Discrete-Time Inverted Decoupling Internal Model Control of Multivariable Systems Based on Improved Fractional-Order Butterworth Filter

A novel discrete-time inverted decoupling internal model control (IMC) strategy is proposed for discrete-time multivariable systems with time-delays and RHP zeros. The strategy integrates an improved fractional-order Butterworth filter (FOBF) into the control framework. Key contributions include the design of a high-order improved FOBF by cascading stable fractional-order and integer-order filters, guaranteeing stability through W-plane mapping analysis, and developing an efficient direct discretization method based on frequency response matching. Simulation examples demonstrate the controller’s effectiveness in enhancing tracking performance and robustness against disturbances and model uncertainties.