**4. Conclusions**

The paper describes the start-up process of a hydrostatic transmission controlled with a serial throttle. Additionally, it includes analyses of a transmission installed in a system equipped with a PI regulator controller. Based on the resulting waveforms over time, it can be concluded that during the start-up phase of an open-loop-controlled transmission with the serial throttle method, the positive-displacement pump operates under high load regardless of the ramp time of the proportional spool valve control signal. The pump high load time is correlated with the start-up time and the pressure waveform on the motor. However, the high load time of the pump can be reduced by suitably adjusting the parameters of the control signal supplied to the coils of the proportional spool valve. It was demonstrated that the maximum pressure value at the inlet port of the hydraulic motor during its start-up can be modified by adjusting the shape of the proportional spool valve control signal. In this way, it is also possible to reduce the noise generated by the transmission during start-up [25,26]. Therefore, reduction in the maximum pressure is an effective method for reducing the noise emission levels of a hydrostatic transmission in both transient and steady states. By adjusting start-up parameters (the control signal waveform), it is possible to regulate the maximum pressure value, the start-up time, and the reaction time. The start-up process can be also modified by selecting the shape of the spool of the proportional spool valve (e.g., symmetrical, asymmetrical) or by adjusting the stationary overlap and operational overlap, but these methods are not analysed in this paper. These

methods also result in reduction in the load of the elements of the transmission, which extends its operational life.

The method of modelling the hydraulic system presented in this paper, in particular the method of modelling the opening characteristics of the proportional spool valve, allows improving the simulation results obtained. The detailed construction of the model and conducting simulations enable initial adjustment and analysis of the control or regulation parameters prior to their application on the target machine. This is extremely important because it reduces the risk of errors during the prototype start-up phase, and therefore it reduces the time and costs of prototyping.

The presented detailed model for the start-up of the hydrostatic transmission equipped with a proportional valve can be used for the purpose of optimising the start-up process in terms of the execution of the objective function for the following parameters: dynamic surplus of a selected value, start-up time, reaction time, or the energy efficiency of the system.

**Author Contributions:** Conceptualization, M.S., P.B. and K.U.; methodology, M.S. and P.B; software, M.S. and P.B.; validation, M.S. and P.B.; formal analysis, M.S., P.B. and K.U.; investigation, M.S., P.B., A.K, M.K. and K.U.; resources, M.S. and P.B.; data curation, P.B.; writing—original draft preparation, M.S. and P.B; writing—review and editing, M.S., P.B., A.K., M.K. and A.M.; visualization, P.B., M.S. and A.M.; supervision, M.S. and P.B.; project administration, M.S.; funding acquisition, M.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** All coded generated during the study and experimental data are available from the corresponding author by request.

**Conflicts of Interest:** The authors declare no conflict of interest.
