Control and stabilisation of the resonant converters are essential problems in power electronics. The conventional model of the dc-dc series resonant converter (SRC) is derived using the sinusoidal approximation and generalised averaging followed by linearisation about an operating point. This model involves considerable approximation and is not applicable for large variation of load and supply voltage. The authors have already proposed a direct piece-wise affine (DPWA) modelling and control approach for the SRC that operates above resonant frequency. However, the DPWA technique is not applicable to an SRC that operates below resonance because of the presence of harmonics. In this study, a dynamic voltage-controlled oscillator (VCO) is introduced, so that the overall system consisting of the proposed VCO following by the SRC is modelled as a PWA system. Then, a hybrid controller is designed in order to regulate the dc output voltage of the SRC operating below resonance. Also, the stability analysis of the closed-loop system is presented in the form of linear matrix inequalities. A prototype of the SRC is constructed and the proposed hybrid controller is implemented on a digital signal processor (DSP) core. The simulation and experimental results show the effectiveness of this modelling and control approach.

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A B S T R A C TDynamic modeling and control of dc-dc series resonant converter (SRC) especially when operating in discontinuous conduction mode (DCM) is still a challenge in power electronics. Due to semiconductors switching, SRC is naturally represented as a switched linear system, a class of hybrid systems. Nevertheless, the hybrid nature of the SRC is commonly neglected and it is modeled as a purely continuous dynamics based on the sinusoidal approximation and averaging. However, an SRC may be purposely designed to operate in DCM so the sinusoidal approximation is no longer acceptable. Therefore, it is essential to analyze the stability using a more sophisticated model. This paper presents a novel hybrid control strategy for the output voltage regulation of the SRC operating in DCM. Neither sinusoidal nor averaging is used. The stability of the closed-loop system is systematically fulfilled by satisfying some linear matrix inequalities. The proposed hybrid control approach has simple hardware implementation which does not require fast sampling of the resonant tank waveforms and external voltage-controlled oscillator. A prototype of the SRC is constructed and the hybrid controller is realized on a TMS320F2812 DSP core. The effectiveness of the proposed method is verified by simulation and experimental results.

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