Modeling And Vibration Control Of Distributed Piezoelectric Smart Structures

Along with the technology development of aviation, aerospace and mechanism,research on vibration control has been an important and issues. Traditional structuresand control methods are very difficult to meet the environment requirement. With theemergence of smart structure and its application recently, research of smart structureis becoming a very active area in research and application of structural vibrationcontrol. The piezoelectric materials have been widely used in the field of structuralactive vibration control as a new type of smart materials because of their excellentmechanical-electrical coupling characteristics.Based on partial differential equations(PDEs), this thesis focuses on thediscretization of the infinite equation, optimization placement, damping model,parameter estimations and vibration suppression in active vibration control ofdistributed piezoelectric smart beam.Distributed piezoelectric smart structure is a distributed parameter system ofinfinite dimensions and the vibration features can be accurately described with thePDEs. In order to analysis the influence of piezoelectric structure and for theconvenience of control design, the PDE is approximate to ordinary differentialequations by using Galerkin discretization. Firstly the accuracy of discretization thatdepends on the number of space basis functions is studied, especially the relationshipbetween the basis number and ratio of the beam and the PZT. Furthermore, due tosticking on the PZT and its geometric parameter, quantitative analysis of the naturefrequency and transfer functions analysis is further researched by utilizing thedisctretization equations.It is presented that a methodology for obtaining the optimal placement of PZTactuator/sensor under considering stick effect and measure noise in the activevibration control of piezoelectric beam. Firstly, suppose the candidate positions arefinite, and use Kalman separate principle to obtain the actuator location. Based on theactuator location and the observer performance, the sensor location will be found.This methodology does not need to find the optimal placement necessarily at the sametime. The procedure is greatly simplified, reduces the optimal numerical computation and gives the optimal placement result in acoustic condition. Numerical example ofthe flexible beam is presented to support the methodology is efficient and fast, andthat gives a uncollated placement result what is different to the common result and thesensor position changes more.In order to get the accurate physical parameter of the piezoelectric clamped beam,the estimation of parameter will be used. Considering the features of beam andexperiment system and combining the advantages of frequency domain analysis, thisthesis accomplishes the parameter estimations process. When two commonly useddamping models (viscous damping model and hysteresis damping) are introduced, thechange of all models damping ratio in the system transfer functions is thoroughlyanalyzed and the results of two model and experiment are compared. At last, it isindicated that the cause of parameter estimation errors is the different damping model.The damp is always an important part and an very difficult process of the modelingof the large space structures. This thesis proposes a new modified damping model:piecewise damping model based on viscous damp model. The new damping model isdepended on the frequency compared with the old static damping model and thecoefficients could be got by identification. The static viscosity damping model couldnot accurately describe the whole structure. When compared with conventional staticmodels, the new model could offer a accurate description for the dynamic output andsystem magnitude response of the integrated PZT systems. The experiment results ofclamped beam haveshown the conclusions and the new model will be efficient forparameter estimations.The higher plant model should be reduced for the response analysis and controldesign. Two model reduction methods in control theory and modal truncation in thedynamics of structures are illustrated with the clamped beam and they are equivalentunder certain conditions of the actuator/sensor placement. According to the reducedmodel, the LQR controller based on the observer is designed. Three equivalent weightmatrices are proposed, and that the performance of the controller corresponding withthree weights has shown it. The controller effectively suppresses the vibration of thebeam in the experiment. As LQG controller leads to the control spillover in theexperiments, the reverse recovery of LQG is represented for the Non-minimum phasesystem in this thesis. This mouthed reduces the virtual noise to a certain extent andthen obtains the tradeoff between the control performance and system stability.Finally the controller is successfully used without spillover in the experiment. As the piezoelectric structure is easy to damaged the research on active fault controlof the piezoelectric smart structure is imperative and much important. This thesisconsiders the model modified and active vibration control of MIMO system.Preliminary study on active fault control for some actuator fault has been carried outThe simulation computation has verified the control design.