Multimodal vibration suppression of a flexible thin plate using a mimo control methodology

Abstract

This paper investigates a multi input multi output (MIMO) control strategy for controlling multimodal vibration of a flexible plate. The active vibration control system built in this study uses a velocity feedback controller by employing piezoelectric patches as actuators and sensors for vibration measurements. The MIMO controller design is performed for the case of 2 inputs and 2 outputs where each actuator/sensor pair is collocated. There is a closed loop around each pair. These pairs are physically linked to each other by the plate structure. As a result, there exists an input-output relation between the un-collocated sensors and actuators, as well. This relation couples the dynamic behavior of each individual loop, hence, turn it into a MIMO system. The optimal feedback gains which provide maximum suppression for all the considered modes are determined numerically. For numerical studies, a finite element model of the flexible plate together with the piezoelectric patches is built. After deciding the positions of the collocated sensor/actuator pairs for each structural vibration mode, the MIMO velocity feedback controller is designed using simulated frequency response functions (FRFs) for various feedback gains in the presence of forced vibrations. In the MEMO controller, the cross relations of the un-collocated sensors and actuators are also included in the simulation model. The controller gains of the first and second loops are altered and stable regions for the MIMO controller is investigated for the first three modes of the structure. It was shown that the plate vibrations can be effectively suppressed for the first three modes of the structure using the proposed controller.