## 3 Problem Analysis  
### Model of the Cylinder Control System  
The classic approach to the design of hydraulic systems typically does not allow for the influence of the position of control valves with respect to the operating element and the power source. The above fact results from the assumption of a quasi-static model of flows and pressure changes in the system. In effect, during the design phase, the mutual position of the hydrostatic system elements, in the classic approach, is typically dictated by the geometry-related requirements of the driven machine. Incorporating dynamic phenomena in the analysis of hydrostatic systems is currently one of the most intensively followed directions in the development of both individual elements and the entire systems. It broadens the scope of the analysis and allows predictions of such adverse phenomena as hydraulic shocks, momentary significant pressure increases or resonance in the system. In such analysis, the mutual position of the system elements is one of the basic input variables, as demonstrated in the results of comparative analyses [16]. The position of the control elements has an impact on the recorded stiffness of the cylinders and thus on the recorded maximum pressure values at the moment of valve switching [20]. However, although a significant number of research works focus on the analysis of individual elements of hydraulic systems, some research works, including this, focus more narrowly on the mutual interactions between the elements in a hydraulic system. During the development works, the accuracy of the cylinder movements was found to depend not only on the architecture of the system, but also on the extend of external loads acting on the hydraulic cylinder. The influence of accelerations and the resulting inertia forces recorded during velocity changes of the driven element should be allowed for along with the influence of the resulting pressure changes on the operation of the hydraulic valves, and thus on the possibility of fluid flow through the valves, as an effect of this type of processes, should also be taken into account. Such formulation of the research problem allows the characteristics of a hydraulic system to be interrelated with external excitations, which have a secondary influence on the dynamic aspects of its operation. This phenomenon may be observedinter alia in the case of stopping boom systems in required positions. The characteristics of the recorded system movement should be different depending on the valves installation location and control methods, with the individual architectures of the system ensuring the best movement accuracy levels in certain ranges of variable pressure loads. This thesis has been verified by measuring the response of the system to the switching of the valves and to the stopping of the work system during the lifting of a boom system loaded with variable masses. This phenomenon was analyzed in more detail in an experiment whose results are presented below. Three control hydraulic system architectures were tested on the same research hydraulic system test stand. The first was a classic system controlled by a pool valve moved away from the cylinder. The second was a system with a pair of 2-way simultaneously controlled valves mounted on the cylinder. In order to determine the impact of pressure changes on valves mounted in series directly next to the cylinder, the tests also involved a third system which is controlled only by means of a 2-way valve mounted on the actuator supply line. The responses of the dynamic system (Figure 1) were measured as a function of time and in relation to the response time of the system after changing the valve control signal. The model shown in Figure 1 is an entirely acceptable approximation in the case of full and hermetic closure of the power supply line, if assumed that the pressure values of liquid in the cylinder chamber and in the power supply line (\(p\)) are identical.