## 1 Introduction
It is mainly unaffected by load but does not consider the system's energy consumption [17]. [PERSON] adopted the distribution decoupling control strategy based on hydraulic pump efficiency for the variable-speed and variable-displacement pump-controlled hydraulic cylinder system to solve the nonlinear problem of control-variable multiplication [18]. [PERSON] proposed a control strategy based on working condition decoupling and a fuzzy gain-scheduling control algorithm for electro-hydrostatic servo actuators under the combined control of speed and displacement. Simulation and actual experiments proved that the proposed composite-control strategy can effectively improve the dynamic performance of the electro-hydrostatic actuator system [19]. The compensation loop of the passive valve using a hydraulic control check valve for flow compensation is simple and suitable for working conditions with small load-direction changes. A circuit using multiple pumps to compensate for the unbalanced flow rate also has high stability, but an increase in the number of pumps leads to increased installed power [20]. With the development of control technology, research on pump-controlled hydraulic cylinder systems has become more in-depth, especially research on the control strategy of pump-controlled hydraulic cylinders, which improves the control accuracy and response performance of the pump-controlled hydraulic cylinder and the more widely used PID control. PID control is widely used because of its strong adaptability and flexibility and easy implementation in practical applications [21]. [PERSON] designed a fuzzy PID controller for a direct-drive pump-controlled hydraulic cylinder system to give the system better dynamic characteristics [22]. [PERSON] applied the sliding-mode controller to the pump-controlled hydraulic cylinder system, significantly improving the system's robustness [23]. [PERSON] designed an adaptive fuzzy controller for the position-control system of a variable-speed pump-controlled hydraulic cylinder and proved that the system has good position-control function through experimental research [24]. [PERSON] from the United States adopted the singularity perturbation theory to eliminate fluctuations in the working commutation speed of the pump-controlled cylinder [25]. [PERSON] of Ulsan University in South Korea adopted an adaptive backthrusting control algorithm for the pump-control system, which significantly improved the robustness and anti-interference of the system [26]. In addition to the theoretical research on pump-controlled hydraulic cylinder technology, foreign experts have already achieved more achievements in applying pump-controlled hydraulic cylinder technology in aerospace, robot control, and other fields. American engineers applied variable-speed and constant-displacement pump-controlled hydraulic cylinders to fighter aircraft, achieving good operational test results [27]. [PERSON] and [PERSON] applied pump-controlled hydraulic cylinders to robot platforms, reducing the platform impact and improving the control performance [28; 29]. Foreign experts have already achieved more in applying pump-controlled hydraulic cylinder technology in aerospace, robot control, and other fields.To sum up, foreign research on pump-controlled single-exit rod hydraulic cylinder systems mainly focuses on the asymmetric flow balance of the system and the control strategy of the pump-controlled hydraulic cylinder system as well as the application and promotion of pump-controlled hydraulic cylinder technology, and specific achievements have been achieved in the theoretical research and practical application of pump-controlled hydraulic cylinder systems. A comprehensive control strategy that integrates speed and displacement is proposed to optimize motor velocity, achieve load-power matching, and adjust the hydraulic pump displacement for closed-loop control of the hydraulic cylinder's position.