Statistically Oriented Optimal Control and Disturbance Prediction for Piezoelectric Semi-Active Vibration Suppression

This study proposes a novel predictive input optimization and disturbance prediction strategy for semi-active vibration control using a piezoelectric transducer, leveraging the statistically oriented prediction and optimization scheme and Gaussian process (GP) enhanced disturbance prediction. Here, semi-active switching, which manipulates the piezoelectric charge, is executed to suppress vibration. State-dependent discontinuity of the semi-active input trajectory owing to the switching makes it challenging to formulate a prediction-based optimization strategy in conventional methods. Incorporating the dynamical model of disturbance is also crucial to compensate for those undesired effects effectively. The proposed GP-enhanced disturbance predictor, which combines the empirical model and GP regression, provides the disturbance trajectory over a finite time horizon. The empirical model approximates the periodic disturbance with known frequencies, while the GP regression model handles other unknown components, enabling the predictor to function under different conditions. Furthermore, the predicted disturbance trajectory is applied for control optimization, allowing the controller to determine the optimal control input trajectory that compensates for future disturbances. The proposed strategy employs the tree-based scheme to formulate a prediction and optimization algorithm that determines the optimal semi-active input trajectory. Further, it includes a statistically oriented switching criterion that reduces the computational costs by selecting the trajectory to be predicted. This criterion utilizes kernel density estimation to learn the probability density function of suppression performance, allowing the controller to adaptively select trajectories to predict online while not excluding promising ones. The effectiveness of the proposed statistically oriented predictive switching vibration control with tree-based formulation and optimization (S-PSTFO) strategy was validated through experiments, demonstrating superior suppression performance over the conventional method.