Fuzzy Adaptive Sliding Mode Control for the precision position of piezo-actuated nano positioning stage

This paper concerns hysteresis and creep of a piezo-actuated nano positioning stage. The hysteresis and creep, considered as bounded disturbance or uncertainty, are suppressed without a nonlinear model. An improved Fuzzy Adaptive Sliding Mode Control (FASMC) with a Proportional-Integral-Derivative sliding surface is designed to cancel both hysteresis and creep. However, the constant slopes of the sliding function may increase oscillations. Some variable gains with adaptive rules are introduced to overcome this drawback by changing the sliding function values online. Fuzzy control is applied to tune the switching control part to improve performance. Furthermore, an adaptation law is used to approximate the optimal value of the switching control. The stability of the sliding mode control law is proved in the sense of Lyapunov stability theorem. To eliminate chattering and obtain a smooth signal, the switching control is modified and a smooth function is introduced to substitute the signum function. An anti-saturation control is introduced to keep the input voltage within safety scope. Experimental results show that FASMC can achieve faster response for step input and sinusoid signal. Both hysteresis and creep of the piezoelectric actuator are suppressed by the proposed FASMC. Therefore, the FASMC can reduce the tracking errors of the piezo-actuated stage.