Design of Non-rational MIMO Feedback Systems with Inputs and Outputs Satisfying Certain Bounding Conditions by Using Rational Approximants  

作　　者：Suchin Arunsawatwong Tadchanon Chuman 

机构地区：[1]Department of Electrical Engineering,Faculty of Engineering,Chulalongkorn University, Bangkok 10330, Thailand

出　　处：《International Journal of Automation and computing》2017年第3期360-370,共11页国际自动化与计算杂志（英文版）

基　　金：financial support from the honour program of the Department of Electrical Engineering,Faculty of Engineering,Chulalongkorn University

摘　　要：When a feedback system has components described by non-rational transfer functions, a standard practice in designing such a system is to replace the non-rational functions with rational approximants and then carry out the design with the approximants by means of a method that copes with rational systems. In order to ensure that the design carried out with the approximants still provides satisfactory results for the original system, a criterion of approximation should be explicitly taken into account in the design formulation. This paper derives such a criterion for multi-input multi-output（MIMO） feedback systems whose design objective is to ensure that the absolute values of every error and every controller output components always stay within prescribed bounds whenever the inputs satisfy certain bounding conditions. The obtained criterion generalizes a known result which was derived for single-input single-output（SISO） systems; furthermore, for a given rational approximant matrix, it is expressed as a set of inequalities that can be solved in practice. Finally, a controller for a binary distillation column is designed by using the criterion in conjunction with the method of inequalities. The numerical results clearly demonstrate that the usefulness of the criterion in obtaining a design solution for the original system.When a feedback system has components described by non-rational transfer functions, a standard practice in designing such a system is to replace the non-rational functions with rational approximants and then carry out the design with the approximants by means of a method that copes with rational systems. In order to ensure that the design carried out with the approximants still provides satisfactory results for the original system, a criterion of approximation should be explicitly taken into account in the design formulation. This paper derives such a criterion for multi-input multi-output（MIMO） feedback systems whose design objective is to ensure that the absolute values of every error and every controller output components always stay within prescribed bounds whenever the inputs satisfy certain bounding conditions. The obtained criterion generalizes a known result which was derived for single-input single-output（SISO） systems; furthermore, for a given rational approximant matrix, it is expressed as a set of inequalities that can be solved in practice. Finally, a controller for a binary distillation column is designed by using the criterion in conjunction with the method of inequalities. The numerical results clearly demonstrate that the usefulness of the criterion in obtaining a design solution for the original system.

关 键 词：Control design multi-input multi-output （MIMO） feedback systems non-rational systems rational approximants principle of matching method of inequalities 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]