Robust control with unknown dynamic estimation for multi-axial piezoelectric actuators with coupled dynamics

Piezoelectric actuators are widely used for precise micro-positioning. The ability of fine positioning is strictly under the effect of hysteresis nonlinear behavior. Simultaneous micro-positioning in multi-dimensions has also attracted much attention in recent years. In addition to hysteresis behavior, a nonlinear dynamic coupling exists between the different degrees of freedom in multi-axis piezoelectric actuators. The nonlinear coupling phenomenon is called the Axes Coupling Effect (ACE). A modified Prandtl–Ishlinskii (PI) operator and its inverse are utilized for both the identification and real time compensation of the hysteresis effect in this article. Considering the PI estimation error and probable un-modeled dynamics, a variable structure controller coupled with the neural network is proposed for position tracking. Due to the model-based structure of the proposed controller, the dynamic model of actuator should be identified. Coupling between nonlinear hysteresis behavior and the linear dynamic model causes a complicated identification. The ACE has also an unknown trend. Eliminating the necessity of dynamic parameters and ACE identification, a Radial Basis Function (RBF) neural network approach would estimate the unknown dynamics of the designed controller. Stability of the controller in the presence of estimated unknown dynamics is demonstrated analytically. Experimental results depict that the proposed approach can achieve precise tracking of multi-frequency trajectories and appropriate estimation of unknown dynamics.