A Linear Approach to the Control of Vortex Induced Vibrations of Circular Cylinders with a 2-D Van der Pol Model for Structural Oscillator

In the present paper, a new 2-D Van der Polstructural oscillator model is introduced for the vortex induced vibrations of circular cylinders.The main purpose of this task is to control the recently introduced model by means of modern control definitions in state space. In order to control the system, the whole model is linearized about its equilibrium point by deriving state-space matrices. Then, the linear transfer function is obtained and controlled by pole-placement technique which is based on the state variables feedback. Afterwards, this linear controller is applied to the nonlinear system about its equilibrium point by assuming that there is no uncertainty in both physical and mathematical models. Eventually,the results for linear and nonlinear systems are compared.