ROBUST DYNAMICAL FEEDBACK DESIGN FOR BALL POSITION CONTROL ON ROTARY PLATFORM

Abstract

Subject of Research. The paper presents a method of dynamical control design for a robot with a parallel kinematic scheme. The stabilization problem of 2-Degree-of-Freedom Ball and Plate system is solved. It is assumed that the rotation angles of the platform are limited. Method. The proposed method is based on transforming the considered nonlinear system to the form of a homogeneous differential inclusion. Since the considered control object is described by a continuous and nonhomogeneous system of ordinary differential equations, the proposed method is based on the use of a homogeneous extension. The differential inclusion obtained by the homogeneous extension method is homogeneous with a negative degree, that provides the finite-time stability of the closed-loop system. Main Results. The dynamical feedback is robust and allows compensating non-Lipschitz disturbances of a certain class. Simulation results demonstrate the efficiency of the proposed approach. Despite the fact that the considered system and the obtained control law are nonlinear, the proposed dynamical feedback has a simple tuning procedure based on the solution of linear matrix inequalities. Practical Relevance. The proposed method is designed for robots with parallel kinematic scheme widely used, for example, in machine tools, flight simulators. The developed algorithm provides robust properties that are necessary in practice.

Keywords

• tiltable plate
• dynamical feedback control
• homogeneous systems
• differential inclusions