Rate-dependent hysteresis nonlinearity in piezoelectric actuators severely limits micro- and nanoscale system performance. It is necessary to establish a dynamic model to describe the full behavior of rate-dependent hysteresis. In this article, the Elman neural network–based hysteresis model is developed for piezoelectric actuators. An improved dynamic hysteretic operator is proposed to transform the multi-valued mapping of hysteresis into one-to-one mapping on a newly constructed expanded input space. Then, Elman neural network incorporated with the improved dynamic hysteretic operator is utilized to approximate the behavior of rate-dependent hysteresis. The combination of Elman neural network and the improved dynamic hysteretic operator can dually embody the dynamic property and is capable of fully extracting the characteristics of rate-dependent hysteresis. The experimental results are presented to illustrate the potential of the proposed modeling technique.
To control a nonlinear system with both hysteresis and disturbance, it is necessary to establish a hysteresis model and improve the disturbance rejection ability. However, the input signal implicitly involved in the classical hysteresis model can lead to difficulty in constructing a compensator. In this study, a hysteresis model in explicit form is proposed with a bounded auxiliary variable. Then, a model‐based inverse is constructed for approximate compensation for the hysteresis. Moreover, the compensation error, which is considered a part of the disturbance, is proved to be bounded. Disturbance estimation triggered control (DETC) is utilized to address the compensation error coupled with the external disturbance. According to the disturbance effect indicator (DEI), DETC can improve the system control performance by considering the disturbance effect judgment. Experimental results are presented to illustrate the potential of the proposed technique.
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