The Transverse Vibration Control Of An Axially Moving Rectangular Membrane

In this paper, the transverse vibration control of an axially moving rectangular membrane is analyzed. The main research work is as follows:(1) Using the finite difference method, the state equation of the transverse vibration of an axially moving rectangular membrane is derived. Based on the suboptimal control method and velocity feedback method, the transverse vibration control of an axially moving rectangular membrane is studied, and the optimal control law is obtained, then the stability of the control system is ensured. The simulation results of Matlab show that this method can effectively control the transverse vibration of an axially moving membrane and reduce the consumption of the controlling energy.(2) Based on the Galerkin method, the state equation of the transverse vibration of an axially moving rectangular membrane is derived. By means of the state space, the transverse vibration control of an axially moving membrane is studied, and the state observer is designed to control the system by using state feedback, and the optimal control law is obtained. The adoption of the velocity feedback ensure the stability of the control system. The results show that this method can effectively control the transverse vibration of an axially moving membrane(3) The metering equipment of stochastic system including noise is considered. By the Kalman filter, the optimal linear estimate of the system state is obtained according to the system definite input and the random survey output, and the linear feedback control to the axially moving rectangular membrane is carried on by replacing the real state of the system by the estimated status messages. The system comprising the survey noise output can achieve the optimal control effect when the Kalman filter and the stochastic condition regulator is considered together and the optimal state feedback is designed.(4) The vibration control of system subjected to uncertain external disturbances is studied. According to robust control theory, the controller is designed to make the H_∞ norm of the transmission function of the loop system minimum. For optimal H_∞ control, here the H_∞ control solution method based on the linear matrix inequality is used to comprehensively analyze the transverse vibration control systems of the axially...