Tracking of piezoelectric actuators with hysteresis: a nonlinear robust output regulation approach

Hysteretic characteristics commonly exist in piezoelectric actuators (PEAs) and degrade the positioning accuracy particularly in the case of low-frequency trajectory tracking. A PEA with hysteretic characteristics is usually difficult to precisely control because the unmeasurable hysteretic force is typically generated by a complicated nonlinear dynamic model. This task can be theoretically formulated as a robust output regulation problem with a specific nonlinear and non-autonomous exosystem. In this paper, the theoretical problem is first solved within a novel internal model architecture. With the proposed controller, the PEA is able to asymptotically track a desired reference trajectory with the robustness to plant uncertainties. The effectiveness of the design is verified by extensive experiments.