Novel Phasor Transformation for Feedback Control Design of Induction Heating Systems With Experimental Results

For analyzing the transients of induction heating (IH) systems, time-dependent phasor transformations were proposed so far in the literature. Applying these transformations to linear circuit equations leads to differential equations in the complex domain from which equivalent circuits modeling the envelopes of sinusoidal waveforms were derived. This paper proposes a phasor transformation, which is based on fictitiously replacing the real voltage and current signals of a system by complex voltage and current signals. It leads to transformed system equations in the real domain where instantaneous amplitudes, phases, and frequencies explicitly appear, which makes the transformed equations suitable for the feedback control design. The methodology is applied to a parallel IH system to design a sliding-mode controller. The theory is supported by simulations, experiments, and comparisons.