*Article* **A Case Study of Open- and Closed-Loop Control of Hydrostatic Transmission with Proportional Valve Start-Up Process**

**Paweł Bury 1, Michał Stosiak 1,\*, Kamil Urbanowicz 2, Apoloniusz Kodura 3, Michał Kubrak <sup>3</sup> and Agnieszka Malesi ´nska <sup>3</sup>**


**Abstract:** This paper concerns the start-up process of a hydrostatic transmission with a fixed displacement pump, with particular emphasis on dynamic surplus pressure. A numerically controlled transmission using a proportional directional valve was analysed by simulation and experimental verification. The transmission is controlled by the throttle method, and the variable resistance is the throttling gap of the proportional spool valve. A mathematical description of the gear start-up process was obtained using a lumped-parameters model based on ordinary differential equations. The proportional spool valve was described using a modified model, which significantly improved the performance of the model in the closed-loop control process. After assuming the initial conditions and parameterization of the equation coefficients, a simulation of the transition start-up was performed in the MATLAB–Simulink environment. Simulations and experimental studies were carried out for control signals of various shapes and for various feedback from the hydraulic system. The pressure at the pump discharge port and the inlet port of the hydraulic motor, as well as the rotational speed of the hydraulic motor, were analysed in detail as functions of time. In the experimental verification, complete measuring lines for pressure, speed of the hydraulic motor, flow rate, and temperature of the working liquid were used.

**Keywords:** hydrostatic transmission; hydrostatic transmission start up; hydraulic drive
