Fuzzy model-based disturbance rejection control for atomic force microscopy with input constraint

Accurate representation of the atomic force microscopy (AFM) system is not only necessary to achieve control objectives, but it is also beneficial for detecting the nanomechanical properties of the samples. To this end, this paper addresses the issue of controller design for the AFM system based on an accurate nonaffine nonlinear distributed-parameters model in which flexibility and distributed mass effects of the microcantilever beam are considered properly. First, a T-S fuzzy model is derived for this dynamical model of the AFM system in order to simplify the procedure of controller design. Then, a fuzzy model-based controller is designed to suppress the chaos and attenuate the disturbance in the AFM system through the linear matrix inequality (LMI) formulation. Moreover, by considering some criteria for disturbance rejection and transient performance, and some constraints on control input and states, new stabilization conditions are proposed based on a fuzzy Lyapunov function. Finally, simulation results are represented to demonstrate the effectiveness of the proposed method.