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中文摘要：
在断续导电模式下，建立了电压型双频率控制开关变换器的动力学模型，并推导了相应的特征值方程．根据动力学模型，采用分岔图研究了电路参数变化时变换器存在的边界碰撞分岔行为和周期2，周期3，周期4等多周期行为，结果表明：变换器经历了周期1态、多周期态、周期1态的分岔路由；周期态的转变均是由边界碰撞分岔引起的．根据特征值方程，采用Lyapunov指数研究了变换器的稳定性，结果表明：随着电路参数的变化，Lyapunov指数始终小于零，变换器一直工作于稳定的周期态，验证了电压型双频率控制开关变换器的周期3行为并不意味着变换器会必然发生混沌．通过电路仿真，分析了负载变化时变换器的时域波形、相轨图和频谱图，验证了动力学模型的可行性和理论分析的正确性．实验结果验证了文中的仿真结果．
英文摘要：
A dynamical model is proposed and the corresponding characteristic aligns are derived for voltage-mode bi-frequency controlled switching converter operating in discontinuous conduction mode. According to the dynamical model, the border-collision bifurcation and multi-period behaviors, such as period-2, period-3, period-4, and so on, are studied using bifurcation diagrams as the circuit parameters are varied. It is found that the converter behaves along the bifurcation route of period-l, multi-period, and period-l, and the change of period state is induced by border-collision bifurcation. Based on the characteristic equation, the converter stability is investigated by the Lyapunov exponent. It is shown that Lyapunov exponent is always smaller than zero with the variation of circuit parameters and the converter operates in stable period state all the time. Also, it is validated that period-3 behavior of voltage-mode bi-frequency controlled switching converter does not predicate its inevitable chaos. Time-domain waveforms, phase portraits, and frequency spectra of voltage-mode bi-frequency controlled switching converter are analyzed by circuit simulation, which validates the feasibility of dynamical model and the correctness of theoretical analysis. Simulation results are verified by experiments in this paper.
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