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Robust dahl model based Sliding Mode Control for micro/nano positioning applications

This paper proposes a novel and robust Sliding Mode Control (SMC) technique for hysteresis linearization of a stack actuated piezoelectric micro/nano positioner. This work documents a classical second order Dahl model to capture the effects of rate dependent hysteresis. An advantage of this model is its easier implementation and better depiction of asymmetric hysteresis loops than a same order Bouc-Wen model. In existing works on SMC with piezoelectric actuators, Dahl model has received scant attention. In contrast, this work explores second order Dahl model as a candidate for SMC implementation. The proposed approach is unique in the sense that it does not need a separate hysteresis observer. The stability of the controller is verified by Lyapunov stability analysis and zero steady state error is theoretically proved. SMC strategy accounts for the uncertain hysteresis as well as unanticipated fluctuations in the input. Simulation results establish the trajectory tracking robustness and effectiveness of the proposed control technique.