## 3 Results
### Tuning the PI Algorithm  
Due to the limitation of the long simulation time of the creep test laboratory model, the initial values of the PI controller parameters were found based on an analysis of the frequency characteristics of the created low-pass filter. The parameters were chosen in such a way that the dynamic of the filter was close to that of the linear part of the furnace model of the single-sample creep test machine. Then, the quality of the control and the conditions were checked for compliance with the permissible temperature deviations in the furnace in running simulations of the creep test laboratory model. For PI controller parameters of \(K=0.01\), \(T_{i}=50\) s, \(e_{sp}=50\), at steady state, with little disturbance, the system behaves stably, and power peaks are at the level of switching on one heater. The temperature in the  
Figure 8: Maximum and minimum power values measured with a period of 1 s in the Creep Test Laboratory.  
Figure 9: Temperature of zone 1 of the PJ17 furnace of a one-sample creep test machine (**a**) a real object, (**b**) a model simulated in the MATLAB Simulink environment.  
furnaces at steady state varied within 0.5 \({}^{\circ}\)C. However, for the heating state of the furnaces, or a large power fluctuation caused, for example, by several furnaces shutting down, the system became temporarily unstable. This is easily explained because the furnaces of the creep test machines are non-linear objects and, consequently, their characteristics differ significantly from those of the linear model whose characteristics were compared. Therefore, the parameters were experimentally changed by reducing the pass bandwidth of the filter. Testing in a simulation environment was carried out in order to determine experimentally the optimal parameters of the designed algorithm, as well as to determine the value of the margin around the optimal parameters, which does not cause a significant increase in power peaks. The frequency characteristics of the linear model of the creep test machine furnace and the low-pass filter are shown in Figure 10. The parameters of the control algorithm, which are the starting point for further research, are presented in Table 1.  
Figure 11 shows the power waveforms for phases L1, L2, and L3 obtained for the laboratory model and the parameters presented in Table 1. Regarding the waveforms for non-synchronised control, a significant attenuation of the power peaks can be observed, which confirms the efficiency of the applied algorithm. Due to the asymmetry of the number of heaters connected to the particular phases, differences in damped peaks can be noticed between them, however, they are not significant. Therefore, in the following part of the article, due to the fact that the parameter changes give similar results for each phase, the results will be presented only for phase L1.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(K\) & 0.15 \\ \(T_{i}\) & 150 \\ \(e_{sp}\) & 50 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Experimentally determined parameters of the algorithm limiting power peaks for the creep test laboratory model.  
Figure 10: Frequency characteristics of the zone 1 furnace model of a single-sample creep test machine and the filter used in the power peaks limiting algorithm.