# Research on Semi-Active Vibration Control of Pipeline Based on Magneto-Rheological Damper
## 1 Introduction  
Pipeline system is an important carrier for the transmission of fluid and energy, which is widely used in power machinery, ship, aerospace, petrochemical industry, thermal system, sewage treatment system, water supply, drainage system and other fields [1; 2]. During the flow process of fluid medium in pipeline, the pressure and velocity of fluid medium in pipeline will change due to the change of pipe diameter, pipe turning and other factors, as well as the opening, regulating and closing of valves in pipeline. The impact of pulsating fluid on the pipe wall will cause the vibration of the pipeline [3]. Moreover, the external vibration will also transmit the vibration of the matrix structure to the pipeline system through the pipeline connection fixture. Thus, vibration reduction of the pipeline system is crucial to the industrial production.  
Over the past several decades, many research efforts have been made to study the dynamic behavior of pipeline, and several methods are proposed to settle structural vibration problems [4; 5; 6; 7]. In a related field of vibration control, attaching a tuned mass damper (TMD) has become a widely accepted method for flexible and low-damped structures. [PERSON] et al. [8; 9] proposed a bounding tuned mass damper (PTMD) which used the impact of a tuned mass with viscoelastic materials to mitigate the vibration of the flexible pipeline structures. [PERSON] et al. [10] designed a pipe wall actuator, which was driven by anelectromagnetic element for the active control of structure-borne and fluid-borne waves in a polyvinyl chloride (PVC): pipe filled with low-pressure water. [PERSON] [11] designed two types of fluid actuators (a side-branch actuator driven by an electromagnetic shaker and a Helmholtz resonator assembly with piezoelectric composite inside) to reduce the vibration power flow in a low-pressure fluid-filled pipe (7000 Pa). [PERSON] et al. [12] presented an active control system using piezoelectric actuators based on regulator theory and robust control theory to restrain vibration of self-excited pipes.  
Magneto-rheological (MR) damper based semi-active control systems could provide the reliability of a passive system and approach the effectiveness of an active control system without requiring heavy power supply. MR dampers have the advantages of strong damping force, broad temperature range, low energy consumption, fast response and simple structure [13; 14]. Therefore, MR dampers have been widely applied in vibration and shock control, high-rise building anti vibration, vehicle suspension system, precision machining and crash worthiness systems [15; 16]. It is feasible to control the vibration of pipeline by installing MR dampers in the fluid dynamic pipeline system, and using intelligent control strategy to control the vibration automatically according to the pipeline's vibration response. The pipeline vibration control system based on MR damper is shown in Figure 1.  
In this research, to reduce the low-frequency vibration, a semi-active control method for pipeline vibration based on MR damper is proposed. Firstly, a MR damper for pipeline vibration control is developed and the dynamic model of the MR damper is established. Then, the mechanism of pipeline vibration is expounded, the state equation of pipeline system is established, the transfer function of pipeline system is deduced, and the stability of pipeline system and sinusoidal excitation response are analyzed. Finally, the semi-active vibration control algorithms of pipeline, such as two-state, PID and sliding-mode-variable-structure (SMVS), are proposed, and the vibration control law of pipeline is deduced and simulated. The semi-active vibration measurement and control system of pipeline based on MR damper is built, and the vibration control performances of different pipeline vibration control algorithms are tested.