System modeling and DMPC control of AFM in X-axis

Based on the system construction of AFM in X-axis, system modeling and a discrete-time model predictive controller design are presented in this paper, which achieve accurate tracking control for a desired trajectory. Specifically, considering the features of the piezo-scanner, a segmented swept signal with decreasing amplitude is planned as the input signal to the piezo-scanner in X direction, and a dynamic model of the system is obtained by the N4SID algorithm. Meanwhile, an improved model with varying gain is acquired by polynomial fitting method, where the nonlinear behavior of the measurement system is taken into account. Additionally, based on the predictive advantage of the dynamic behavior of the system which can be used to improve the response speed of the system, and the strategy of the optimal control which further enhances the system robustness, a DMPC algorithm based on the improved model is applied to the closed-loop control of the system. Some experimental results show that the improved model describes the relationship of the system input and output exactly, while the DMPC strategy presents superior performance for tracking control in high scanning speed in contrast with the PI controller.