电压型控制SIDO CCM Buck变换器的统一离散迭代映射模型及稳定性研究

Unified Discrete Iterative Map Model and Stability Research of Voltage-mode Controlled Single-inductor Dual-output CCM Buck Converter

以工作于电感电流连续模式（continue conduction mode,CCM）的电压型控制单电感双输出（single-inductor dual-output,SIDO）Buck变换器为研究对象,描述了电压型控制SIDO CCM Buck变换器的工作原理,指出变换器存在两种开关状态切换路径。基于状态方程和开关切换函数,建立了电压型比例（P）控制和比例积分（PI）控制SIDO CCM Buck变换器工作于两种开关状态切换路径时的统一离散迭代映射模型。利用输出电压分岔图和统一离散迭代映射模型的雅克比矩阵特征值,分析了P控制和PI控制的比例系数和积分系数对变换器的稳定性影响。研究结果表明：不同于传统电压型控制CCM Buck变换器随误差放大器的比例系数增大而发生分岔的现象,电压型控制SIDO CCM Buck变换器随支路开关管电压控制回路的比例系数减小或主开关管电压控制回路的比例系数增大而发生Hopf分岔,变换器从稳定工作状态进入不稳定的低频振荡。且积分系数越大,变换器越不稳定,比例系数的稳定范围越小。最后,建立了电压型控制SIDO CCM Buck变换器的仿真和实验电路,验证了理论分析的正确性。

The stability issue of voltage-mode controlled single-inductor dual-output（SIDO） Buck converter in continue conduction mode（CCM） was studied. Two switching paths were revealed with the analysis of the operating principle of voltage-mode P controlled and PI controlled SIDO CCM Buck converter, and the discrete iterative map model of the converter was established based on the state equations and switching functions. Then, with the bifurcation diagram and eigenvalues of the Jacobian matrix, the stability of the converter was analyzed with respect to the various proportional parameters and integral parameters of error amplifiers of the two voltage control loops respectively. The research results show that the Hopf bifurcation and low frequency oscillation would occur with respect to proportional parameters of error amplifiers of sub-switching control loop decreasing or that of main-switching control loop increasing which was different from the traditional voltage-mode controlled Buck converter. The increased integral parameters would decrease the stability region of the proportional parameters. Finally, the results of simulation and experiment of voltage-mode controlled SIDO CCM Buck converter verified the theoretical analysis.