Hysteresis model and adaptive vibration suppression for a smart beam with time delay

This paper mainly presents experimental verifications of vibration suppression for a cantilever beam bonded with a piezoelectric actuator by an adaptive controller. Using the Hamilton Principle and the Bouc–Wen Equation, a dynamical mathematical model is proposed to describe a hysteresis property with different time delay for the smart beam. It is concluded that the hysteresis characteristic of the smart beam is influenced not only by the amplitude and frequency of the input voltage but also by the time delay. Based on the nonlinear model, the adaptive controller with time delay is adopted to attenuate the free vibration of the smart beam. Through some simulations and experiments, the vibration suppression effect can be improved with a proper small time delay in the control system. Moreover, the vibration amplitude attenuation rates at the fundamental frequency with the simulations and the experiments are up to 85.938% and 84.505% respectively. Obviously the adaptive regulator with a proper small time delay is proved to have the capacity of improving the vibration suppression effect.