Synthesis of a Control Algorithm for Nonlinear Plant Using Correction of Controlled Plant Dynamics and Compensation of Perturbations

G. K. Shadrin

2020

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DOI 10.17587/mau.21.667-674
Data confidence 70 medium
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Abstract

This paper introduces a new approach to control of nonlinear non-stationary multichannel plant with lumped parameters and additive perturbations. Controlled plant is represented as a set of equations in matrix-vector form, with number of output variables equal to the number of controlled variables. The problem is stated as follows: to control plant output provided that output variables and state variables are observable. Plant equations are converted into a state dependent coefficient (SDC) form, then method of correction of plant dynamics and compensation of perturbations is used. A variant of conversion to the SDC form based on E. A. Barabashin’s method is suggested. Reverse models of the plant are defined with respect to reference and deviation channels. Algebraic equations are presented, which, when solved, yield reverse models. Definitions of etalon filters are introduced, allowing a physical implementation of a controller when used in conjunction with reverse models. Conditions to which matrices of etalon filters must conform are considered. It was found by examples that part of coefficients of etalon filters can be chosen arbitrarily. Using the method of correction of controlled plant dynamics and perturbations, utilizing reverse models and etalon filters, a physically implementable controller algorithm was constructed. Then it was transformed to physically implementable form using equivalent transformations. Components of the final algorithm are obtained by the means of algebraic transformations of functional matrices of the plant and etalon filter. Equations for closed control system are presented. It follows from these equations that system is asymptotically stable and that transient processes correspond with their respective etalon filters. Even though compensation method was used, a multichannel closed-loop control system was obtained. An advantage of suggested method is that it allows a simple procedure for the control algorithm synthesis using evident physical initial data. The efficacy of obtained algorithms was verified using several examples. Computer simulation showed that control systems are robust and comply with specified requirements. Directions for further research were suggested.