## 3 Results and Discussion
### Development of a Method for Controlling the Temperature of the Lightweight Nozzle
Then one can obtain (13):  
\[W_{R}(z)=k_{p}+\frac{k_{i}\cdot T_{d}}{z-1}+\frac{k_{d}(z-1)}{T_{d}\cdot z}, \tag{13}\]  
\(W_{D}(s)\) is the transfer function of the measuring device, which introduces pure time delay (14):  
\[W_{D}(s)=e^{-s\tau}, \tag{14}\]  
where \(\tau\) is the time delay equal to the time spent on registration and processing of the feedback signal (\(\tau=20\) ms for 17-bit target resolution of the oversampled output). The discrete time for the PID controller is assumed as follows \(T_{d}=20\) ms. Modeling the operation of a discrete control system in the Simulink application of the Matlab package made it possible to determine the coefficients of the PID controller, to evaluate the quality of regulation when operating over the entire operating temperature range of the nozzle (\(T_{set}=260\), 440 and 750 \({}^{\circ}\)C). Table 3 shows the results of an experiment on temperature control by linear ACS with PID controllers optimized for the selected values of \(T_{set}\). The experiment showed that with such approximation, the use of a classical PID controller leads to significant deviation of the transient response parameters from the estimated ones: the maximum settling time is 9.6 s, the maximum overshoot is 8% vs. the estimated parameters of 3 s and 1%, respectively, for all selected \(T_{set}\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{3}{*}{**Setpoint, \({}^{\circ}\)C**} & **PID Controller Optimized for** & **PID Controller Optimized for** & **PID Controller Optimized for** & **260 \({}^{\circ}\)C** & **440 \({}^{\circ}\)C** & **750 \({}^{\circ}\)C** \\ \cline{2-6}  & **Max** & **Vershoot, \%** & **Settling Time, s** & **Max** & **Vershoot, \%** & **Settling Time, s** \\ \hline
260 & 0.9 & 3.8 & 5 & 3.3 & 8 & 4.8 \\
440 & 1.5 & 7.2 & 1.1 & 4.2 & 5.5 & 5.8 \\
750 & 2.3 & 9.6 & 0.7 & 6.6 & 0.4 & 7.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The results of the experiment devoted to the temperature control of the nozzle in a wide range for linear ACS with classical PID controller. Before proceeding to the reasons for these deviations, it is also worth paying attention to assessing the influence of the polymer material extrusion speed on the quality of control. For this, there were used the results presented in Section 2 in Figure 7. The results show the decrease in \(k_{0}\) and \(T_{1}\) of the plant as \(V_{ext}\) increases. For a linear ACS with a PID controller optimized for \(T_{set}\) = 260 \({}^{\circ}\)C, the coefficients \(k_{p}\), \(k_{i}\), \(k_{d}\) are equal to 0.034, 0.0115 1/s, and 0.0017 s, respectively, and \(k_{0}\) = 1181. Extreme cases at \(V_{ext}\) = 40 and 100 mm/s, for which there is a decrease in the gain of the plant by 1.4 and 2 times, and the time constant by 2 and 3 times, respectively were considered. Simulation results with the same \(k_{p}\), \(k_{i}\), \(k_{d}\) and substitution of values for 40 mm/s (\(k_{0}\) = 843, \(T_{1}\) = 6 s) and for 100 mm/s (\(k_{0}\) = 590, \(T_{1}\) = 4 s) into the linear ACS model demonstrate reduction of overshoot and settling time with an increase in extrusion speed. At \(V_{ext}\) = 40 mm/s, the settling time is 2.4 s, and the overshoot is 2.7%; 1.6 s and 1.1% at \(V_{ext}\) = 100 mm/s, respectively. Thus, increasing the extrusion speed has a positive effect on the quality of nozzle temperature control. The non-linear nature of the dependence of the power consumed by the inductor on the phase shift \(\chi\) was established, and then its linearization was carried out. The concept of the power level of the HF generator from 0% to 100% is introduced, on which the power consumed by the inductor depends linearly, and the phase shift \(\chi\) has a quadratic dependence (with this approximation R\({}^{2}\) = 0.999).