Robust control design for ball screw system via descriptor representation and loop shaping

This paper proposes a method to solve practical problems of positioning control using a ball screw system. The practical problems contain two difficulties. First difficulty is that friction affects the performance of it. In this paper, the friction is divided into three components, nonlinear term including static friction and coulomb friction, Stribeck effect and linear term including viscous friction. Nonlinear friction and Stribeck effect are considered as disturbance. These are compensated by designing controller including integrator and loop shaping. In contrast, linear term friction can be considered in framework of linear control synthesis. Second difficulty is that the change in mass of load affects the system response. Moreover, the experiment shows viscous friction coefficient varies. The controller is designed to guarantee the robust stability for uncertain parameters, which are the mass of load and the viscous friction coefficient. It is designed by using descriptor representation, polytopic representation and linear matrix inequality. The effectiveness of the proposed method is verified by simulations and experiments.