Reduced-Order Models of Series Resonant Inverters in Induction Heating Applications

From the controller design framework, a simple analytical model that captures the dominant behavior in the range of interest is the optimal. When modeling resonant circuits, complex mathematical models are obtained. These high-order models are not the most suitable for controller design. Although some assumptions can be made for simplifying these models, variable frequency operation or load uncertainty can make these premises no longer valid. In this study, a systematic modeling order reduction technique, slowly varying amplitude and phase (SVAP), is considered for obtaining simpler analytical models of resonant inverters. SVAP gives identical results as the classical model-order residualization technique from automatic control theory. A slight modification of SVAP, slowly varying amplitude derivative and phase (SVADP) is applied in this paper to obtain a better validity range. SVADP is validated for a half-bridge series resonant inverter and for a high-order plant, a dual-half bridge series resonant inverter giving analytical second-order transfer functions for both topologies. Simulation and experimental results are provided to show the validity range of the reduced-order models.