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.
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