Robust active vibration control of thin plate systems with parameters uncertainties

Abstract

In engineering practices, most of the complicated systems or structures, e.g., wing of aircraft, chassis of automobile or case, etc. are modelled as thin plates, and subjected to various kinds of excitations, such as machinery dynamic unbalance, earthquake, wind, wave etc. which induce vibrations. Usually, vibrations that occur in these systems or structures are undesirable. Not only can they accelerate fatigue and failure of the structures, but also degrade the system's performances. Hence, vibration control becomes one of the most important research topics, and leads to its rapid development and successful application in the fields of mechanical, structural and aeronautical engineering for decades. This thesis focuses on robust analysis and active controller synthesis for thin plate systems with parameter uncertainties. To thoroughly address the issues of robust active vibration control (RAVC) design for such systems, three aspects have been studied: modelling and vibration analysis; controllability and observability analyses, selection of optimal actuator/sensor locations; and controller synthesis. Firstly, the modelling and vibration analysis for thin plate systems with parameters uncertainties are presented. Vibration analysis is discussed using complex modal theory and state space description techniques. An algorithm is developed real-time for system modal parameter identification from the test data contaminated with noise using recursive ARMAX approach. Robust determination of model order is studied based on the Hankel singular value by optimizing average component cost and performance index. Modal tests are carried out to provide the accurate data for modelling. Secondly, the controllability and observability for thin plate systems are investigated using SVD and the degree of controllability and observability. Based on the robustness index, the analyses are expanded to the systems with parameters uncertainties, and some new criteria are proposed to determine the number and location of actuator/sensor. The influences of measurement noise on the optimal actuator/sensor locations are discussed using matrix perturbation theory and condition number approach. Thirdly, a novel robust synthesis method of active vibration controller for thin plate systems with parameters uncertainties is developed using variable parameter feedback control. It includes the following two steps: (1). for a nominal vibration system, an active controller based on the eigenvalue assignment is synthesized using the complex modal theory, parameter optimization, linear matrix inequality and stability techniques, i.e., AVC design; (2). for the systems with parameters uncertainties, the robust active controller is synthesized by adjusting the parameters of the obtained AVC system, using the δ -stability control, Lyapunov approach and robust eigenvalue assignment. It is a simple and effective method, and is easy to be realized for real-time control. Fourthly, a fuzzy model-based controller is developed using fuzzy logic control (FLC) approach for comparison. In the first step the fuzzy model of the studied system is identified using rule-based or relation-based approach. In the second step, an adaptive fuzzy controller is developed, and the algorithms assess the output of the controller online, a suitable control signal is computed from the fuzzy relation and applied to the excitation loop every time-step. It is robust against parameters uncertainties and external disturbances. Finally, the numerical simulation and experimental investigation of robust control for a thin plate with parameters uncertainties are carried out. The control algorithms and program are also outlined, and implemented on a real system.