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

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.