Discrete-time rate-dependent hysteresis modeling and parameter identification of piezoelectric actuators

Abstract

A discrete-time-modified Bouc–Wen model is proposed to describe the non-symmetrical and rate-dependent hysteresis of piezoelectric actuators for micro-vibration control applications. The modified model combines a non-symmetrical Bouc–Wen model and a frequency-dependent dynamic module. A series of experiments are conducted to characterize the rate-dependent hysteresis of piezoelectric stack actuators under sinusoidal excitations at a range of 1 to 20 Hz. The experimental results verify the validity of the modified model. The modified Bouc–Wen model increases the complexity of Bouc–Wen hysteresis nonlinear differential equation, which brings difficulties to parameter identification. To identify the parameters of Bouc–Wen model, an improved hybrid differential evolution and Jaya (DE-Jaya) algorithm is introduced with a hybrid mutant operator and Jaya operator that tried to balance between convergence speed and solution accuracy. The improved algorithm is tested on benchmark functions and compared with other optimizations to prove its effectiveness. The comparison results show that hybrid DE-Jaya algorithm has better performance in convergence speed and solution accuracy. The identified discrete-time-modified Bouc–Wen model is used as the secondary path in a filtered-x variable step-size affine projection algorithm (FXVSSAPA), and experimental verifications are done on a micro-vibration control platform. The experimental results show that the FXVSSAPA algorithm can converge to the steady-state error faster and verify the effectiveness of the proposed discrete-time-modified Bouc–Wen model.

Hysteretic behaviour of uniaxially thermoformed auxetic foams under 3-point bending low-frequency vibration

“…The parameter e q represents the inverse of the apparent yield point of the nonlinear component of the BW model, and e r describes the ratio of the slope of the hysteresis loop at the velocity direction changing point versus the slope of the linear region [71]. The stiffness The classical BW model is not frequency-dependent [47,53,72] and is therefore unable to capture the noticeable effect of the frequency over the stiffness and damping of the PU foams. According to Nagy's theory, the modulus of open-cell PU foams under compression has a linear dependence to the strain rate on log-log scale; the latter assumption is valid within the low strain rate range of quasi-static and low-speed dynamic and impact tests [54] as described in Eq.…”

“…The BW model can describe well the different types of generalized forcedisplacement hysteretic loops. However, the classical BW model is invariant with the various input frequencies [48,52] [49]; and Shao et al have used a second-order discrete system for the dynamic linear part [53]. All these variations proposed to the original formulation of the BW can cater for frequency-dependent behaviours, but also make the updated models more complicated, by using parameters and components without evident physical meaning.…”

Experimental Validation of Two Types of Force Actuators: A Performance Comparison

“…Over the past few decades, the design principles governing piezoelectric actuators have undergone significant evolution, leading to the development of various types of actuators. Among these, piezoelectric stack actuators possess several advantageous characteristics, including rapid response times, low power consumption, and the ability to generate outputs with enhanced precision in terms of the displacement and greater force generation capabilities [ 8 , 9 , 10 ].…”

Exponential convergence in the mean-square sense of nonlocal stochastic almost automorphic genetic regulatory lattice networks

“…Second, the synthesized controller is directly implemented in a digital processor. Therefore, control methodologies developed for discrete-time nonlinear systems can be implemented in real systems more effectively (Garrappa and Popolizio, 2011; Shao et al, 2022; Yang et al, 2022; Zhang and Xu, 2019; Zhang et al, 2020; Znidi et al, 2022). A number of processes have a certain regularity; however, they are not completely periodic.…”