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 山东大学学报(工学版)  2018, Vol. 48 Issue (1): 112-116  DOI: 10.6040/j.issn.1672-3961.0.2015.403 0

### 引用本文

SONG Zhengqiang, YANG Huiling, XIAO Dan. Current and speed controllers driven by IPMSM based on online particle swarm optimization method[J]. Journal of Shandong University (Engineering Science), 2018, 48(1): 112-116. DOI: 10.6040/j.issn.1672-3961.0.2015.403.

### 文章历史

1. 扬州市职业大学电气与汽车工程学院, 江苏 扬州 2250092;
2. 新南威尔士大学电子工程系, 悉尼 00098G, 澳大利亚

Current and speed controllers driven by IPMSM based on online particle swarm optimization method
SONG Zhengqiang1, YANG Huiling1, XIAO Dan2
1. School of Electrical and Automotive Engineering, Yangzhou Polytechnic College, Yangzhou 225009, Jiangsu, China;
2. Department of Electronic Engineering, University of New South Wales, Sydney 00098G, Austrilia
Abstract: A novel online particle swarm optimization method was proposed to design speed and current controller of vector controlled interior permanent magnet synchronous motor. In the proposed drive system, the space vector modulation technique was employed to generate the switching signals for a two-level voltage-source inverter. In order to simulate the system in the practical condition, the non-linearity of the inverter was also taken into account due to the dead-time, threshold and voltage drop of the switching devices. Speed and PI current controller gains were optimized with PSO online, sampling period was 100 μs, hardware test platform was DSPACE1104, and the fitness function was changed according to the system dynamic and steady states. The proposed optimization algorithm was compared with conventional PI control method in the condition of step speed change and stator resistance variation, which showed that the proposed online optimization method had better robustness and dynamic characteristics compared with conventional PI controller design.
Key words: permanent magnet synchronous motor    online PSO    intelligent control
0 引言

1 IPMSM实时仿真模型

IPMSM在转子坐标系下的数学模型为:

 $\left[ {\begin{array}{*{20}{c}} {{u_{d\left( t \right)}}}\\ {{u_{q\left( t \right)}}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{R_s}}&0\\ 0&{{R_s}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{i_{d\left( t \right)}}}\\ {{i_{q\left( t \right)}}} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} p&{ - {\omega _{{\rm{re}}\left( t \right)}}}\\ {{\omega _{{\rm{re}}\left( t \right)}}}&p \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{\phi _{d\left( t \right)}}}\\ {{\phi _{q\left( t \right)}}} \end{array}} \right],$ (1)
 ${\phi _{d\left( t \right)}} = {L_d}{i_{d\left( t \right)}} + {\phi _f},$ (2)
 ${\phi _{q\left( t \right)}} = {L_q}{i_{q\left( t \right)}},$ (3)
 ${T_{{\rm{em}}\left( t \right)}} = \frac{3}{2}{P_{\rm{n}}} \cdot \left( {{\phi _{d\left( t \right)}} \cdot {i_{q\left( t \right)}} - {\phi _{q\left( t \right)}} \cdot {i_{d\left( t \right)}}} \right),$ (4)
 ${T_{{\rm{em}}\left( t \right)}} - {T_{L\left( t \right)}} = \frac{J}{{{P_{\rm{n}}}}}\frac{{{\rm{d}}{\omega _{{\rm{re}}\left( t \right)}}}}{{{\rm{d}}t}}。$ (5)

IPMSM驱动系统如图 1所示。利用在线实时PSO方法来调整速度和q-d轴电流控制器参数, 从而实现磁场定向控制, 并通过检测电机实际运行时的电流和速度建立多个不同的目标函数值。其中, d轴和q轴电流PI控制器的传递函数分别为kid(1+τids)/skiq(1+τiqs)/s, q轴电流参考指令为iqref, 由速度控制器(ks_p+ks_i·$\frac{1}{s}$)提供。

 图 1 基于PSO方法的PMSM矢量控制结构图 Figure 1 Block diagram of a vector-controlled PMSM drive based on PSO controller

