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In this research, we examined an adaptive control method to suppress overshooting in a precise positioning device with a damper composed of a visco-elastic material and a constrained plate. A two-degrees-of-freedom control system was adopted with conditions, to shape the response characteristics of the desired response using feedforward controller. Moreover, by using a feedback controller to inhibit the influence of the damper, the gain of a PID controller could be adjusted using a neural network. The validity of our technique will be verified via simulation.