Modeling And Control Design Of Flexible Beam Structure

With the development of science and society, flexible beam structure has been used inmany engineering field, especially in aerospace and mechanical engineering field, such asantenna in the large space station, solar panels and flexible mechanical arm of the robot. Sincethe flexible beam structure has small stiffness, large flexibility and geometric nonlinearfeature, it will easily be made to vibrate unstably for a long time, which is caused by smallelastic deformation, when the flexible beam is disturbed or in large motion. The vibration willnot only influence the precision and efficiency of system, but also speedup the fatigue damageof structure which seriously shortens the service life of materials and brings economic losses.Therefore, vibration control research of the flexible beam structure has been one of theresearch hotspots at home and abroad.Compared with passive control, active control is of strong environmental adaptabilityand flexibility. So this paper will take a research on the modeling and vibration control offlexible beam, based on the active control and boundary control method. The following is themain contents of this paper.1. Flexible beam structure is a kind of typical distributed parameter systems and itsmathematical model is a set of partial differential equations. In the second chapter of thispaper, the partial differential equations and boundary conditions of the flexible beam will begiven based on the Euler–Bernoulli beam by using Hamilton theory. In addition, varyingtension and boundary unknown disturbance will be considered into the model of flexiblebeam.2. Combining Lyapunov direct method and boundary control technology, we design PD,robust and adaptive control law at the right boundary of the flexible beam, to inhibit vibrationof the system. Furthermore, the Lyapunov theory is used to prove availability of the proposedcontrol method so that the flexible beam system is uniformly bounded and exponentiallystable, thereby avoiding control overflow and stability problems based on truncation model.3. With the help of finite difference method, we take a simulation of the flexible beamsystem to illustrate the effectiveness of the proposed control method. And the result not onlyshows the effectiveness of the proposed control method expectedly but also displays the effects of varying tension on the flexible beam.