**1. Introduction**

In the case of heavy working machinery, some actuators often require low rotational speed values, ranging from a few to tens of rotations per minute. A crane rotation mechanism is an example of such equipment.

Hydrostatic drive units for low rotational speed movement can be constructed using two methods: with a high-speed hydraulic motor combined with an additional mechanical transmission, or with a low-speed motor coupled directly to the driven mechanism. In practice, however, a solution based on a hydrostatic transmission with a high-speed motor and mechanical transmission is used, as this is the only solution that can be applied in the case of a crane rotation mechanism [1]. This results from the need to comply with industry-specific legal regulations, which require using a mechanical brake to securely block the rotation mechanism in the event of external forces (wind, sloping ground within admissible limits, etc.). When a direct drive with a low-speed motor is used, the dimensions of the mechanical brake are quite large, particularly in the case of high load values.

The designer of the drive unit, apart from basic parameters, such as output power, speed range of the driven element, efficiency [2], etc., has to ensure specific dynamic

**Citation:** Bury, P.; Stosiak, M.; Urbanowicz, K.; Kodura, A.; Kubrak, M.; Malesi ´nska, A. A Case Study of Open- and Closed-Loop Control of Hydrostatic Transmission with Proportional Valve Start-Up Process. *Energies* **2022**, *15*, 1860. https:// doi.org/10.3390/en15051860

Academic Editors: Artur Bartosik and Helena M. Ramos

Received: 4 February 2022 Accepted: 1 March 2022 Published: 3 March 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

characteristics corresponding to the nature of the designed machinery [3]. In some cases, dynamic surplus is not allowed; for example, in the case of CNC machining tools, where the tool must be positioned right next to the machined surface without overshoot of the tool position.

Furthermore, the requirements applicable to machinery in dynamic states are constantly increasing. Modern machine and equipment evaluation criteria have recently been expanded to include vibration- and noise-level criteria, especially for hydrostatic drive machines [4]. Apart from their well-known advantages, hydrostatic drive units have a significant drawback—they generate relatively high noise emission levels, a factor which can disqualify this type of drive by causing them to exceed the standard noise emission levels (which are being gradually reduced), determined by ergonomic considerations [5–8]. It also means the necessity to reduce the risk of cavitation in hydrostatic systems [9] and the need for its proper modelling. However, limiting the maximum pressure during start-up will result in a reduction in the global noise emission level generated by the transmission in a transient state [10]. On the other hand, reducing the time during which the maximum pressure is generated will result in shortening of the time of the maximum noise levels of the unit during the start-up of the transmission. For a number of years, there has been an increasing tendency to reduce energy losses in mechanical systems, including hydraulic ones [11]. An increase in the efficiency of hydraulic systems can be achieved through control and adjustment of the hydraulic elements (valves, pumps, receivers), the use of systems featuring energy recuperation or hybrid systems, and reduction in dynamic loads [12]. Specific solutions make it possible to increase the efficiency of hydrostatic systems by several tens of percent. In the case of systems offering energy recuperation, the consumption of energy can be reduced by approx. 30% [13]. In hydrostatic systems, this can be achieved in a number of ways, depending on whether the system features fixed or variable displacement pumps. In systems with fixed displacement pumps controlled by throttle methods, the predominant approach is to limit the operation of the safety valve (where serial throttle control is used). The introduction of proportionally controlled valves (a proportional relief valve or a proportional spool valve) can also result in a reduction in energy consumption by the hydrostatic system, particularly in a transient state [14,15].

Additionally, dynamic surpluses (pressure and speed) occurring within the system contribute to excessive wear of the system elements and reduce the uptime [16].
