Robust Control Of The Transverse Vibration Of Wheel System

Axially moving string system is widely used in the fields of military,aerospace,civil and mechanical etc..belt drive system moves along the axial direction at the same time under large axial tension,belt has small gravity and its bending stiffness characteristics is neglected,so it can be simplified to the axially moving string model.But vibration of axially moving strings brings bad effect in engineering applications,so that its applications is limited.Because the system model has parameter uncertainty,structural uncertainty,external interference other uncertain factors,The traditional control methods are difficult to meet the requirements of high precision control of vibration system.It is an important subject how to design a reasonable controller that meets the requirements of robust,stability and reliability.The thesis makes some preliminary researches how to establish dynamic equation of the system and control model and to design robust controller.1.Based on the thought of differential,the equations of transverse vibration that contain a constant speed axially moving string system with external disturbance had been derived.And the dynamic differential equation has been solved with the method of separation of variable.According to the theory of the string-actuator vibration coupling and the solution of dynamic differential equation of string,the relative actuator dynamics differential equations had be derived.2.For the model of the transverse vibration of axially moving strings control is established with structural uncertainty,according to the two stability theory,the actuator dynamics differential equation is expressed into a state space form.Based on two stabilization control,designing a controller ensured stabilization,robust and reliable stability in the stable radius,it can effectively control actuator vibration,lateral vibration of an axially moving string.The numerical simulation by Matlab demonstrates the effectiveness of the control method.3.Aiming at external interference in moving string and structured uncertainties in control model,a robust H? control method was proposed by describing dynamics differential equations of actuator into corresponding state space to eliminate outside interference and the influence of uncertainty to control performance model.The availability that H? state feedback control on the vibration of the coupled system comprising the axial movement of the string and the actuator was checked by numerical simulation test.4.Because there are two Riccati equations to solve when we design two stabilization control law and H? the state feedback control law,needing to adjust some parameters and the positive definite matrix in solving the corresponding Riccati equation process,it brings some trouble.In order to solve this problem,this paper,based on the linear matrix inequality approach,designs the corresponding H? state feedback control strategy,it bring great convenience the design of controller.Finally it is to verify the effectiveness of the method through the numerical simulation of belt drive system.