Sensitivity to switching-function variations in a time-optimal positional system

Abstract

The paper deals with the sensitivity to switching-function variations of a time–optimal system which is controlling a positional mechanism. The model chosen has a second-order differential equation with non-linear and discontinuous right–hand side. Such a model covers a large class of motion resistances, in particular all types of friction. Differential inequality theory and the theory of discontinuous differential equations, and in particular a method of generalized jT solutions, are used to show that time-optimal switching-function variations cause the origin to become an unstable equilibrium point of the state-plane and the control system to generate limit–cycles. Some suggestions for applications are given, as is a practical example.