Multi-modal vibration control for all-clamped plate subjected to periodic disturbances by ESO-based frequency-shaped LQR

Abstract

Model uncertainties, external excitations and complex boundary conditions, etc. present in the control system lead to poor robustness of the controller. Therefore, an extended state observer (ESO) is utilized to compensate for these disturbances. However, a conventional ESO is not sufficiently capable to deal with rapid periodic disturbances. A frequency-shaped linear quadratic regulator (FSLQR) is, hence, developed by employing a frequency independent cost function according to the disturbance spectrum. In addition, knowing that periodic disturbances may have unknown or varying frequencies, a frequency-adaptive mechanism is introduced to address such issues, which enables the proposed method to mitigate the influences of frequency deviations. This is the first attempt to introduce frequency shaping technology into the control framework based on extended state observer. The control scheme of the introduced approach is general, but is conveyed here using solely an all-clamped plate structure with an inertial actuator, which is considered a typically benchmark for vibration phenomenon. The effectiveness and advantage of the proposed strategy are validated with comparative experimental studies on a hardware-in-the-loop laboratory testbed and a theoretical analysis based on Lyapunov theorem. Compared with the classical method based on ESO, the vibration experimental results demonstrate that the control performance of the first mode and the second mode are improved, both having upgraded approximately 6 dB.