Abstract--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can be made for simplifying these models, variable frequency operation or load uncertainty can make these premises no longer valid.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 work, 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 (HBSRI) and for a highorder plant, a dual-half bridge series resonant inverter (DHBSRI) 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.

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The state-of-the-art of induction heating technology requires more and more multivariable control systems able to provide a suitable response for a wide set of vessels to be heated. The goal of this paper is to propose a small signal model of a multivariable system, a dual half-bridge series resonant inverter sharing a common resonant capacitor. A Phase Shift Square Wave Modulation (PSSWM) is considered to control the output power of two induction heating loads where the switching frequency and the phase shift are the control inputs. Thus, the topology to be controlled is a Two-Input-Two-Output (TITO) system that presents significant interactions between the inputs and the outputs. A transfer function matrix based on the harmonic balance approach is proposed and validated in simulation. Moreover, stability, output controllability and performance limitations are analyzed highlighting the control problems that arise in this particular application.

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