Adaptive Robust Precision Motion Control of a Piezoelectric Positioning Stage

Positioning stages using piezoelectric stack actuators (PEA) have very high theoretical bandwidth and resolution. However, it is difficult to achieve precise dynamic motion tracking using traditional linear controllers such as PID due to the inherent hysteresis nonlinearity of piezoelectric materials and the phase lag associated with such controllers. In this paper, it is demonstrated that, in the frequency range for which only the piezoelectric dynamics dominates, high tracking accuracy is possible through an intelligent integration of advanced adaptive robust control strategy with a control-oriented modeling of nonlinear piezoelectric effects. Specifically, the fast and slow dynamics of the total stage displacement due to various piezoelectric effects including the rate-dependent hysteresis nonlinearity, the drifting, and the broad spectrum of domain switching time constants are first identified. With a control oriented modeling in mind, a simple first-order nonlinear model with unknown parameters and bounded disturbances is used to capture the essence of those fast and slow dynamics. An adaptive robust controller (ARC) is subsequently designed to compensate for the effect of unknown model parameters and bounded disturbances effectively, which provides an online adaptation-based dynamic model compensation that minimizes tracking errors. Experimental results from tracking control of sinusoidal trajectories up to 100 Hz and point-to-point trajectories show that tracking accuracy down to the same magnitude of sensor noise is achieved, demonstrating the effectiveness of the approach.