参考文献
Sensorless Control Method for PMSM Based on Frequency-Adaptive Disturbance Observer
Sensorless Control Strategy for Salient-Pole PMSM Based on Extended EMF in Rotating Reference Frame
“Active Flux” DTFC-SVM Sensorless Control of IPMSM–Ion Boldea, Fellow
Sensorless Operation of Permanent Magnet Motor Using Direct Voltage Sensing Circuit
文献的查找思路:
- 基于有效磁链(扩展反电势方案)
- 基于现代控制理论;
主要目的:
- 研究有效磁链在永磁同步电机应用中的方法;
- 复习、提炼现代控制理论在电机控制中的作用应用方法;
扩展反电势的理论推导
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写成扩展反电势的形式:
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复矢量的形式:
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\begin{cases} u_{sd}=R_si_{sd}+L_d\frac{di_{sd}}{dt}-\omega _rL_qi_{sq}\\ u_{sq}=R_si_{sq}+L_q\frac{di_{sq}}{dt}+\omega _rL_di_{sd}+\omega _r\varPsi _f\\ \end{cases} \\ \text{写成矩阵形式:} \\ \left[ \begin{array}{c} u_{sd}\\ u_{sq}\\ \end{array} \right] =\left[ \begin{matrix} R_s+pL_d& -\omega _rL_q\\ \omega _rL_d& R_s+pL_q\\ \end{matrix} \right] \left[ \begin{array}{c} i_d\\ i_q\\ \end{array} \right] +\left[ \begin{array}{c} 0\\ \omega _r\\ \end{array} \right] \varPsi _f \\ \text{写成扩展反电势的形式:} \\ \left[ \begin{array}{c} u_{sd}\\ u_{sq}\\ \end{array} \right] =\left[ \begin{matrix} R_s+pL_q& -\omega _rL_q\\ \omega _rL_q& R_s+pL_q\\ \end{matrix} \right] \left[ \begin{array}{c} i_d\\ i_q\\ \end{array} \right] +\left[ \begin{array}{c} p\left( L_d-L_q \right)\\ \omega _r\left( L_d-L_q \right)\\ \end{array} \right] i_d+\left[ \begin{array}{c} 0\\ \omega _r\\ \end{array} \right] \varPsi _f \\ \text{令有效磁链为:} \\ \varPsi _{fm}=\varPsi _f+\left( L_d-L_q \right) i_d \\ \text{则:} \\ \left[ \begin{array}{c} u_{sd}\\ u_{sq}\\ \end{array} \right] =\left[ \begin{matrix} R_s+pL_q& -\omega _rL_q\\ \omega _rL_q& R_s+pL_q\\ \end{matrix} \right] \left[ \begin{array}{c} i_d\\ i_q\\ \end{array} \right] +\left[ \begin{array}{c} s\\ \omega _r\\ \end{array} \right] \varPsi _{fm} \\ \text{复矢量的形式:} \\ \vec{u}_s=R_s\vec{i}_s+L_q\frac{d\vec{i}_s}{dt}+j\omega _rL_q\vec{i}_s+\left( s+j\omega _r \right) \varPsi _{fm}
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扩展反电势模型的特点
- 与转矩公式刚好吻合,有效磁链x转矩电流为输出转矩。包含总的等效磁链(包含磁阻转矩贡献的磁链)
- 当有效磁链估计不准确时,转矩计算将不准确,因此需要单独的转矩观测器,以提高转矩观测精度;
- 当采用定子磁链定向时,不需要计算实际的转子磁链,因此简化了计算,不需要Lq饱和曲线;
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当计即Lq的定子等效电感压降时,转子有效磁链可计算如下,转子有效磁链的大小和方向严重受Lq饱和特性的影响,当凸极的饱和程度较大时,有效磁链定向会受到干扰。
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\text{在静止坐标系下,}\vec{i}_s=\vec{i}_{dqs}*e^{j\omega _r},\vec{i}_{dqs}=\vec{i}_s*e^{-j\omega _r},\varPsi _{fm}=\vec{\varPsi}_{sm}e^{-j\omega _r} \\ \\ \vec{u}_s*e^{-j\omega _r}=R_s\vec{i}_s*e^{-j\omega _r}+L_q\frac{d\left( \vec{i}_s*e^{-j\omega _r} \right)}{dt}+j\omega _rL_q\vec{i}_s*e^{-j\omega _r}+\left( s+j\omega _r \right) \left( \vec{\varPsi}_{sm}e^{-j\omega _r} \right) \\ \text{化简:} \\ \vec{u}_s*e^{-j\omega _r}=R_s\vec{i}_s*e^{-j\omega _r}+L_q\frac{d\vec{i}_s}{dt}*e^{-j\omega _r}+\frac{d\vec{\varPsi}_{sm}}{dt}e^{-j\omega _r} \\ u_s=R_s\vec{i}_s+L_q\frac{d\vec{i}_s}{dt}+\frac{d\vec{\varPsi}_{sm}}{dt} \\ \overrightarrow{\varPsi }_{fm}=\int{\left( \vec{u}_s-R_s\vec{i}_{dqs}-L_q\frac{\vec{i}_s}{dt} \right)}dt \\ \text{等价为:} \\ \overrightarrow{\varPsi }_{fm}=\int{\left( \vec{u}_s-R_s\vec{i}_{dqs} \right)}dt-L_q\vec{i}_s
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扩展反电势电压电流模型磁链观测
通过考虑Lq的饱和特性曲线,实现精确的有效磁链计算。Lq的饱和特性严重影响有效磁链的观测精度。
通过PLL或者反正切和导数计算得到估计转速;
基于闭环扩张观测器的IPMSM无传感器控制
参考文献:Sensorless Operation of Permanent Magnet Motor Using Direct Voltage Sensing Circuit
理论基础:
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模型推导;
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扰动观测器的理论原理
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基本思路学习