Abstract: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 compensate 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.