Optimization of the Inverted Pendulum Controller with Friction Compensation by Means of the New Method of Lyapunov Exponents Estimation

Abstract

Abstract This text covers optimization of an inverted pendulum control system with friction compensator. The control system is tuned with respect to a performance index based on the novel method of the Largest Lyapunov Exponent estimation. The detailed description of the method is provided. Model of the control object is presented. A simple controller is proposed. Two control systems are compared: the one with compensator and the one without. Parameters of both controllers are optimized with respect to the novel criterion by means of the Differential Evolution method. Results of numerical simulations are presented. It is shown that the new criterion can be successfully applied to both: typical linear regulators and controllers with compensators.