Interplay between linear integral and discontinuous relay feedback: challenging issue for standard PI/PID controllers in presence of Coulomb friction
We consider linear time invariant system plants with an unbounded integral control action and discontinuous relay in feedback. Examples for that are the standard PI/PID controllers, widely used in various types of robotic and mechatronic systems. Inherent challenge of a discontinuous relay feedback can be directly associated with presence of the Coulomb friction and mechanical setups, that downgrades the convergence performance of motion control systems for set-point stabilization tasks. Other application examples in which a relay non-linearity in the loop represents part of the plant dynamics are also conceivable. As a matter of fact, a slowly converging stick-slip behavior with continuously growing periods appears in such systems, owing to an interplay between the integral feedback and relay nonlinearity. In this talk, we will look into analysis of the convergence behavior and highlight the appearance of sticking phases and set of possible trajectories in vicinity to the globally stable equilibrium and associated region of attraction. A novel solution to convergence analysis of such systems, based on the classical sliding mode principles, will be presented. Some aspects of estimating upper bound of the convergence time will also be treated at the edge. The talk will also include several motivating numerical examples and experimental observations known from the other published works.