Effects Of Delayed Feedback Control On Stability In The Cantilever Pipe Conveying Fluid

The fluid-induced oscillation of the pipe conveying fluid is a fluid-solid interaction problem. The problem researched profoundly affect everyone life and work every day. Through the development of more than 100 years, people constantly study the typical system for controlling vibration of the pipe conveying fluid. Along with the modern technology development by leaps and bounds, the time delayed feedback control vibration technique is a new one of active vibration suppression. It has gradually become one of the most challenge problems in academe and engineering. In this paper, we propose a delayed feedback to control the vibration of the vertical cantilever pipe conveying fluid. Based on mode analysis theory, the Direct Method is employed to analyze the stability of the delayed feedback control system. The focus is the effect of the gain and time delay on the critical velocity of flow.The main works include the following aspects.(1) Recent research on the pipe conveying fluid system domestic and abroad is summarized and concluded. The delayed feedback to control the vibration of the vertical cantilever pipe conveying fluid is proposed firstly.(2) The delayed feedback dynamical equations of the vertical cantilever pipe conveying fluid are deduced through adding the delayed feedback object. The partial differential equation is transformed into a set of ordinary differential equations using the Galerkin method. Then, the static stability of first two modes about the system is discussed using the Direct Method. The effect of the gain and time delay on the performance of improving the critical velocity of flow also is investigated in this paper.(3) Take the delayed position feedback and velocity feedback on the system respectively. The differences of two feedback methods are discussed based on the theoretic analysis. In improving the same the critical velocity of flow case, the delayed velocity feedback has more advantage than the delayed position feedback. Conclusions of Numerical approach acts in accord with theoretic analysis. It verifies that delayed feedback can improve the critical values of the fluid velocity by controlling the gain and time delay.