Enhanced adaptive motion tracking control of piezo-actuated flexure-based four-bar mechanisms for micro/nano manipulation

This paper establishes and investigates an enhanced adaptive motion tracking control methodology for piezo-actuated flexure-based four-bar micro/nano manipulation mechanisms. This control methodology is proposed for tracking desired motion trajectories in the presence of unknown or uncertain system parameters, non-linearities including the hysteresis effect, and external disturbances in the motion systems. In this paper, the equations for the modelling of a flexure-hinged four-bar micro/nano mechanism are established. These include the angular stiffness, ‘static’ linear stiffness, equation of motion, and lowest structural resonance of the mechanism. In addition, a lumped parameter dynamic model that combines the piezoelectric actuator and the micro/nano mechanism is established for the formulation of the proposed control methodology. The stability of the control approach is analysed, and the convergence of the position and velocity tracking errors to zero is proven theoretically. A precise tracking performance in following a desired motion trajectory is also demonstrated in the experimental study. An important advantage of this control methodology is that the approach requires only a knowledge of the estimated lumped system parameters in the physical realisation. This proposed motion tracking control methodology is very attractive for the implementation of high performance flexure-based micro/nano manipulation control applications.