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.

A class of linear discrete multi parameter stable control systems is considered which is notorious for its computational stiffness. For finding the exact solution of these systems special numerical methods need to be used. As an alternative, a singular perturbation method (SPM) is presented for initial and boundary value problems. Power systems are modeled as multi parameter systems due to their multi time scale nature. This SPM is applied to a load frequency control model of two area power system with three parameters as a case study. The results are presented up to second order approximation. They amply support the SPM presented.

A linear discrete stable control system is considered. The Power Factor Correction (PFC) converter to allow independent control of current and voltage. It converter are fast and slow states to inheres sty present small parameters inductor and capacitor its computes stiffness and to include switching ripple effects. As an alternative a Singular Perturbation Method (SPM) is presented Initial Value Problem (IVP) and Boundary Value Problem (BVP). It is applied to two state switching power converters to provide rigorous justification of the time scale separation. It is modeled as a one parameter singularly perturbed system. SPM consists of an outer series solution and one boundary layer correction (BLC) solution. A boundary layer correction is required to recover the initial conditions lost in the process of degeneration and to improve the solution. SPM is carried out up to second-order approximate solution for the PFC converter model for IVP and BVP. The results are compared with the exact solution (between with and without parameters). The results substantiate the application.