Optimal LuGre friction model identification based on genetic algorithm and sliding mode control of a piezoelectric-actuating table

A piezoelectric friction actuating mechanism is employed to construct a long travelling range sub-micro X-Y positioning table. The piezoelectric material is used to generate high-frequency oscillation for actuating a fingertip, which in is contact with a slide to induce back-and-forth motion. The LuGre friction model is chosen to simulate the friction dynamics of this positioning mechanism. The genetic algorithm (GA) is employed to search for the optimal friction model parameters. However, this piezoelectric actuating system has an obvious non-linear and time-varying dead-zone offset control voltage related to the static friction and preload. The GA-estimated LuGre dynamic model is still not accurate enough for model-based precision control design. Hence, sliding mode control (SMC) with robust behaviour is employed to design a non-linear controller for this piezoelectric friction actuating mechanism. The Laypunov-like design strategy is adopted to satisfy the system stability criterion. Tracking control of different trajectories is planned to investigate the motion control performances and the steady-state errors of the SMC non-linear controller based on the GA-estimated model. The dynamic experimental results of the proposed non-linear controllers are also compared with that of a model-based PID controller.