The Furuta´s pendulum stabilization without the use of a mathematical model: Attractive Ellipsoid Method with KL-adaptation

This paper presents a development of adaptive state estimator and output controller based on Attractive Ellipsoid Method (AEM) for the stabilization of the Furuta´s pendulum. The proposed method guaranties that the controlled system trajectories are stabilized within an ellipsoid of a “minimal size”. We expand the classical AEM without adaptation to a class of observer and controller compensator with time varying gain matrices K and L adjusted on-line by specific adaptation procedure, that guaranties the convergence of the trajectories to an ellipsoid of less size compared to one without adaptation. In the case of the considered pendulum the incorporated adaptation procedures provides a stabilization in the vertical position practically with negligible vibrations, or in other words, without any “chattering effect”.