Analysis Of Vibration Suppression Of Two Kinds Of Elastic Systems

With the rapid development of space science and robotics,it is well known that the stability and optimality analysis of flexible structure control systems is one of the main research directions.The stability analysis and optimal control of several kinds elastic system models are worth studying.In this thesis,two kinds of elastic system models are studied:one is Timoshenko beam system with bounded variation control function;the other is a weakly coupled plate-wave system with local viscoelastic damping.In this thesis,we first transform the two types of system equations into abstract evolution equations,and then,using the relevant knowledge of linear operator semigroup theory,it is obtained that two types of systems are well posed.Go a step further,for the first kind of system,it is obtained that the suboptimal trajectory of the system is exponential stable by using the receding horizon control method;for the second kind of system,the exponential stability is obtained by using the piecewise multiplier method and the discussion of contradictions.This thesis consists of five chapters:In the first chapter,the background of two types of distributed parameter systems studied in this thesis,namely,the Timoshenko beam model and the weakly coupled plate wave model with local viscoelastic damping,is introduced,and the research status of these two types of distributed parameter systems is analyzed.Finally,the main research contents,methods,and results of this thesis are presented.In the second chapter,some basic concepts and theories to pave the way for the next two parts to study the stability and optimality of the system are introduced.In the third chapter,using the relevant knowledge of linear operator semigroup theory,we first prove the following system is well posed.And then,it is proved that the suboptimal trajectory of the system is exponential stable by using the receding horizon control method.In the fourth chapter,the frequency domain method and multiplier technique are used to study the following plate-wave system.The energy is uniformly exponentially decayed.The last chapter of this thesis makes a brief summary of the full text,and makes a prospect for further research.