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中文摘要：
在多频率控制开关变换器的工作原理及状态方程的基础上，建立了多频率控制断续导电模式开关变换器的离散迭代映射模型，并推导了相应的特征值方程和Lyapunov指数。根据离散迭代映射模型，对多频率控制开关变换器进行了分岔分析。结果表明：在电路参数变化时，变换器存在边界碰撞分岔行为和多周期行为；当误差界限电压较大时，变换器表现出自相似现象，而当误差界限电压较小时，变换器则表现出混频现象。采用Lyapunov指数研究了变换器的稳定性，验证了分岔分析的正确性。经过电路仿真，进一步分析了负载变化时变换器的时域波形和相轨图，并验证了离散迭代映射模型的有效性和理论分析的正确性。最后通过实验结果验证了文中的仿真结果。
英文摘要：
Based on the operation principle and state equations of multi-frequency （MF） controlled switching converter, the discrete iterative map model is established, the corresponding characteristics equation and Lyapunov exponent of MF controlled switching converter operating in discontinuous conduction mode are derived. According to the discrete iterative map model, its bifurcation behaviors are investigated. It is found that the border-collision bifurcation and the multi-period behaviors occur in converter, when the circuit parameters are varied. When the voltage error boundary is too large, the converter behaves as self-similarity phenomenon, and when the voltage error boundary is too small, the converter behaves as frequency-mixing phenomenon. The converter stability is investigated by Lyapunov exponent, which validates the correctness of bifurcation analysis. Time-domain waveforms and phase portraits of converter with the load varied, are analyzed by circuit simulation, which validates the validity of discrete iterative map model and the correctness of theoretical analysis. Finally, simulation results in this paper are verified by experimental results.
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