## 2 Materials and Methods  
Known temperature automatic control systems (TACS) of the FDM process [51; 52] and related processes are, as a rule, closed-loop with temperature feedback and use of known proportional-integral-derivative (PID) control laws. The team proposed an original design of the nozzle and inductor (Figure 1). The non-contact nature of the induction heating method made it possible to reduce the mass of the heated part (hot-end) to the mass of a specially shaped nozzle itself with the overall value equal or less than 1 g. The lack of fast temperature measurement methods for the lightweight nozzle was one of the major technological drawbacks hindering the efficient using of induction heating in FDM 3D manufacturing. To control the temperature of a lightweight nozzle, the research team proposes the amplitude-phase resonant temperature measurement method instead of the known frequency methods, as well as the amplitude method previously proposed by the research team [53]. The induction heating method provides the possibility of supplying a significant peak power (more than 500 W against 50 W in a CE); the possibility of heating the active zone with an arbitrary shape; the possibility of changing the heating parameters by modifying the inductor. A special nozzle was made, as shown in Figure 1. The nozzle material was ferromagnetic alloy AISI420 with a Curie temperature of about 1000 \({}^{\circ}\)C. Axial symmetry of the proposed inductor and nozzle provides greater uniformity of heating of polymer inside the nozzle. Figure 2 contains the block diagram of the nozzle TACS. In the installation for FDM containing the inductor L\({}_{1}\) (1) and the nozzle (2), using the HF generator (3), the temperature of the nozzle (2) is controlled, which affects the properties of the material of the nozzle (2) and leads to a change in the phase and amplitude characteristics of the current \(I\) of the inductor L\({}_{1}\) (1) circuit. The inductor L\({}_{1}\) (1) is supplemented by a measuring coil L\({}_{3}\) (4), where, as a result of transformation, a useful signal is generated and then fed through the measuring circuit to the signal registration and processing unit (5), where the actual temperature of the nozzle \(T\) is determined. Temperature readings are transmitted to the  
Figure 1: The developed extruder: (**a**) external appearance of the hot-end; (**b**) nozzle of a special shape; (**c**) nozzle section: (**1**) forming hole; (**2**) active zone; (**3**) heat break; (**4**) fasteners to the heatsink. PID controller (6), where the error signal is determined relative to the setpoint value of \(T_{set}\) and a new input stimulus (phase shift \(\chi\)) is formed for the HF generator (3). A testbed system was designed, which comprises laboratory power supplies with V\({}_{0}\) = 24 V, I\({}_{\text{max}}\) = 30 A, a DRV8302-based power controller, a HF voltage source inverter using power MOSFETs, and a Control Board based on an ARM-microcontroller STM32F334R8 by STMicroelectronics. The inductive load was extended to the inductor-capacitor-inductor (LCL) series-parallel resonant circuit by adding a capacitive device C\({}_{1}\) in parallel with the inductor L\({}_{1}\) and inductive device L\({}_{2}\) in series with the parallel resonant circuit L\({}_{1}\)C\({}_{1}\). Component values in the LCL resonant circuit were converted to fit the predetermined operating frequency of \(f\) = 115 kHz. The inductor winding of a specified diameter and height was formed with 17 turns of copper HF lit wire (d = 0.75 mm, 2 layers). The LCL resonant circuit was supplied by a HF full-bridge inverter (Figure 3), which is controlled using phase-shift modulation (PSM) method [54; 55]. Using PSM transistors, located on the one bridge leg, operate with a 50% duty cycle and a phase shift of 180\({}^{\circ}\) relative to each other. The voltage between transistors of the same diagonal takes the value of either zero or the voltage of the power source V\({}_{0}\).