Inverted Decoupling Internal Model Control for MIMO Time-Delay Systems Based on Improved Butterworth Filter

A novel inverted decoupling internal model control (IMC) design is studied in this paper. The traditional inverted decoupling method is extended to multi-dimensional complex systems with multiple time-delays and right half plane (RHP) zeros, in which the necessary condition for the existence of the inverted decoupling elements is theoretically analyzed and deduced for the first time. To guarantee the realizability of the decoupling matrix elements, compensation and approximation methods for the relative degree, time-delays and RHP zeros are discussed. The proposed inverted decoupling method is suitable for both square and non-square multi-input multi-output (MIMO) systems with the advantages of simple calculation and more flexibility. In addition, using the IMC structure to facilitate the controller design and obtain a better control effect, the conventional low-pass IMC filter is replaced by a novel improved Butterworth filter. The characteristics of the traditional and improved Butterworth filters are compared and analyzed, which shows the improved Butterworth filter has better regulating abilities to get a trade-off between tracking performance and robustness. The proposed IMC controller also provides satisfactory performance with model mismatch and additive uncertainties. Theoretical analysis and simulation comparisons verify the validity and effectiveness of the proposed scheme.