Controller Design And Stability Analysis Of Timoshenko Beam With Delay

Due to extensive applications of the system with delay,more and more scholars devoted to study the stabilization of the system with controller delay.In this thesis,the feedback control strategy is designed for Timoshenko beam with delay,and the stability of the systems is investigated.1.Feedback controller design method and exponential stability analysis for Timoshenko beam with distributed delay in the boundary control have been given.We suppose that the state of the system is measurable,the partial state of the system is predicted by Smith predictor.By simple calculation,the system with controller delay is transformed into un-delay system.Based on the decay of the energy for the un-delay system,we design the feedback controller and obtain a closed loop system.We prove the dual system is exactly observable in finite time,and hence the closed-loop system is exponentially stable.Next,we prove the error system between the un-delay system and the original delay system is exponentially decay,thus,under certain condition,the original system with distributed delay in the boundary control is also exponentially stable(or asymptotically stable).2.Under assumption for the state not measurable,we study the exponential stability for Timoshenko beam with distributed delay in the boundary.Firstly,we design the state observer of exponential-stable type.Secondly,we design the partial state predictor for the state observer.Thirdly,we obtain a un-delay system and prove the error system between the un-delay system and the observation system is exponentially decay.The error system between the observation system and the original delay system is also exponential stable.At last,The exponential stability(or asymptotically stability)for the original delay system is derived.3.Suppose that the state is measurable,we study the exponential stability for Timoshenko beam with different delays in the boundary.We adopt similar means to the thirdly chapter and design the new feedback controller.Under satisfying certain conditions,the system can be exponentially stable(or asymptotically stable).4.We consider the exponential stabilization for Timoshenko beam with input and output delays.The state time is divided into two parts.The exponential observer is established for one part state,Another part state is predicted.We obtain the approximate one for the original system.By the means of the Luenberger observer and partial state predictor,we obtain the exponential stabilization about Timoshenko beam with output and input delays.