Tracking control of a biaxial piezo-actuated positioning stage using generalized Duhem model

Nonlinear hysteresis modeling is studied using a novel PZT-actuated flexure-based mechanism. To compare the performance of variant hysteresis models with respect to the tracking reference, we reformulate the Bouc-Wen model, the Dahl model and the Duhem model as a generalized Duhem model. System parameters for these three hysteresis models are formulated into nonlinear optimization problems with constraints. These optimization problems are solved by the particle swarm optimization method. Since the Duhem model includes both electrical and mechanical domains, it has a smaller modeling error compared to the other two hysteresis models. The simulation results are confirmed by modeling the proposed biaxial piezo-actuated positioning stage of these hysteresis models. Cross-coupling effects between the X- and Y-axis actuation are also alleviated by a novel feedforward compensation mechanism based on the Duhem model with crossover terms. Finally, a real-time experiment is performed to confirm the feasibility of the proposed method. The experimental results validate the capability of the proposed controller to achieve precision tracking tasks with submicron precision.