**3. Experimental Verification of the Mathematical Model**

Experimental studies were conducted to verify the mathematical model, the assumed values of the parameters, and the assumptions. The experimental studies also made it possible to determine the relation between the shape (parameters) of the control signal for the proportional spool valve and the dynamic surplus pressure (at the inlet port of the motor) and the speed on the shaft of the motor. Additionally, the duration of the start-up process was analysed for various waveforms of the control signal for the proportional spool valve.

Figure 13 shows the test stand that was used to verify the model. The hydraulic power source is based on an axial variable displacement piston pump (flow was set to 14 L/min). The system is protected by a direct operating relief valve (nominal flow 25 L/min). A direct proportional spool valve (nominal flow 16 L/min) with spool position feedback was used to control the gear motor (size 32 cm3/rev). The control signal was generated using a multifunction DAQ device with analogue I/O (NI USB-6001) connected to a PC with dedicated LabVIEW-based software. The measurement system was based on a 16-bit recorder (Hydrotechnik Multi System 8050) and piezoresistive pressure transducers (Hydrotechnik HySense PR100). The speed was measured using a tachometer (PZO E2/CPPB4).

**Figure 13.** The hydrostatic transmission test stand: 1—planetary gear; 2—coupling housing; 3 hydraulic gear motor; 4—hydraulic power source.

Figures 14–16 show the waveforms obtained during the start-up of the transmission controlled by the serial throttle method with a proportional spool valve.

**Figure 14.** Measurement and result of simulation of the waveform of pressure on the motor *ps* for the control signal rise time *t*<sup>0</sup> = 1 s.

**Figure 15.** Measurement and result of simulation of the waveform of rotational speed on the motor, *ns*, for the control signal rise time *t*<sup>0</sup> = 1 s.

**Figure 16.** Measurement and result of simulation of the waveform of pressure on the pump *pp* for the control signal rise time *t*<sup>0</sup> = 1 s.

In Figure 14, for the simulation time *t* = 0, the difference in pressure between the experiment and the result of simulation can be noticed. This difference is caused by the residual pressure remaining in the line from directional spool valve to the motor.

Figure 17 presents the result of two simulations compared with the experimental run. The simulation labelled "sim." is the result of the simulation including the opening characteristic fit (Equation (4)). In addition, the simulation labelled "sim.\*" is shown, which assumes a linear dependence of flow on slider displacement (*s* = *sm*), as in [18]. In the first control phase, a significant difference between the responses of different modelling approaches can be observed, which has a significant impact on the evaluation of the control dynamics.

**Figure 17.** Measurement and result of simulation of the waveform of speed on the motor *ns* for the control system (*KP* = 0.02, *TI* = 0.5 s). Waveforms labelled "sim." and "sim.\*" shows the difference between simulation results with and without the modified spool valve model (Equation (4)).

The experimental verification studies demonstrate that the simulations satisfactorily model the actual transmission. This enables further work intended to optimise the parameters and the waveform of the control signal, which will result in a reduction in the dynamic surplus of the selected parameter (e.g., pressure at the inlet port of the motor) while maintaining control of the duration of the transitional process.
