Vibration Cancellation in Plate Structures

Author: Qingqing Chen

Chen, Qingqing, 2016 Vibration Cancellation in Plate Structures, Flinders University, School of Computer Science, Engineering and Mathematics

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In a mechanical system, unwanted vibration is usually considered as noise because it can affect the accuracy of the system or even damage the entire system. The task of vibration cancellation therefore plays an important role in the design of the mechanical system.

In this project, a multi-input multi-output (MIMO) vibration cancellation problem is demonstrated using a laboratory plate structure, which consists of one base plate, three sensor/actuator pairs, one disturbance transducer, and one top plate. The vibration to be controlled on the top plate is introduced by the disturbance transducer that is mounted on the base plate. The main goal of this project is to control the first three modes of the vibration on the top plate while the external vibration caused by the disturbance transducer persistently exists.

Theoretical analysis method and physical experiment method are utilized to derive the transfer function matrix of the plate. Modal analysis software, ModalVIEW, is used to obtain the frequency response function (FRF) of the plate as well as the parameters of the transfer functions including natural frequencies, damping ratios, and mode shapes. For the purpose of the controller design, the measured model of the plate is truncated to the first three modes and a model correction technique based on spatial H2 norm is applied to the truncated model to minimize the truncation error.

Based on the transfer function matrix obtained in the modeling stage, positive position feedback (PPF) control technique is selected to design the controllers because of its quick roll-off property at higher frequencies and its stability of the corresponding closed-loop system. The plate structure is considered, respectively, as a group of individual SISO systems or a single interconnected MIMO system for the design and implementation of the PPF controllers. Natural frequencies of the PPF controllers are set to be the same as the target modes in order to add extra damping according to the PPF design principle. Selection of the damping ratios and controller gains is considered as a spatial H infinity optimization problem. SISO and MIMO PPF controllers are designed, respectively, for the corresponding SISO and MIMO models of the plate.

The designed SISO-PPF and MIMO-PPF controllers are validated via simulation and experiment separately. It is seen that the simulated PPF controlled system can achieve the desired control effects, and the current experimental results can achieve on average a 30.1% of vibration attenuation. With further tuning of the parameters of the PPF controllers as well as the mathematical models of the plate structure, it is anticipated that the experimental vibration attenuation can be further improved

Keywords: vibration cancellation, positive position feedback, plate structure, MIMO

Subject: Engineering thesis

Thesis type: Masters
Completed: 2016
School: School of Computer Science, Engineering and Mathematics
Supervisor: Fangpo He