Academic Journal of Science and Technology ISSN: 2771-3032 | Vol. 14, No. 1, 2025 12 Research on the Speed Synchronization Control System of The Rotary Blowout Preventer Hydraulic Motor Xue Zheng, Hangxin Wei, Kuancheng Lei, Ruixuan Li, Jingyuan Wang School of Mechanical Engineering, Xi’an Shiyou University, Xi’an 710065, China Abstract: Aiming at the problem of unsynchronised rotational speed of the new drilling rotary blowout prevention type hydraulic rotary motor, the rotary hydraulic control system was designed. Using the method of mathematical analysis, a mathematical model was constructed for analysis, and a fuzzy PID controller was designed according to the analysis results, and the hydraulic motor speed control system was simulated and analysed using Matlab/Simulink software. Simulation results show that: in the motor speed control system, the designed controller control effect is obvious, the stability of the system is significantly improved, and for the complex external load environment of the turntable, the adaptability is good and robust. Keywords: Hydraulic motor; Simulink; Fuzzy Logic Control. 1. Introduction The hydraulic rotary table is one of the key pieces of equipment in drilling engineering, used to transfer hydraulic power and torque to achieve rotation of the drill bit. Currently, various hydraulic rotary tables from multiple manufacturers, such as NOV, WIRTH (Germany), and Baoshi Machinery (China), have been widely applied in petroleum drilling operations[1]. However, these systems only meet general rotational power requirements and struggle to control the blowout prevention sealing in the annulus during rotation operations[2]. The new type of rotary blowout preventer hydraulic rotary table can be used as a standard hydraulic rotary table without installing a sealing rubber sleeve, and, when the sealing sleeve is installed, it serves as a blowout preventer for both rotation and pipe handling operations. This rotary table features a complete range of functions, a compact structure, high torque transmission capacity, stable operation, stepless speed regulation, and controllable anti-torque release[3]. In operations such as active drilling tools and various downhole logging tasks, the motor speed output is easily disturbed by external load conditions due to the complex external load environment of the rotary table. This presents a high requirement for the motor speed control system[4]. Therefore, this study addresses the external load interference issue in the new rotary blowout preventer hydraulic motor speed control system by designing a self-tuning fuzzy PID controller. The system adjusts the motor speed by electrically controlling the tilt angle of the variable displacement pump's swashplate to mitigate the load interference[5]. 2. Hydraulic System Principles and Mathematical Modeling 2.1. Hydraulic System Working Principle The new rotary blowout preventer hydraulic motor speed control system mainly consists of a controller, electro- hydraulic proportional valve, hydraulic cylinder, variable displacement pump, and hydraulic motor. The electro- hydraulic proportional valve receives adjustment signals from the controller, which controls the displacement of the valve core[6]. This, in turn, alters the flow entering the hydraulic cylinder, causing displacement that drives the swashplate mechanism of the variable displacement pump to adjust the tilt angle of the swashplate, thus controlling the hydraulic motor's speed[7]. flushing valve Transducer Controller M3 M2 M1 M Figure 1. Schematic Diagram of the Rotary Blowout Preventer Hydraulic Motor Speed Control System 13 2.2. Hydraulic System Mathematical Modeling 2.2.1. Valve-Controlled Cylinder System Transfer Function 1) Electro-hydraulic proportional valve flow equation: x cxL v Lq K K p  (1) Meaning of the Symbols: qL-the flow output of the proportional valve,; Xv-the valve core displacement; Kx-the valve flow gain; PL-the load pressure drop; Kc-the flow pressure coefficient. 2) Hydraulic Cylinder Flow Equation: p t L L tc L p e dx V dp Q C P A dt dt     (2) Meaning of the Symbols: Ctc-the total leakage coefficient of the variable hydraulic cylinder; Xp-the piston displacement; Vt-the total volume of the cylinder's two chambers; 𝛽e-the oil elasticity modulus of the hydraulic cylinder; Ap-the effective area of the hydraulic cylinder piston. By performing Laplace transforms and solving: c( ) ( ) ( )L x v LQ s K X s K P s  (3) ( ) ( ) ( ) ( )t L tc L p p L e V Q s C p s A sx s sp s     (4) The transfer function of the valve-controlled hydraulic cylinder system is obtained. x 2 2 ( ) ( ) 2 1 v P p n n n K x s A x s s s s            (5) ωn is the hydraulic natural frequency, εn is the hydraulic damping ratio. 24 2e m e n m t m t m D D V J V J     n 4 ce e m m t m t md e m k J B V D V D J     2.2.2. Pump-Controlled Motor System Transfer Function 1)Pump Flow Equation: ( )p p p ip h s ep hQ D n C p p C p    (6) p pD k r (7) Meaning of the Symbols: Qp-the variable pump flow; Dp-the pump displacement Np-the pump speed Cip-the internal leakage coefficient Cep-external leakage coefficient ph , ps-high-pressure and low-pressure side pressure kp-pump displacement gradient 𝛾-pump swashplate tilt angle 2) Motor Flow Equation: 0 m ( ) m h im h s em h m e d V dp Q C p p C p D dt dt        (8) Meaning of the Symbols: Cim-motor internal leakage coefficient; Cem-motor external leakage coefficient; θm-motor output rotational angle; Dm-motor displacement; ωm-motor angular velocity; V0-total volume of the working chamber. 