H∞ loop shaping for positioning control system with nonlinear friction

In this study, we propose a method of the positioning control for a ball screw system achieved by H_∞ loop shaping. The H_∞ controller is synthesized for friction compensation, zero steady error, and reference tracking performance by using weighting functions. A dynamic weighting function and a constant matrix are used for the loop shaping framework. The dynamic weighting function is selected for friction compensation and steady error. Frequency characteristics of friction is focused on in our approach. The frequency region where static friction and stick-slip motion appears predominantly is identified for choosing an appropriate dynamic weighting function. The other constant weighting matrix is selected to improve tracking performance. By considering the relationship between the loop shaping framework and LQ control framework, trial and error for choosing an appropriate weighting matrix is simplified. The effectiveness of the proposed method is verified by simulations with nonlinear friction and experiments.