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

作     者：Ogunba, Kolawole S. Fakunle, Afeez A. Ogunfunmi, Tokunbo Taiwo, Oluwafemi 

作者机构：Santa Clara Univ Dept Elect & Comp Engn Santa Clara CA 95053 USA Obafemi Awolowo Univ Dept Chem Engn Proc Syst Engn Lab Ife 220282 Osun Nigeria 

出 版 物：《IEEE ACCESS》 (IEEE Access)

年 卷 期：2023年第11卷

页      面：32201-32228页

核心收录：

基　　金：Alexander von Humboldt Foundation Fund Santa Clara University School of Engineering Inclusive Excellence Postdoctoral Fellowship for 2022/2023 Session 

主　　题：Triangular decoupling multivariable systems multi-input multi-output systems square systems open-loop-stable systems nonminimum-phase systems RHP transmission zeros internal model control input delays model simplification 

摘      要：The Analytical Triangular Decoupling Internal Model Control (ATDIMC) technique for 2 x 2 systems is generalized to n x n systems (n = 2) with delays and right-half-plane (RHP) transmission zeros. The formulation is done by first creating a triangular closed-loop transfer function matrix corresponding to the achievement of the triangular decoupling objective of restraining inverse-response and control-loop-interaction characteristics to a single plant output. Subsequently, the corresponding multivariable internal model controller is calculated, with transfer-function approximations made using an optimization algorithm that minimizes the Integral Time-Weighted Absolute Error (ITAE) of the difference between the step responses of the original and reduced expressions. It is shown that n ATDIMC designs emerge that achieve the shifting of inverse responses and interactions to a least-desired output, with delays retained for all outputs and asymptotic tracking of setpoints achieved for all n outputs of each design. To mitigate the possible effect of severe interaction on the least-desired output, a modification of this formulation is performed to spread inverse-response behavior to a second output, while minimizing the interaction of that output with the initial least-desired output. Simulation results for selected 3 x 3 and 4 x 4 systems show the effectiveness of these propositions.