The extended Bouc-Wen model with structural element and its application to the compensation of rate-dependent hysteresis of a piezoelectric actuator

Tatebatake, Ken'ichi; Fujii, Fumitake

doi:10.1109/sii.2017.8279294

Cited by 6 publications

(3 citation statements)

References 17 publications

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“…It is natural to infer that the model we develop should have mathematical structures to account for both the hysteresis and the phase lag originating from the cantilever structure of the actuator. We have accordingly proposed the extended Bouc-Wen model to capture this behavior [9]. The extended Bouc-Wen model is formulated by…”

Section: Extended Bouc-wen Model For Bimorph Piezoelectric Actuator Smentioning

confidence: 99%

“…for the fifth-order harmonic model (7). In the experimental verification disclosed in Section 5 , we will use our extended Bouc-Wen model in [9] for comparison. It is easy to see that the extended Bouc-Wen model can also be written in the linear regression form (8) and the algebraic descriptions of θ and x for the extended Bouc-Wen model are omitted accordingly.…”

Section: Preparation For the Parameter Identificationmentioning

confidence: 99%

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A Bouc–Wen Model-Based Compensation of the Frequency-Dependent Hysteresis of a Piezoelectric Actuator Exhibiting Odd Harmonic Oscillation

et al. 2018

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This paper proposes an enhancement of the Bouc-Wen hysteresis model to capture the frequency-dependent hysteretic behavior of a thin bimorph-type piezoelectric actuator which also exhibits odd harmonic oscillation (OHO) at specific input frequencies. The odd harmonic repetitive controller has recently been proposed to compensate for the hysteresis, and attenuates the OHO of the piezoelectric actuator for which the hysteresis nonlinearity is regarded as a disturbance. This paper proposes an alternate treatment of the hysteresis compensation with the attenuation of the OHO observed at some input frequencies. It will be shown that the proposed compensator fully utilizes the mathematical structure of the enhanced Bouc-Wen model proposed in this paper to compensate the hysteresis and to attenuate the OHO. The results of the hysteresis compensation experiment illustrate the excellent performance of the proposed control system, especially at the frequencies where OHO is conspicuous.Actuators 2018, 7, 37 2 of 16 in both the modeling and compensation of various hysteresis-related phenomena. Rakotondrabe [8] proposed a control system to compensate hysteresis nonlinearity using the Bouc-Wen model. His work can be classified as feedforward control in the control engineering context. His excellent contribution owes its theoretical basis to the structure of the Bouc-Wen model, and there is no need to synthesize the inverse hysteresis model to cancel the hysteresis. The authors of the current paper recently proposed an extension of the Bouc-Wen model [9] to capture the behavior of a thin bimorph-type piezoelectric actuator which exhibits frequency-dependent hysteresis, and synthesized a compensator based on the idea proposed by Rakotondrabe. Hadineza et al. [10] formulated the multi-variable generalized Bouc-Wen model and used it in the control of their experimental plant, in which multiple piezoelectric actuators are installed.Recently, Li et al. [11] reported the existence of a special form of frequency-dependent hysteresis nonlinearity in their piezo-driven nanopositioning stage which is referred to as the odd harmonic oscillation (OHO). We have also observed the odd harmonic oscillation with our bimorph piezoelectric actuator (e.g., the response to a 23 Hz pure sinusoidal input shown in Figure 18 [9]). Li clearly stated that the odd harmonic oscillation is caused by the hysteresis nonlinearity of the piezoelectric actuator, but they treated it as a disturbance and synthesized an odd harmonic repetitive controller to attenuate the odd harmonic oscillation. We are highly motivated by the work of Li et al., as we believe that attenuation of the odd harmonic oscillation can be treated in the course of model-based hysteresis compensation. The present paper accordingly addresses the results of our effort on modeling the frequency-dependent hysteresis of a thin bimorph piezoelectric actuator which also exhibits OHO. We will hereafter refer to the model proposed in this paper as the enhanced Bouc-Wen model.We will also propose a co...

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Section: Extended Bouc-wen Model For Bimorph Piezoelectric Actuator Smentioning

confidence: 99%

Section: Preparation For the Parameter Identificationmentioning

confidence: 99%

A Bouc–Wen Model-Based Compensation of the Frequency-Dependent Hysteresis of a Piezoelectric Actuator Exhibiting Odd Harmonic Oscillation

et al. 2018

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“…However, these models will increase the number of parameters. To use Bouc–Wen model in discrete-time systems, the discretization of the continuous model is investigated in Minh and Chen (2014), Ramli and Chen (2016), Ramli et al (2019), and Tatebatake and Fujii (2017). Discretization model also increases the complexity and brings challenges to parameter identification.…”

Section: Introductionmentioning

confidence: 99%

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

Shao

Wang

Zhu

2022

Transactions of the Institute of Measurement and Control

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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.

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An Extension of Modified Bouc-Wen Model to Capture Frequency Dependent Hysteresis of a Bimorph Piezo Actuator Exhibiting Odd Harmonic Oscillation

Fujii

Tatebatake

2018

2018 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM)

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The extended Bouc-Wen model with structural element and its application to the compensation of rate-dependent hysteresis of a piezoelectric actuator

Cited by 6 publications

References 17 publications

A Bouc–Wen Model-Based Compensation of the Frequency-Dependent Hysteresis of a Piezoelectric Actuator Exhibiting Odd Harmonic Oscillation

A Bouc–Wen Model-Based Compensation of the Frequency-Dependent Hysteresis of a Piezoelectric Actuator Exhibiting Odd Harmonic Oscillation

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

An Extension of Modified Bouc-Wen Model to Capture Frequency Dependent Hysteresis of a Bimorph Piezo Actuator Exhibiting Odd Harmonic Oscillation

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