Hysteresis is an inherent characteristic of piezoelectric materials that can be determined by not only the historical input but also the input signal frequency. Hysteresis severely degrades the positioning precision of piezoelectric micropositioning stages. In this study, the hysteresis characteristics and the excitation frequency effects on the hysteresis behaviors of the piezoelectric micropositioning stage are investigated. Accordingly, a rate-dependent asymmetric hysteresis Prandtl-Ishlinskii (RDAPI) model is developed by introducing a dynamic envelope function into the play operators of the Prandtl-Ishlinskii (PI) model. The RDAPI model uses a relatively simple analytical structure with fewer parameters then other modified PI model to characterize the rate-dependent and asymmetric hysteresis behavior in piezoelectric micropositioning stages. Considering practical situations with the uncertainties and external disturbances associated with the piezoelectric micropositioning stages, the system dynamics are described using a secondorder differential equation. On this basis, a corresponding adaptive robust control method that does not involve the construction of a complex hysteretic inverse model is developed. The Lyapunov analysis method proves the stability of the entire closed-loop control system. Experiments confirm that the proposed RDAPI model achieves a significantly improved accuracy compared with the PI model. Fur-
A composite learning dynamic surface control is proposed for a class of multi-machine power systems with uncertainties and external disturbances by using fuzzy logic systems (FLSs) and disturbance observer (DOB). The main characteristics of the proposed strategy are as follows: (1) The approximation ability of FLSs for nonlinear model of multi-machine power systems is enhanced considerably by using the composite learning method and providing additional correction information for the FLSs. These findings differ considerably from previous designs that focus directly on the system's tracking performance. (2) The filtering errors caused by the utilizations of the first-order low-pass filters in dynamic surface control (DSC) are compensated effectively by designing the compensating signals in the control law design process. (3) The compound disturbances including the FLSs' approximation error and external disturbances are estimated and mitigated by constructing DOB. Finally, the proposed control algorithm is verified on the StarSim Hardware-in-loop experimental platform, and the experimental results validate the effectiveness of the proposed control strategy in suppressing disturbances and enhancing the robustness of the controller.
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