Robust generalised impedance control of piezo-actuated flexure-based four-bar mechanisms for micro/nano manipulation

This paper presents a novel robust generalised impedance control methodology for piezo-actuated flexure-based four-bar micro/nano manipulation mechanisms. This control approach is proposed for compliant manipulation in which desired motion and force trajectories are controlled to achieve a specified generalised impedance. The control methodology is also formulated to accommodate not only the parametric uncertainties and unknown force conversion function, but also non-linearities including the hysteresis effect and external disturbances in the motion systems. In this paper, the equations for dynamic modelling of a flexure-hinged four-bar micro/nano mechanism making contact with its environment are established. 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 tracking errors to achieve the generalised impedance is proven theoretically. Desirable control performances in following the desired motion and force trajectories are demonstrated in the experimental study. An important advantage of this control methodology is that this approach does not require the exact values for the system parameters and the force conversion function in the physical realisation. This proposed compliant manipulation control methodology is useful for the implementation of high performance flexure-based micro/nano manipulation applications demanding for both sensing and control of motion and force trajectories.