Minimum Time Control of Second Order Pulse-Width-Modulated Sampled-Data Systems

Abstract

This paper treats the minimal time control problem for two second order pulse-width-modulated sampled-data systems, one with a double integrator type plant and one with a plant described by an integral and a time constant. Such plants are encountered in systems with hydraulic components. It is shown rigorously that for minimal time control the phase plane can be divided into two regions: a striplike region around the optimal switching trajectory for a continuous relay system with the same plants, in which the pulse width must be adjusted for optimal action; and the rest of the phase plane in which an optimal p.w.m. system of the type described behaves like a continuous optimal relay system, the pulse duration being equal to the sampling period. A brief description of an electromechanical computer capable of implementing minimal time control for these systems is also given.