Open AccessCriterion of Approximation for Designing 2 × 2 Feedback Systems with Inputs Satisfying Bounding Conditions
Author(s) -
Tadcha Chuman,
Suchin Arunsawatwong
Publication year - 2014
Publication title -
ecti transactions on electrical eng. / electronics and communications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.148
H-Index - 7
ISSN - 1685-9545
DOI - 10.37936/ecti-eec.2015131.170968
Subject(s) - bounding overwatch , control theory (sociology) , mathematics , set (abstract data type) , controller (irrigation) , circle criterion , matrix (chemical analysis) , binary number , fractionating column , mathematical optimization , computer science , distillation , control (management) , exponential stability , nonlinear system , chemistry , physics , materials science , arithmetic , organic chemistry , quantum mechanics , artificial intelligence , agronomy , composite material , biology , programming language
A common practice in designing a feedback system with a non-rational transfer matrix is to replace the non-rational matrix with an appropriate rational approximant during the design process so that reliable and effcient computational tools for rational systems can be utilized. Consequently, a criterion of approximation is required to ensure that the controller obtained from the approximant still provides satisfactory results for the original system. This paper derives such a criterion for the case of two-input two-output feedback systems in which the design objective is to ensure that the errors and the controller outputs always stay within prescribed bounds whenever the inputs satisfy certain bounding conditions. For a given rational approximant matrix, the criterion is expressed as a set of inequalities that can be solved in practice. It will be seen that the criterion generalizes a known result for single-input single-output systems. Finally, a controller for a binary distillation column is designed by using the criterion in conjunction with the method of inequalities.