﻿ 基于动态补偿的多电机控制算法
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1. 西北工业大学 自动化学院, 西安 710129;
2. 北京邮电大学 灾备技术国家工程实验室, 北京 100876

Multi-motor control algorithm based on dynamic compensation
ZHOU Guangfei1, HOU Bochuan2, YANG Jianhua1, WU Yangfei1
1. School of Automation, Northwestern Polytechnical University, Xi'an 710129, China;
2. National Engineering Laboratory for Disaster Recovery Technology, Beijing University of Post and Telecommunications, Beijing 100876, China
Abstract: A key problem in the motor control is to achieve the same speed in the multi-motor coordinated control achieves the same speed. When the load changes and the motor parameters change, the motor performance will be degraded, and will not be reach a desirable control effect. In order to keep the speed between the motors synchronized, the mathematical model of vector control for the permanent magnet synchronous motor d-q coordinate system is established. Based on the speed following control, a variable gain speed compensator based on the single neuron PID is proposed for the deviation coupling control. The simulation model of three permanent magnet synchronous motors is established in MATLAB/Simulink. The simulation results show that compared with the traditional PID fixed gain speed compensator algorithm, the variable gain compensator of single neuron PID has stronger robustness and faster convergence.
Keywords: multi-motor    cooperative control    deviation coupling    single neuron PID    speed regulation

1 永磁同步电机矢量控制

PMSM是一个多变量、强耦合的非线性时变系统[9]，为简化对PMSM分析，建立高效可行的数学模型，先做如下假设:

1) 定子三相绕组以及永磁体产生的磁场为空间正弦分布，稳定运行时相绕组中的感应电动势波形为正弦波。

2) 忽略定子齿槽对气隙磁阻及磁场分布的影响。

3) 定子及转子的铁芯磁导率为无穷大，电机的绕组电感不随工况变化[10]

 $\left\{ {\begin{array}{*{20}{l}} {{u_d} = {R_{\rm{s}}}{i_d} + {L_d}\frac{{{\rm{d}}{i_d}}}{{{\rm{d}}t}} - {\omega _{\rm{r}}}{L_q}{i_d}}\\ {{u_q} = {R_{\rm{s}}}{i_q} + {L_q}\frac{{{\rm{d}}{i_q}}}{{{\rm{d}}t}} + {\omega _{\rm{r}}}({L_d}{i_d} + {\varPsi _{\rm{f}}})} \end{array}} \right.$ （1）

 ${T_{\rm{e}}} = \frac{3}{2}p[{\varPsi _{\rm{f}}}{i_q} + ({L_d} - {L_q}){i_q}{i_d}]$ （2）

 图 1 矢量控制框图 Fig. 1 Diagram of vector control block
2 多台永磁同步电机偏差耦合算法

 图 2 带速度补偿的多电机协同控制框图 Fig. 2 Multi-motor coordinated control block diagram with speed compensation

 $\left\{ {\begin{array}{*{20}{l}} { {\rm{err}}{ _{12}}(t) = {K_1}{\omega _1} - {K_2}{\omega _2}}\\ { {\rm{err}}{ _{23}}(t) = {K_2}{\omega _2} - {K_3}{\omega _3}} \end{array}} \right.$ （3）

 $\left\{ {\begin{array}{*{20}{l}} { {\rm{err}}{ _{12}}(t) = \mathop {{\rm{lim}}}\limits_{t \to \infty } ({K_1}{\omega _1} - {K_2}{\omega _2}) = 0}\\ { {\rm{err}}{ _{23}}(t) = \mathop {{\rm{lim}}}\limits_{t \to \infty } ({K_2}{\omega _2} - {K_3}{\omega _3}) = 0} \end{array}} \right.$ （4）

 $\Delta \omega = {K_{12}}({K_1}{\omega _1} - {K_2}{\omega _2}) + {K_{23}}({K_2}{\omega _2} - {K_3}{\omega _3})$ （5）

 图 3 变增益速度偏差补偿 Fig. 3 Compensation of speed deviation of variable gain
3 单神经元PID速度补偿器

 $\left\{ \begin{array}{l} \begin{array}{*{20}{l}} {u(k) = u(k - 1) + K\sum\limits_{i = 1}^3 {\omega _i^\prime } {x_i}(k)}\\ {\omega _i^\prime (k) = {\omega _i}(k)/\sum\limits_{i = 1}^3 | {\omega _i}(k)|} \end{array}\\ \begin{array}{*{20}{l}} {{\omega _1}(k) = {\omega _1}(k - 1) + {\eta _{\rm{P}}}z(k)u(k){x_1}(k)}\\ {{\omega _2}(k) = {\omega _2}(k - 1) + {\eta _{\rm{I}}}z(k)u(k){x_2}(k)}\\ {{\omega _3}(k) = {\omega _3}(k - 1) + {\eta _{\rm{D}}}z(k)u(k){x_3}(k)}\\ {{x_1}(k) = e(k)}\\ {{x_2}(k) = \Delta e(k) = e(k) - e(k - 1)}\\ {{x_3}(k) = {\Delta ^2}e(k) = e(k) - 2e(k - 1) + e(k - 2)} \end{array} \end{array} \right.$ （6）

 $\left\{ \begin{array}{l} \begin{array}{*{20}{l}} {u(k) = u(k - 1) + K\sum\limits_{i = 1}^3 {\omega _i^\prime } {x_i}(k)}\\ {\omega _i^\prime (k) = {\omega _i}(k)/\sum\limits_{i = 1}^3 | {\omega _i}(k)|} \end{array}\\ \begin{array}{*{20}{l}} {{\omega _1}(k) = {\omega _1}(k - 1) + {\eta _{\rm{P}}}z(k)u(k)(e(k) + \Delta e(k))}\\ {{\omega _2}(k) = {\omega _2}(k - 1) + {\eta _{\rm{I}}}z(k)u(k)(e(k) + \Delta e(k))}\\ {{\omega _3}(k) = {\omega _3}(k - 1) + {\eta _{\rm{D}}}z(k)u(k)(e(k) + \Delta e(k))} \end{array} \end{array} \right.$ （7）
4 仿真模型及控制策略

 序号 Pn/kW p vn/(r·min-1) J/(10-3 kg·m2) 1 2 4 1 600 0.8 2 2 4 1 600 0.8 3 2 4 1 600 0.8

 图 4 固定增益增量式PID速度调节曲线 Fig. 4 Curves of speed adjustment for fixed gain incremental PID
 图 5 变增益单神经元PID速度调节曲线 Fig. 5 Curves of speed adjustment for variable gain single neuron PID

5 结论

1) 通过变增益电机偏差耦合控制，使得系统能够很快地跟踪目标并降低速度误差，对于电动机车等速度精度要求较高的场合有一定的借鉴意义。

2) 本文在传统PID多电机耦合系统控制方案基础上采用单神经元结构，在不改变系统稳定性的情况下，进一步改善多电机系统在不同工况下的控制性能，表现出优异的鲁棒性。

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http://dx.doi.org/10.7527/S1000-6893.2019.23771

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#### 文章信息

ZHOU Guangfei, HOU Bochuan, YANG Jianhua, WU Yangfei

Multi-motor control algorithm based on dynamic compensation

Acta Aeronautica et Astronautica Sinica, 2020, 41(S1): 723771.
http://dx.doi.org/10.7527/S1000-6893.2019.23771