带有输入时滞的Timoshenko梁系统的控制器设计与稳定性分析

摘要

为了研究输入时滞对Timoshenko梁系统稳定性的影响,镇定边界具有输入时滞和载荷的Timoshenko梁系统,利用Backstepping 方法,设计了一种新的控制器来补偿输入时滞带来的影响,从而得到一个稳定的闭环系统.首先,给出一个与原时滞系统等价的无时滞系统;然后,构造一个Backstepping线性变换,并证明这个线性变换是有界可逆的;最后,通过这个变换将无时滞系统转化为一个稳定的目标系统,并设计出相应的控制器.结果表明,此无时滞系统与目标系统是等价的,其反馈控制律可以镇定原来的时滞系统.研究方法解决了输入时滞对弹性系统的负面影响,丰富了分布参数控制系统的控制器设计方法及其稳定性理论,在工程实践中具有一定的借鉴意义.%In order to study the influence of input time delay on the stability of Timoshenko beam system and stabilize the Timoshenko beam system with input delay and load,by using the Backstepping method,a new controller is designed to com-pensate for the input delay,and then a stable closed-loop system is obtained.At first,a delay-free system is given,which is equivalent to the original time-delay system.Then,a bounded linear transformation is constructed,and it is proved that the linear transformation is bounded and invertible.Finally,the delay-free system is transformed into a stable target system by the linear transformation,and the corresponding controller is given,which implies that the delay-free system is equivalent to the target system.Therefore,the original time-delay system can be stabilized by the feedback control law.The negative effect of input delay on elastic system is solved by this method,which enriches the controller design method and stability theory of distributed parameter control system,and has a certain theoretical significance in engineering practice.