Hybrid hysteresis modeling and inverse model compensation of piezoelectric actuators

Abstract

Piezoelectric actuators have shown great application potential in active vibration suppression and noise reduction. However, the nonlinear hysteresis effect in piezoelectric materials often compromises the control efficiency in practical application. This paper aims at presenting an innovative hybrid hysteresis model combining an original static operator and the frequencydependent dynamic module. The static hysteresis operator is obtained through a system-level approach, using a butterfly-shape function which is inspired from the shape analysis of hysteresis loops. For the dynamic component, the classical Bouc-Wen model and the transfer function is introduced to predict the initial loop and frequency-dependent response, respectively. The comparison between the hybrid hysteresis model and experimental result performed on a unipolar piezoelectric actuator shows a good agreement with respect to the voltage range and the frequency bandwidth of interest. Meanwhile, it is able to track the transient initial loading loop and the major-minor loops switching phenomenon. Based on the identified hybrid hysteresis model, an inverse model compensation scheme is developed to linearize the relationship between the desired output and the practical output of the piezoelectric actuators. The mechanism of the inverse model compensator is theoretically investigated and experimentally verified. Therefore, it is a quite simple yet efficient compensation approach due to the accuracy and adaptability of the proposed hybrid hysteresis model.

Transient and Harmonic Unipolar Hysteresis Model of Piezoelectric Actuators Using a System-Level Approach

“…Based on the previous model that includes static, transient, and harmonic regimes, it is proposed in this section to illustrate the interest in the exposed approach for providing a mean for efficiently and accurately controlling a piezoelectric actuator with respect to a given strain command. This illustrative example will be numerically evaluated by considering an experimentally validated model of the same actuator used in the previous section and exposed in [28], using a Bouc-Wen model for relating the transient regime and a fourth-order transfer function for the harmonic behavior ( Figure 13). Note that compared to the work in [28], the harmonic transfer function has been converted to Laplace domain through bilinear transform as:…”

“…This illustrative example will be numerically evaluated by considering an experimentally validated model of the same actuator used in the previous section and exposed in [28], using a Bouc-Wen model for relating the transient regime and a fourth-order transfer function for the harmonic behavior ( Figure 13). Note that compared to the work in [28], the harmonic transfer function has been converted to Laplace domain through bilinear transform as:…”

“…with S the actuator output strain and S stat the output of the quasi-static model (made of linear, system-level, and Bouc-Wen blocks). Also, to accommodate with the slight discrepancies between the hybrid model in [28] and actual experimental device, the values of λ t , τ t , and τ d have been marginally changed to 0.2, 32 × 10 −5 s and 2.2 × 10 −3 s, respectively (note that for the transient-related fractional transfer function, this changes the coefficient of the frequency-dependent term from 0.19 s 0.15 to 0.2 s 0.2 ). All the other parameters are kept the same as per Table 1.…”

“…This model is besides mainly dedicated to devices while the large majority of other approaches target material characteristics. However, this model, considering the coefficient relating the derivative of the strain with respect to the input voltage derivative, has so far been developed for quasi-static regime without any inclusion of dynamic effects directly within the model (hybrid approach was proposed in [28]). The reported study therefore proposes to directly include in the model relaxation effects as well as repolarization process for providing a generalized method allowing faithful response prediction as driving voltage frequency is varying and/or waveforms get more complex than a pure sine wave.…”

“…Then, Section 3 aims at validating this approach by comparing with experimental measurements performed on a stack actuator. As an example of application, Section 4 provides a numerical implementation of the present model in a compensation loop for precise position control, with the actuator modeled using a previously experimentally validated approach based on hybridization of the quasi-static model with Bouc-Wen approach and filtering [28]. Finally, Section 5 aims at recalling the main points of the paper and concludes about the model validity and potentials.…”