].…”