Composite Control for Nonlinear Singularly Perturbed Systems Based on Feedback Linearization Method

摘要

This article is devoted to the synthesis of composite control for nonlinear singularly perturbed system using feedback linearization (FL). The idea of this method consists in converting the original nonlinear system into a linear one by means of state feedback and coordinate transformation. Then, methods of control theory for linear systems are used for system design. If the original nonlinear system cannot be linearized exactly by state feedback, the method of approximate feedback linearization (AFL) is used. The essence of approximate feedback linearization methods lies in the feedback linearization only of the some part of the original nonlinear system (not the entire system). In this paper, we propose a method of approximate feedback linearization control of nonlinear singularly perturbed (SP) systems. Proposed method is based on the decomposition of the original SP system and the construction of control input in the form of asymptotic composition of FL controls for slow and fast subsystems. The resulting AFL control is obtained in the form of composite control. The application of the proposed approach is illustrated through the speed control of a DC series motor.