3)The transfer function of the valve-controlled cylinder System: 2 2 ( ) 2( ) ( 1) x p p nv n n k x s A sx s s       (9) The transfer function of the pump-controlled motor system: p 2 2 ( ) 2( ) ( 1) q m m r r r k s D sr s s s        (10) 2.3. System Transfer Function The principle of the motor electro-hydraulic proportional control system is shown in the[8]. The main parameters of the mathematical model are shown in[9]. The open-loop transfer function of the system is obtained. pA Kx + _  sI 1K )(sxp)(0 sU )(sU + F        1 2 2 2 s s s D k r r r m qp           1 2 1 2 2 s s s n n n    Figure 2 The principle of the motor electro-hydraulic proportional control system 14 Table 1. The main parameters of the mathematical model Symbol Symbol Meaning Parameter Dm Hydraulic Motor Volume Displacement per Radian 1.5×10-4 m3/rad ωn Hydraulic Natural Frequency of Valve-Controlled Cylinder System 231.9 rad/s 𝜀n Hydraulic Damping Ratio of Valve-Controlled Cylinder System 0.126 βe Comprehensive Oil Elasticity Modulus of Hydraulic Cylinder 6.8×108 N/m2 V0 Total Volume of the Working Chamber 2.8×10-4 m3 kx Steady-State Flow Gain of Electro-Hydraulic Proportional Valve 2.5×10-3 m3(Aꞏs) ωv Frequency of Electro-Hydraulic Proportional Valve 377rad/s 𝜀v Equivalent Damping Coefficient of Electro-Hydraulic Proportional Valve 0.6 Ap Effective Area of Hydraulic Cylinder Piston 3.14×10-4 m2 3. Fuzzy PID Controller Design 3.1. Control Principle Fuzzy PID control based on the traditional PID algorithm works by using the deviation E between the desired signal and the actual measured signal, as well as the rate of change of the deviation EC, as inputs. Fuzzy rules are matched to determine the adjustment quantities for tuning the PID parameters (i.e., Kp, Kd, and Ki) for real-time correction. The corrected parameters are obtained through a defuzzification process. This controller adapts to internal parameter changes and has strong capabilities in overcoming external disturbances, allowing the controlled system to have good dynamic and static characteristics[10]. The principle of fuzzy PID control is shown in the diagram. The adjustment formula for Kp, Kd, and Ki is as follows: ' ' ' p p p i i i d d d k k k k k k k k k            (11) 3.2. Fuzzy Controller Design Define the input variables E and EC, and the fuzzy subsets and meanings of the output variables Kp, Kd, and Ki as {NB (Negative Big), NM (Negative Medium), NS (Negative Small), ZO (Zero), PS (Positive Small), PM (Positive Medium), PB (Positive Big)}. The domain of these variables is defined in the range of [-6, 6]. In the fuzzy logic toolbox's membership function editor, the membership functions for the input variables E and EC are chosen to be Gaussian, while the membership functions for the output variables Kp, Kd, and Ki are triangular[11]. The specific related parameters are shown in the Figure 3. Figure 3. Fuzzy controller parameter settings 15 3.3. Fuzzy Control Rules Inducing the relationship between the input variables E, EC, and the output variables Kp, Kd, and Ki[12]. The fuzzy rules for the PID controller parameters Kp, Kd, and Ki are established as shown in Figure 4. Figure 4. Fuzzy Rules for Kp Ki Kd 4. System Modeling and Simulation Analysis Using MATLAB/Simulink, a simulation model of the control system based on the derived transfer functions is built. Both PID control and self-tuning fuzzy PID control algorithms are simulated to verify their effectiveness[13]. Figure 5. Fuzzy Rules for Kp Ki Kd 16 4.1. PID Control System Model and Fuzzy PID Control System Model Based on the transfer function, the Simulink control model of the PID control system and the fuzzy PID control system is obtained as shown in Figure 6[14]. Figure 6. PID control system and the fuzzy PID control system model 4.2. Simulation Set the system simulation sampling time to 10 second.Tune the three PID parameters, ultimately obtaining Kp = 0.25, , Ki = 0.24, Kd = 0.02.Substitute the three parameters into the controller. Based on the above steps, simulation analysis of the hydraulic turntable motor speed synchronization control system is conducted using both the PID controller and the fuzzy PID controller[15]. 4.2.1. Simulation results The simulation results of the hydraulic motor speed under PID control and the fuzzy PID control are presented. Figure 7. Speed curves of hydraulic motors under two types of control From the simulation results, it can be seen that: when the target speed signal is input, the two kinds of control reach the steady state after going through the adjustment, and the steady state error is basically zero. In the rotational speed response stage, the traditional PID control showed overshooting, with an overshooting amount of 1.25, and a response time of 4.5s, while the fuzzy PID control did not show overshooting and had a response time of 3.2s, which was substantially improved compared to the traditional PID control[16]. 5. Conclusion The study focuses on the development of a speed synchronization control system for a rotary blowout preventer hydraulic motor, addressing the external load interference that affects motor speed stability in drilling operations. To mitigate these disturbances, a fuzzy PID controller was designed to adjust the hydraulic motor speed by controlling the tilt angle of the variable displacement pump's swashplate[17]. 17 Key conclusions from the study include: 1) The hydraulic system’s working principle and mathematical models were established, including the valve- controlled cylinder and pump-controlled motor systems. 2) A fuzzy PID controller was designed, which helps in overcoming load disturbances and enhancing dynamic and static performance. 3) Simulation results indicated that the fuzzy PID controller significantly outperforms traditional PID control in terms of system stability and tracking performance. In conclusion, the proposed speed synchronization control system using a fuzzy PID controller effectively improves the stability and responsiveness of the rotary blowout preventer hydraulic motor under varying operational conditions. References [1] Luo K, Luo YL. 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