Research on state discrete time model of buck converter and its limit voltage response control strategy
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摘要:
为了提高开关电源变换器的建模精度和控制性能,提出了一种状态切换离散时间模型(State Switching Discrete time Model,SSDM).该模型在建模时考虑的是每个开关周期内的状态,而不是变换器的平均状态,故在高频下其精度比传统的状态平均模型更高. 基于开关持续时间的全微分方程,精确计算一个周期内的电感电流和输出电压,从而推导出SSDM. 此外,通过SSDM推导出极限电压响应(Limiting Voltage Response,LVR)控制策略.该策略通过电压预测计算出合适的占空比,以在最小开关周期内将输出电压调节为参考值. 通过这种策略,变换器不仅实现了非常快的负载/线路瞬态响应和参考跟踪速度,而且在偏差电感下表现出很高的稳定性. 最后,通过频率响应分析和实验验证了SSDM的准确性和系统的稳定性. 实验结果表明,在不同工况下,LVR控制策略下的输出电压瞬态响应时间相比传统控制策略下的输出电压瞬态响应时间缩短了70%以上；当电感值偏离23%时,在LVR控制策略下的输出电压仍然保持稳定.
Abstract:In order to improve the modeling accuracy and control performance of switching power converters, a state-switching discrete time model (SSDM) is proposed. The model considers the state of each switching period instead of the average state of the converter. Therefore, its accuracy is higher than that of the traditional state average model at high frequency. Based on the full differential equation of the switching duration, the inductor current and the output voltage in a cycle are accurately calculated, and the SSDM is derived. In addition, the limiting voltage response (LVR) control strategy is deduced by SSDM. The LVR control strategy calculates the appropriate duty cycle by voltage prediction to adjust the output voltage to the reference value in the minimum switching period. With this strategy, the converter not only achieves very fast load/line transient response and reference tracking speed, but also exhibits high stability under deviated inductance. Finally, the accuracy of the proposed strategy and the stability of the system are verified by frequency response analysis and experiments. The experimental results show that the transient response time of the output voltage under the LVR control strategy is more than 70% shorter than that under the traditional control strategy under different working conditions. When the inductance value deviates by 23%, the output voltage remains stable under the LVR control strategy.
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Key words:
- buck /
- DC-DC /
- discrete-time model /
- limit response control
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图 2 极限电压响应（LVR）控制下的buck变换器方案
Figure 2. Scheme of the buck converter under Limit voltage response (LVR) control
图 6 具有积分补偿和消除DPWM饱和的实用LVR控制器
Figure 6. Practical LVR controller with integral compensation and eliminated DPWM saturation
图 7 稳态下的输出电压,其中d[k+1]=1且d[k+1]=0
Figure 7. Output voltage under a steady state, where d[k + 1] = 1 and d[k + 1] = 0
图 8 SSDM、SADM和电路模型下从d到vout,s的频率响应
Figure 8. Frequency response from d to vout,s under the State Switched Discrete-time Model (SSDM), State Averaged Discrete-time Model (SADM), and circuit model
图 9 SSDM、SADM和电路模型下从vin到vout,s的频率响应
Figure 9. Frequency response from vin to vout,s under the SSDM, SADM, and circuit model
图 10 SSDM、SADM和电路模型下从R到vout,s的频率响应
Figure 10. Frequency response from R to vout,s under the SSDM, SADM, and circuit model
图 11 电路模型和等效模型的频率响应
Figure 11. Frequency responses of the circuit model and the equivalent model
图 12 当R从10 Ω到5 Ω时的瞬态电压和电流
Figure 12. Transient voltage and current when R steps from 10 to 5 Ω
图 13 当vin从12 V到9.5 V时的瞬态电压和电流
Figure 13. Transient voltages and current when vin steps from 12 to 9.5 V
图 14 当vREF从5 V到6 V时的瞬态电压和电流
Figure 14. Transient voltages and current when vREF steps from 5 to 6 V
图 15 当R从5 Ω到10 Ω时,LVR控制下的输出电压瞬变
Figure 15. Output voltage transients under DPVP control when R steps from 5 to 10 Ω
图 16 当vin从12 V到9.5 V时,LVR控制下的输出电压瞬变
Figure 16. Output voltage transients under DPVP control when vin steps from 12 to 9.5 V
图 17 当vREF从5 V到6 V时,LVR控制下的输出电压瞬变
Figure 17. Output voltage transients under DPVP control when vREF steps from 5 to 6 V
表 1 式(4)中的变量
Table 1. Variables in Equation (4)
$ {a_{11}} $ $ {e^{\alpha T}}[cos(\beta T) - \alpha sin(\beta T)/\beta ] $ $ {a_{12}} $ $ - {e^{\alpha T}}sin(\beta T)/(L\beta ) $ $ {a_{21}} $ $ {e^{\alpha T}}sin(\beta T)/(\beta C) $ $ {a_{22}} $ $ {e^{\alpha T}}[\alpha sin(\beta T)/\beta + cos(\beta T)] $ $ {b_1} $ $ {e^{\alpha T}}\{ - cos(\beta T)/R + \alpha sin(\beta T)/(R\beta ) + sin(\beta T)/(L\beta )\} $ $ {b_2} $ $ {e^{\alpha T}}\{ \alpha sin(\beta T)/\beta - cos(\beta T)\} $ 
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表 2 buck变换器的规格
Table 2. Specifications of the buck converter
L/µH C/µF R/Ω vout/V vin/V T/µs 47 20 5 5 12 10
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