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摘要: 研究传感器未建模动态对Buck变换器滑模控制系统的性能影响, 提出一种基于奇异摄动理论的稳定性和输出电压谐波分析的新方法.给出滑模控制器的参数整定方法, 选取传感器的上升时间作为摄动时间, 建立其未建模动态的奇异摄动模型, 在多时间尺度框架下, 揭示传感器稳定输出与摄动时间的影响关系.在此基础上, 构造一个类Lyapunov函数分析未建模动态对整个闭环控制系统的稳定性影响, 证明未建模动态诱发谐波的必然性.针对输出电压的谐波, 在频域内利用描述函数法推导出未建模动态摄动时间与其谐波幅值和频率的数学影响关系.仿真结果验证所提方法的正确性和有效性.Abstract: This paper investigates the influence of unmodeled dynamics from the sensor in a sliding mode controlled (SMC) Buck converter, and presents a quantitative analysis approach for the stability and output voltage harmonics on the basis of singular perturbation theory. The design parameter of SMC is first given. Taking the rise time of sensor as a perturbed parameter, the buck converter is modeled as a singularly perturbed system. Then in the frame of multiple-time scale, the influence relationship of stable sensor and the time constant is deduced, and further the stability of the whole closed-loop buck converter system is given by constructing a Lyapunov-like function, proving the existence of harmonics induced by unmodeled dynamics. The describing function method is introduced to analyze the frequency and amplitude of the output voltage harmonics. Simulations validate the proposed method.
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Key words:
- Sliding mode control /
- unmodeled dynamics /
- sensor /
- singular perturbation /
- describing function method
1) 本文责任编委 李鸿一 -
图 3 Buck变换器滑模控制系统的简化框图
Fig. 3 Simplified block diagram of sliding mode controlled buck converter system
图 4 Buck变换器滑模控制系统的等价变换
Fig. 4 Equivalent block diagram of sliding mode controlled Buck converter system
图 6 理想和实际Buck变换器的仿真性能比
Fig. 6 Performance comparison of ideal and real Buck converters
图 7 $\psi $对输出电压$v_{c}$的性能影响
Fig. 7 Effect of $\psi $ on the output voltage performance
表 1 Buck变换器的电路参数
Table 1 Circuit parameters of Buck converter
电路参数 数值 电感 $L=50$ mH 电容 $C=100$ ${\rm{ \mathsf{ μ} }}$F 负载电阻 $R=10\, \Omega $ 输入电压 $E=10$ V 给定输出电压 $V_{ref}=5$ V 
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表 2 $\psi $取不同值时的输出电压$v_{c}$性能对比
Table 2 Different values of $\psi $ and their influence on the output voltage $v_{c}$
时间常数 谐波幅值 谐波频率 稳态误差 相对误差 $\psi\, ({\rm{ \mathsf{ μ} }}$s) (mV) (Hz) (mV) (%) 6.647 0.24 1000 0.12 0.0024 32.09 2.8 4515 1.4 0.028 291.26 224 526.31 112 2.24 623.02 842 263.2 421 8.42
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