Asymptotic Analysis of a Class of Singularly Perturbed Nonlinear Electromechanical Dynamic Models

The paper deals with a mathematical model of a cart coupled to a DC motor via a scotch yoke mechanism in the case of a small electrical inductance. The studied model presents a singularly perturbed system. For this system, conditions of Tikhonov’s theorem on limit passage of solutions of a perturbed initial value problem to a solution of the degenerate one under a small parameter tending to zero are valid. For slow variables, this passage takes place for argument values from the closed interval and for the fast variable only for the interval without the starting point. The degenerate system corresponds to eliminating the inductive term from the electrical equation. For the first time, using the boundary functions method by A. B. Vasil’eva, any order uniform asymptotic solution is constructed for the considered initial value problem. A numerical example is given. The presented graphs illustrate the good approximation near the starting point of the exact solution by the constructed first order asymptotic solution.