Data-Driven Adaptive Iterative Learning Method for Active Vibration Control Based on Imprecise Probability

Abstract

A data-driven adaptive iterative learning (IL) method is proposed for the active control of structural vibration. Considering the repeatability of structural dynamic responses in the vibration process, the time-varying proportional-type iterative learning (P-type IL) method was applied for the design of feedback controllers. The model-free adaptive (MFA) control, a data-driven method, was used to self-tune the time-varying learning gains of the P-type IL method for improving the control precision of the system and the learning speed of the controllers. By using multi-source information, the state of the controlled system was detected and identified. The square root values of feedback gains can be considered as characteristic parameters and the theory of imprecise probability was investigated as a tool for designing the stopping criteria. The motion equation was driven from dynamic finite element (FE) formulation of piezoelectric material, and then was linearized and transformed properly to design the MFA controller. The proposed method was numerically and experimentally tested for a piezoelectric cantilever plate. The results demonstrate that the proposed method performs excellent in vibration suppression and the controllers had fast learning speeds.