Design of hysteresis-compensating iterative learning control for piezo-positioners: Application to atomic force microscopes

This article addresses hysteresis-caused positioning error in piezo-based systems, such as atomic force microscopes. First, we present the design of an iterative learning control algorithm based on the Preisach hysteresis model. For a given output bound, we determine the algorithm’s rate of convergence. Second, we compensate for creep in the piezo system to determine a hysteresis model, and then the parameters of the model are used to find an appropriate value of the iteration gain such that convergence of the control algorithm is guaranteed. Finally, we demonstrate the efficacy of the approach, to achieve high-precision positioning, by applying the control algorithm to an experimental atomic force microscope system. Results show that iterative learning control can achieve substantial reduction of hysteresis-caused error, e.g., the tracking error is reduced to 0.24% of the total displacement range, which is approximately the noise level of the sensor measurement.