Interestingly frequency based hysteresis compensation was investigated closely by Othman
Vibration control applications with PEAs have also been investigated. For example, Marinaki, Marinakis, and Stavroulakis (2011) designed PF299 vibration control mechanism for a beam with bonded piezoelectric sensors and actuators. A particle swarm optimization (PSO) algorithm was used for the vibration control of the beam. A close comparison of obtained results between the PSO-based controller and a classical linear quadratic regulator (LQR) for different loadings revealed the high performance of the proposed PSO controller provided better results. Wang and Yang (2009) developed a new type of piezoelectric stack actuator with the purpose of exerting the strong actuating power of piezoelectric stack and facilitating the incorporation of piezoelectric stack within the host structure for vibration control application. A vibration control system of a cantilever beam example was applied. A neural network predictive (NNP) and LQR control strategy were used separately for performing the first bending mode vibration control of the beam. Their simulation results indicated that with this new actuator and NNP control strategy, the first bending mode amplitude of the cantilever beam could be reduced by about 95% compared to those of LQR control strategy where 79% was obtained. Zhang, Li, and Cai (2013) designed an adaptive controller MVSTDR (minimum variance self-tuning direct regulator) for a smart system that consisted of a cantilever beam bonded with a piezoelectric actuator in order to test the vibration suppression. Their experimental results demonstrated that it is feasible to suppress vibration by the MVSTDR for the smart beam with the hysteresis property. The authors showed that the amplitude reduction quantity of the strain within 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 free vibration.