Optimal Control for Vibration of Restrained Cantilever Fluid-Conveying Pipe

Abstract

The cantilever fluid conveying pipe which restrained by linear spring and cubic nonlinear spring at its free end was studied and the nonlinear vibration of this piping system was carried out optimal control making use of piezoelectric patch as actuator. Firstly, the governing equations of the controlled system were derived out. Then the optimizer and mode sensor were schemed out. Finally, the control effect of the designed controller on system vibration was validated and analyzed through numerical simulation. The simulation results showed that the designed optimal controller can actualize effective control for the monocyclic motion, multi-cyclic motion and chaotic motion of the pipe conveying system. Meanwhile, the effect of state weight-matrix and control energy weighing coefficients on control performance of system, the influence of the position and length of piezoelectric patch on minimal performance index of system were also been under discussion. For practical application of this control method, we should synthetically consider all of the practical conditions and demands to select the optimal position and length of piezoelectric patch and the optimal weight value of state matrix and control energy according to different work conditions.