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

Abstract

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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Modeling and Compensation of a Bimorph Type Piezoelectric Actuator Exhibiting Odd-Harmonic Oscillation and Frequency-Dependent, Interleaved Hysteresis

“…Alternative and intensively studied approaches in the literature include the usage of phenomenological hysteresis models [8]. Examples include the Prandtl-Ishlinskii (PI) model [9], the Preisach model [10], the play and stop models [11,12], the Bouc-Wen model [13], and the Duhem model [14]. These phenomenological models are able to capture hysteretic behaviors accurately.…”

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