Hysteresis identification and adaptive vibration control for a smart cantilever beam by a piezoelectric actuator

• An online CARMA model identifies hysteresis property for a smart beam.
• The process parameters of identification are time-varying for hysteresis property.
• The free vibration of a smart beam is suppressed by a MVSTDR.
• The amplitude reduction quantity of strain in frequency spectrum analysis is up to about 83.67%.

This paper presents some experiments not only for depiction of hysteresis property but also for vibration suppression by designing an adaptive controller to a smart system consisted of a cantilever beam bonded with a piezoelectric actuator. The adaptive controller is composed of an identifier and the minimum variance direct control. With the identifier by employing the recursive extended least square method, an online controlled autoregressive moving average (CARMA) model for the smart beam is proposed to characterize the hysteresis phenomena between the output strain near the fixed end of the cantilever beam and the input voltage applied on the piezoelectric actuator. Based on the CARMA model, an adaptive controller is designed to control the vibration of the nonlinear smart system by using the minimum variance self-tuning direct regulator (MVSTDR). The MVSTDR has a significant advantage of trying to obtain an optimal control results for vibration suppression over the control process. The experiment results demonstrate that it is feasible to suppress vibration by the MVSTDR for the smart beam with the hysteresis property and show that the amplitude reduction quantity of the strain in the frequency spectrum analysis is up to about 83.67% with the adaptive controller at the first natural frequency when the smart beam is subjected to a free vibration.