Robust Adaptive Constrained Motion Tracking Control of Piezo-Actuated Flexure-Based Mechanisms for Micro/Nano Manipulation

This paper presents a robust adaptive constrained motion tracking control methodology for piezo-actuated flexure-based micro/nano manipulation mechanisms. This unique control approach is established for the tracking of desired motion trajectories in a constrained environment exhibiting some degree of uncertain stiffness. The control methodology is also formulated to accommodate not only the parametric uncertainties and unknown force conversion function, but also nonlinearities including the hysteresis effect and external disturbances in the motion systems. In this paper, the equations for the dynamic modeling of a flexure-hinged four-bar micro/nano manipulation mechanism operating in a constrained environment are established. A lumped parameter dynamic model that combines the piezoelectric actuator and the micro/nano manipulation mechanism is developed for the formulation of the control methodology. Stability analysis of the proposed closed-loop system is conducted and the convergence of the motion tracking errors is proven theoretically. Furthermore, precise motion tracking ability in following a desired motion trajectory is demonstrated in the experimental study. An important advantage of this control approach is that it does not require the exact values for the system parameters and the force conversion function in the physical realization. This proposed constrained motion tracking control methodology is very useful for applications demanding high-precision motion tracking with force sensing and feedback.