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This paper presents the design of a nonlinear rule based fuzzy logic controller for 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. Next, the positive maximum Lyapunov exponent is obtained to identify that the chaotic motion do exist in AFMs. In order to suppress the undesired chaotic motion in AFMs, we address the design schemes of fuzzy logic controller to stabilize the slave chaotic AFMs to the master periodic AFMs. In the controller design process, it directly constructs 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. Finally, a numerical simulation is used to illustrate the effectiveness of the proposed controller.