Robust Adaptive Control of Coupled Parallel Piezo-Flexural Nanopositioning Stages

Precision control of multiple-axis piezo-flexural stages used in a variety of scanning probe microscopy systems suffers not only from hysteresis nonlinearity, but also from parametric uncertainties and the cross-coupled motions of their axes. Motivated by these shortfalls, a Lyapunov-based control strategy is proposed in this article for simultaneous multiple-axis tracking control of piezo-flexural stages. A double-axis stage is considered for system analysis and controller validation. Hysteresis and coupling nonlinearities are studied through a number of experiments, and it is demonstrated that the widely used proportional-integral (PI) controller lacks accuracy in high-frequency tracking. Adopting the variable structure control method, a robust adaptive controller is then derived with its stability guaranteed through the Lyapunov criterion. It is shown that a parallelogram-type zone of attraction can be explicitly formed for the closed-loop system to which the error phase trajectory converges. Practical implementation of the controller demonstrates effective double-axis tracking control of the stage in the presence of hysteresis and coupling nonlinearities and despite parametric uncertainties for low-and high-frequency trajectories. Moreover, good agreements are achieved between the experiments and theoretical developments.