Singular Perturbation Method Applied for BVP, IVP and Optimal Control to One Parameter Armature Controlled DC Servo Motor

Abstract

DC servo motor discrete model of one-parameter Singular Perturbation Method (SPM) is enlarged showing zero-order, first-order and second-order approximations. In this paper, a one parameter SPM based two time scale model is considered for evaluation. Now by applying this SPM a real time Boundary Value Problems (BVP), Initial Value Problem (IVP) and Optimal Control Problem (OCP) are premeditated. Such evaluated SPM have a boundary layer correction (BLC) solution and an outer series solution. To improve degenerate solution and to recover initial and boundary conditions a BLC solution of SPM is used. The DC servo-motor control model of second order approximation is carried out for BVP, IVP and OCP. The results thus obtained are presented in comparison to the precise solution. The efficacy of the present model is evaluated in MATLAB environment.