To enhance trajectory tracking performance of atomic force microscope system, a two-degree of freedom fractional order PID (2-DOF FOPID) control approach based on back propagation (BP) neural network is proposed in this paper. At first, principle and structure of the proposed control approach is presented. Then, 2-DOF FOPID controller is designed, including in feedforward and feedback controller, fractional calculus and approximation of fractional operator. Meanwhile, the parameters of controller are analyzed. Based on them, a BP neural network is built to adjust the parameters in this control structure according to the error between the reference trajectory and the actual output. Finally, the proposed control approach is conducted in atomic force microscope tracking control experiment, experimental results verify the effectiveness and improvement of the proposed control approach.

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