PDE Based Disturbance Observer Design And Lmi Control Method For Flexible Systems

With rapid development of technology,due to advantages of light weight,low energy consumption,high-speed,small impact force,fast operation,wide operating range and low cost,flexible systems have been increasingly used in aerospace,national defense,industry and other fields.However,flexible systems will inevitably produce vibration in the practical application,which will not only decrease the control accuracy but also influence the control effect of the flexible system.Therefore,the vibration suppression of flexible system is of great significance.Through studying the related researches on flexible systems done by scholars of various countries in recent years,based on PDE models,the observer design and LMI control method for the flexible beam and flexible rope in flexible systems are investigated in this paper.In this paper,LMI method is also introduced to increase the efficiency of the control design and improve the control effect.The contents of the research are listed as follows.Firstly,the distributed parameter modeling of the flexible system with unknown boundary and distributed disturbances is presented.This paper analyzes the kinetic energy,the potential energy and the non-conservative force work of the moving flexible system.The Hamilton principle is used in this paper to derive PDE dynamic models of the flexible string and flexible beam.In addition,boundary conditions of the flexible systems are also given in this paper.Secondly,we design the exponentially stable boundary and distributed disturbance observers to accurately estimate the unknown boundary and spatially distributed disturbances on the basis of the established PDE models in this paper.Thirdly,the boundary control laws are designed respectively for the flexible string and flexible beam without unknown disturbances by using LMI and the vibration suppression of flexible systems is realized in this paper.With the proposed control laws,the closed-loop systems are asymptotically stable.Finally,considering the influence of the unknown disturbances of the flexible system,the boundary and the distributed control laws are designed for the flexible string based on LMI.The closed-loop asymptotic stability of the flexible string with the unknown disturbances can be obtained in this paper.The H? boundary control law is also designed for the flexible beam by using LMI so as to realize the vibration suppression of the flexible beam with boundary disturbance and attenuate the influence of the external distributed disturbance on the flexible beam.