In the thesis named "Robust control of flow-induced vibrations", the effects of moving fluid with a constant velocity on an elastic membrane are investigated, and to avoid probable bad results the system gets stable by designing a controller. By using the potential theory of fluid mechanics; the fluid pressure on the membrane is investigated as a coupled differential equations system. By using the theory of boundary backstepping control of partial differential equations stability analyses and control designs of the systems are achieved. The results are derived by the help of a simulation program.
By using the theory of boundary backstepping control of partial differential equations, results moved to a further stage and boundary backstepping control of partial differential equations are derived for poly-dimensional heat and wave equations which are the canonical problems of the mathematical physics. Stability analyses of the investigated systems are derived by using Lyapunov stability analysis theory. Thus, it is proved that the controller designed in the thesis gets the investigated system into a stable region.
Design of the boundary backstepping control of partial differential equations(PDE) is also used for linear time Invariant(LTI) delay systems. In some cases a system can be unstable because of the delays. When designing a controller for a system, nobody uses delays. In this design a PDE system and a LTI delay system are used as a coupled system, and the controller is derived by PDE system and applied to the LTI delay system. Thus, the investigated system gets into a stable region by using delays in controller design process. The controller derived by this process is applied to a linear vehicle system and the results are gotten by the help of a simulation program.
Finally, the pressure of the fluid on the membrane and the membrane vibrations are investigated as a coupled system. By making flutter analysis the relationship of the fluid velocity and the Eigen frequencies of the membrane are investigated.
In brief, boundary backstepping control of distributed parameter systems theory is applied to flow-induced vibrations. By the results controller design is generalized to poly-dimensional distributed parameter systems. For the controller design of LTI delay systems; systems are used as a coupled system with the distributed parameter systems. Finally the thesis is finished with the flutter analysis. |