Dynamics analysis and fuzzy logic controller design of atomic force microscope system with uncertainties

摘要

In this paper a nonlinear rule based fuzzy logic controller is proposed to control the nonlinear dynamic behavior of the probe tip of an atomic force microscope system (AFMs). At first, we use the bifurcation diagram to analysis the complex dynamic behavior of the atomic force microscope system, and show that the chaotic behaviour exists in the region of A_3 > 2.54. Next, in order to suppress the undesired motion in AFMs with uncertainty, we address the design schemes of fuzzy logic controller to stabilize the slave AFMs with parameter uncertainty to the master AFMs. Based on Lyapunov stability theory and fuzzy rules, the nonlinear controller and some generic sufficient conditions for global asymptotic synchronization are attained. We directly construct the fuzzy rules subject to a common Lyapunov function such that the error dynamics of master and slave AFMs satisfy stability in the Lyapunov sense. It overcomes the trial-and-error tuning for the membership functions and rule base in traditional fuzzy logic control. The effectiveness of presented method is numerically investigated by synchronizing slave AFMs which has chaotic motion or exceeding vibration amplitude to the master AFMs which is periodic motion or has small vibration amplitude.