Application of the Boundary Function Method to Finding Slow Periodic Solutions of Singularly Perturbed Bang-Bang Systems

摘要

Numerous systems with bang-bang control algorithms and mechanical systems with dry friction operate in oscillatory modes. Such systems include, for example, fuel injection control systems [1], in which the sensor shows only the sign of the deviation of the exhaust parameters from given values and the basic operation mode is oscillations in a neighborhood of the given values. Another example of such systems is given by oscillations of a pendulum on an inclined uniformly rotating disk in the presence of dry friction [2]. Such motions have the specific feature that, for some part of the period, the pendulum moves together with the disk (in a sliding mode) and then returns to the original position.