Adaptive Sliding Mode Control with a PID Surface to Control a Nanopositioning System Actuated by Piezoelectric

Nanopositioning devices are a fundamental part of manipulation systems in areas such as nanotechnology, biotechnology, microfabrication, among others. An effective way to achieve movements with submicrometer resolution is through flexible systems with piezoelectric actuation. These devices present nolinear phenomena and eventually external disturbances that can severely affect the closed loop performance. This work presents an adaptive Sliding Mode Control law with a Proportional-Integral-Derivative sliding surface, designed for a flexure stage with a piezoelectric stack actuator. The system to be controlled is modeled as a second order dynamics to include its high frequency response. Additionally, the hysteresis of the piezoelectric is modeled using the Bouc-Wen model. To suppress the typical chattering of the Sliding Mode Control, the hysteresis is compensated by state variable feedback and an adaptive control technique is implemented to adjust the gain of the robust term of the controller. The determination of the closed loop system stability is presented using Lyapunov theory. To evaluate the performance of the proposed controller, a series of positioning experiments are performed, obtaining submicrometric errors, both in trajectory tracking and in target positioning.