Abstract: Aiming at the critical challenge in the precise control of the curve fertilization trajectory for the orchard ring-furrow fertilizer applicator under complex and heavy-duty working conditions, a ring-furrow trajectory control system was designed and analyzed based on a multi-segment arc fertilization trajectory. The control system synthesized the fertilization trajectory by precisely regulating the transverse variable-speed telescopic motion of the furrow opener and coordinating with the constant-speed linear forward motion of the fertilizer applicator. First, the drive system for the furrow opener's transverse telescopic motion was analyzed, based on the variable-speed motion law of the furrow opener's telescopic motion under the multi-segment arc trajectory. The variable-speed control characteristics of three hydraulic speed control circuits driving the transverse telescopic movement of the furrow opener were analyzed by AMESim simulation with adjustment time and linear error as indices, including circuits with proportional speed control valve, proportional throttle valve, and proportional directional valve. Then, a control system co-simulation model was established by AMESim-Matlab based on the proposed segmental PID (proportional-integral-derivative) control method. The model integrated a hydraulic drive system model for the furrow opener's variable-speed telescopic motion and a segmental incremental PID control model, to analyze the adaptability to the working conditions and the control accuracy of the full segment of the trajectory. Finally, the fertilizer-spreading and furrowing tests with curve trajectory were conducted to verify the control system. The results showed that the adjustment times required for the extension and retraction speeds of the hydraulic cylinder in the proportional directional valve circuit to reach 0.28 m/s were 0.02 s and 0.05 s respectively, and the linear errors of extension and retraction speeds within 0～0.4 m/s were 0.16% and 0.07% respectively. The adjustment times and linear errors in the proportional directional valve circuit were significantly lower than those in circuits with proportional speed control valve or throttle valve, demonstrating optimal dynamic and steady-state speed control characteristics. The results of the AMESim-Matlab co-simulation showed that the correlation coefficients between the actual and the target displacement curves of the furrow opener's transverse telescopic movement were all greater than or equal to 0.99986, with all root mean square errors less than or equal to 0.00188 m under four typical working conditions such as no-load, normal operation, compact soil, and sudden resistance change. The segmental PID control method ensured the control accuracy for the full segment of the fertilization trajectory, and showed excellent adaptability to the four typical working conditions. The fertilizer spreading test with curve trajectory showed that the relative errors of the closest distance between the fertilization trajectory and the tree row, the base circle radius of the ring furrow, and the tangent arc radius were 1.76%, 1.27%, and 2.65%, respectively, achieving high control accuracy of the trajectory parameters and good adaptability to the plant spacing. The curve furrowing test indicated that the correlation coefficients between the actual and the target displacement curves of the furrow opener's transverse telescopic movement reached 0.9950 and 0.9991, with root mean square errors of 0.0103 m and 0.0078 m, for the plant spacing of 1.3 m and 2.3 m, respectively. The control accuracy of the system met the requirements under the complex and heavy-duty working conditions of the curve furrowing. The fertilizer-spreading and furrowing tests with the curve trajectory verified the reliability of the control model constructed in this work. The study realized the precise control of the curve fertilization trajectory based on the multi-segment arc. The results can provide the basis and reference for the trajectory control of the working components of the agricultural machinery and the technological development of the mechanized ring-furrow fertilization in orchards.