Friction compensation using observers with time-varying gain

To reject the friction disturbance of the Electro-Optical platform system, suppose that friction torque between the gimbals is described by LuGre model, an adaptive friction compensator is designed. Friction compensation using friction state observers with time-varying gain is put forward. And asymptotic convergence of the tracking error of closed loop system is proved through Lyapunov-like analysis. Simulation results show that, with the design parameters in the time-varying gain function tuned properly, the response time in which the angular velocity tracking error reach the error band of 0.03 rad/s is 44.5 second, and the peak to peak value of steady state error is 0.032 5 rad/s. Comparing with the system using observers with const gain, of which the response time is 62 second and the peak to peak value of steady state error is 0.041 3 rad/s, the response speed is faster and the response accuracy is higher simultaneously.