Transverse Vibration Control Of The Axially Moving Strings

An axially moving string is an important mechanical modal both in engineering and in the study of mechanics. Transverse vibration control of such a system is an important engineering objective. The main purpose of this dissertation is to study the transverse vibration control of a coupled axially moving string system.The main respects of the research are listed as follows1. The dynamics models both linear and nonlinear for an axially moving string with a tensioner are developed. By means of the dynamics relation between the axially moving and the tensioner, the transverse vibration of the string is controlled by the control laws acted on the tensioner.2. The passive and active control strategies are implemented based on the transfer principle of traveling waves.The passive control law is designed by means of the energy transfer principle of traveling waves. The energy in the system is minimized by means of the optimal control coefficient, determined by maximizing the total energy dissipation, and as a result, transverse vibration of the string is stabled. The finite difference method is employed to approximate the simulation results, witch demonstrate the effectiveness of the control method.Active vibration control of the axially moving string based on the principle of the wave propagation is proposed. The control problem is formulated in the s domain and the responses of both the open and the closed systems are given by their transfer functions. The controller designed by wave cancellation consists of velocity sensors, proportional gains and time delays. The method of the numerical inversion of the Laplace transform is employed to approximate the simulation results. The numerical results demonstrate the effectiveness of the controller.3. Lyapunov method is employed to designed the control laws for the linear system.In the study of the first control law, based on Lyapunov theory, the boundedness of the uncontrolled span and the exponential stability of the controlled span under the controller are proved , respectively. The effectiveness of the controller is demonstrated by simulations.In the study of the second control law, the total mechnical energy of the controlled span of the string and the tensioner is a Lyapunov function. With the decay of the total energy, the linear feedback control law is proposed. The asymptotic and exponential stability of the controlled system is proved by the use of semigroup theory.4. The adaptive method is employed to designed the control laws for the linear system. Based on the exact knowledge in chapter 4, to compensate for unknown parameters , an adaptive controller is developed. The asymptotically stability of the controlled system under the controller is proved. the robust of the controller is also demonstrated by simulations.5. Lyapunov theory is employed to designed the control laws for the nonlinear system. The nonlinear controller is designed with Lyapunov , and also asymptotically drive the controlled span displacement to zero.