**3. Results and Discussion**

In this research, as the focus is placed on verifying the ability of our ECTACS to maintain a defined constant value ϕ*const* of the PTTO's twist angle static component, and torsional vibration in the TOMS does not directly affect the process of twist angle control (is not present in the algorithm), only the static component *Mstat* of the load torque transmitted by the PTTO is shown in the presented results.

In Figure 8, the time courses of the static component of the load torque transmitted by the PTTO *Mstat*, compressor output air overpressure *pC* and rotational speed *n* of the TOMS during the experimental measurement are displayed. Three different operating modes (marked with numbers 1–3 in Figure 8) were chosen for testing:


**Figure 8.** Operating modes of the mechanical system used during testing.

The vertical dashed lines in Figure 8 mark the times where the operating modes begin to be steady state (the rotational speed *n* and compressor output air overpressure *pC* do not change).

The sequence of mechanical system operating modes was chosen so that the mechanical system is initially minimally loaded (operating mode 1), then it is partially loaded (operating mode 2) and then it is fully loaded (operating mode 3). The sequence subsequently continues with the unloading of the mechanical system (operating modes 2 and 1).

The aim of our ECTACS is to keep the static component ϕ*stat* = ϕ*const* regardless of the operating mode. Therefore, the ϕ*stat* is the controlled variable. The manipulated variable is the overpressure *pT* in the compression space of the PTTO whose operating range was set to 0–800 kPa. Since the ϕ*stat* is used directly as an input variable, it is a feedback control system. Since our system uses a very accurate mathematical and physical model of the PTTO for the computation of the needed value of *pT*, it also allows us to set the ϕ*stat* very accurately (±0.1 degree without difficulty) during the operation of the mechanical system (Figures 9 and 10).

In Figure 9, the control process by mechanical system loading is shown. The course of the ϕ*stat* is very close to the defined constant value ϕ*const* (in our case ϕ*const* = 2◦) of the PPTO's twist angle static component after the change of operating mode 1 to operating mode 2 and subsequently operating mode 2 to operating mode 3. In the first case, the set point ϕ*const* ± 0.05◦ tolerance was reached in two steps of *pT* change, and in the second case in three steps of *pT* change (although it was very close after two steps of *pT* change).

There are certain idle intervals after the changes of the manipulated variable *pT*. The intervals are necessary in order to stabilize and measure the controlled variable correctly because transitional effects arise after the change of *pT* in the mechanical system. The needed stabilization time depends on the type, character and dynamical behavior of the mechanical system. The selection of a stabilization time for a specific mechanical system requires an individual approach based on theoretical or experimental investigation of the transitional effects caused especially by the rapid coupling pressure changes [38–45].

**Figure 9.** Control process by loading the mechanical system.

**Figure 10.** Control process by unloading the mechanical system.

It is also important to notice that the control system reacts immediately to the change of the ϕ*stat*, and it does not wait for the steady state. Since operation mode 1 is characterized by the minimum rotational speed and negligible compressor output air overpressure, the transmitted load torque is also the minimum and therefore unable to twist the PTTO to the desired ϕ*const* even by zero overpressure *pT* in the compression space of the PTTO.

In Figure 10, the control process by mechanical system unloading is shown. The course of the ϕ*stat* is very close to the defined constant value ϕ*const* = 2◦ after the change of operational state 3 to operational state 2. The set point ϕ*const* ± 0.05◦ tolerance was reached in three steps of *pT* change (although it was very close again after two steps of *pT* change). Therefore, it is very important to select the set point tolerance reasonably (the wider the set point tolerance, the shorter the control process). From our existing research, e.g., [31,33,46–54], it can be said that the set point tolerance of 0.1◦ meets our requirements for practical applications of the PTTO with constant twist angle control. Again, regarding the change to operating mode 1, the transmitted load torque is the minimum and therefore it is unable to twist the PTTO to the desired constant twist angle ϕ*const*.

The customizable graphical user interface of the software of our ECTACS is shown in Figure 11.

**Figure 11.** The graphical user interface of the electronic constant twist angle control system.

The software is developed by us and it is programmed in C++. It allows us to set, via the graphical user interface, all needed parameters, for example, the ϕ*const*, tolerances, stabilization times, parameters of the PTTO's mathematical and physical model, etc., even during the operation of the mechanical system. By monitoring the time courses of the selected parameters, the whole control process and the response of the mechanical system to the changes of the parameters or operating modes in real time can be observed. Furthermore, the data can be stored and viewed or exported for further analysis in post-processing mode.