2 在线PSO控制器参数方法 2.1 PSO基本原则

PSO方法通过不断迭代更新粒子群中每个粒子的信息, 从而搜索到全局最优值。每一个粒子都代表一种解决方法, 且每一个粒子都有各自的位置Xj, g和移动速度vj, g。位置矩阵Xj, g中的每一行代表一个粒子的位置信息, 通过位置信息可以获得每个粒子的评估值。在每一次迭代中, 每一个粒子的存储值都随着粒子的个体最优值Pbestj, g和全局最优值Gbestj, g不断更新而计算粒子群下一步移动速度vj, g。该算法在早期的迭代过程中很容易从局部最优值逃逸出来并且加速后面的迭代过程, 增加了寻找全局最优值的可靠性。

 $\begin{array}{*{20}{c}} {\mathit{\boldsymbol{v}}_{j,g}^{\left( {t + 1} \right)} = w\mathit{\boldsymbol{v}}_{j,g}^{\left( t \right)} + {c_1} \cdot {r_1}\left( {\mathit{\boldsymbol{P}}_{{\rm{best}}j,g}^{\left( t \right)} - \mathit{\boldsymbol{X}}_{j,g}^{\left( t \right)}} \right) + }\\ {{c_2}{r_2}\left( {\mathit{\boldsymbol{G}}_{{\rm{best}}\;g}^{\left( t \right)} - \mathit{\boldsymbol{X}}_{j,g}^{\left( t \right)}} \right),} \end{array}$ (6)
 $\mathit{\boldsymbol{X}}_{j,g}^{\left( {t + 1} \right)} = \mathit{\boldsymbol{X}}_{j,g}^{\left( t \right)} + \mathit{\boldsymbol{v}}_{j,g}^{\left( t \right)}。$ (7)

 ${w^{\left( t \right)}} = {w_{\max }} - t \cdot \left( {{w_{\max }} - {w_{\min }}} \right)/{\rm{ite}}{{\rm{r}}_{\max }},$ (8)

 $v_g^{\max } = k \cdot x_g^{\max },0.1 \le k \le 0.5,$ (9)

2.2 在线PSO方法应用

(1) 评价函数的定义

 $F\left( {{k_{p1}},{k_{p2}},{k_{i1}},{k_{i2}}} \right) = \sum\limits_{i = 1}^3 {\left( {{a_i} \cdot {f_i}} \right)} ,$ (10)
 ${f_1} = {\left( {{\omega _{{\rm{re}}}}\left( k \right) - {\omega _{{\rm{re}}}}\left( {k - 1} \right)} \right)^2},$ (11)
 ${f_2} = {\left( {{\omega _{{\rm{re}}}}\left( k \right) - \omega _{{\rm{re}}}^{{\rm{ref}}}} \right)^2},$ (12)
 $\begin{array}{*{20}{c}} {{f_3} = \left( {{{\left( {{i_a}\left( k \right) - i_a^{{\rm{ref}}}\left( k \right)} \right)}^2}} \right. + {{\left( {{i_b}\left( k \right) - i_b^{{\rm{ref}}}\left( k \right)} \right)}^2} + }\\ {\left( {{{\left( {{i_c}\left( k \right) - {{\hat i}_c}\left( k \right)} \right)}^2}} \right]。} \end{array}$ (13)

3 仿真分析

 图 2 单采样周期内在线PSO流程图 Figure 2 Online PSO flow frame within one sampling time

IPMSM电机参数由表 1提供, 且电机定子电阻为5.8~7.8Ω变化, 用来检测所提方法的鲁棒性。粒子群的粒子数初始值为30, 且每一个粒子拥有4个变量(kp_iq, ki_iq, kp_s, ki_s), 分别代表搜索空间中位置矢量。经过30次迭代后, 将会得到全局最优值矩阵Gbestj, g

 图 3 IPMSM驱动系统PSO目标函数值 Figure 3 Fitness value of PSO for IPMSM drives
 图 4 传统PI控制器方法IPMSM驱动系统响应曲线 Figure 4 Results of IPMSM drive with conventional PI controllers
 图 5 在线PSO方法IPMSM驱动系统响应曲线 Figure 5 Results of IPMSM drive with online PSO-PI controllers
4 试验验证

 图 6 阶跃指令下PMSM分别在有无PSO优化情况下各变量响应曲线 Figure 6 The response curves of PMSM under the presence of PSO optimization with step instructions
4 结论

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