*Hydrostatic Transmission Control Methods*

There are two basic methods for controlling a hydrostatic transmission in a hydrostatic drive unit: a throttle method and a volumetric method [17]. The throttle method involves an intentional modification of the flow resistance value (e.g., via an adjustable throttle valve) to regulate the value of the usable flow supply to the receiver. There are two types of control methods depending on the positioning of the adjustable throttle valve relative to the receiver—serial or parallel. In practice, the variable throttling gap is often obtained on the gaps of the spool–sleeve couple of the proportional spool valve. In the serial throttle control method, the use of a proportional valve for the purpose of throttling the usable flow supply to the receiver is justified by the fact that this solution enables changing the direction of the movement of the hydraulic receiver, among other factors. The continuous volumetric control method involves using a variable displacement pump and/or receiver.

This paper analyses a drive unit based on an M2C 1613 high-speed, hydraulic gear motor and an OH-500 three-stage planetary gear with a total gear ratio of *i* = 69.7. The paper investigates the impact of the parameters of the control signal for the proportional spool valve on the waveforms of the pressure and speed of the transmission, with a particular emphasis on the transient state during start-up. The transmission start-up process was examined according to the serial throttle control method. Additionally, a system featuring feedback from the speed of the hydrostatic motor and a PI numerical control system was analysed.

In the research on the control of hydraulic systems using proportional spool valve, many approaches can be found on how to model the opening characteristics of a hydraulic distributor. Very often, a linear or quadratic relationship between the spool displacement and the flow rate at a given differential pressure is adopted [18,19]. These methods often give satisfactory results for basic analysis of control systems that rarely operate at small valve openings. Unfortunately, when analysing closed-loop control systems, this approach can produce simulation results that differ significantly from experiment, which makes a proper machine control design process difficult.

Another method found in the literature is a very detailed modelling of the spool shape, which allows one to determine the cross-section of the orifice responsible for the flow [20]. This approach gives significantly better results than those of assuming a linear relationship; however, it does not take into account the phenomena associated with flow through a variable orifice. Additionally, such a spool modelling process requires one to obtain detailed documentation from the valve manufacturer, or the disassembly and detailed measurement of the spool and sleeve.

In this paper, a different method of spool modelling is presented, which does not require any additional documentation of the valve beyond the opening characteristic curve typically provided by the manufacturer.

It was assumed that the characteristic curve can be approximated with sufficient accuracy by a polynomial equation. A similar approach was presented by the authors of paper [21], but they did not present the implementation of this solution in the control system.

Figure 1 shows a diagram of a serial throttle control system for a hydrostatic transmission based on the use of a proportional valve, while Figure 2 shows schematics of the analysed control systems.

**Figure 1.** Diagram of the hydraulic system of a hydrostatic transmission with serial throttle control.

**Figure 2.** Diagrams of investigated control systems: (**a**) open-loop system; (**b**) closed-loop system.
