﻿ 基于中立型系统理论的异步电机电流解耦控制方法
 控制与决策  2020, Vol. 35 Issue (2): 329-338 0

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PAN Yue-dou, WANG Guo-fang. Decoupling current control scheme for induction motors based on neutral system theory[J]. Control and Decision, 2020, 35(2): 329-338. DOI: 10.13195/j.kzyjc.2018.0757.
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### 文章历史

Decoupling current control scheme for induction motors based on neutral system theory
PAN Yue-dou , WANG Guo-fang
School of Automation, University of Science and Technology Beijing, Beijing 100083, China
Abstract: In the traditional system modeling of induction motors, the neglect of digital delay results in inaccurate modeling, which exacerbates the cross-coupling between the two currents in the current loop, leads to serious problems such as current distortion of the low-switching frequency drive system, system instability, etc. Using the neutral theory, a neutral-based current decoupling control method for induction motors is proposed, and a neutral current controller is designed. The current control method has the advantages of automatic parameter tuning, small coupling, fast response, and good robustness. The theory solves the influence of the digital delay problem on the control performance of the drive system by establishing an accurate mathematical model. The stability analysis of a neutral type time-delay system for induction motors is carried out. Simulation and experimental results show the feasibility of the designed neutral current controller.
Keywords: induction motor    digital delay    decoupling control    LMI    neutral controller
0 引言

1 异步电机中立型数学模型 1.1 异步电机数学模型

 (1)

 (2)
1.2 中立型系统理论

 (3)

1.3 异步电机中立型时滞系统模型

 (4)

 (5)

 (6)

step 1:将积分区间平均分成N份, 每个小区间的长度为

N个小矩形的面积之和近似积分项的值, 这里N ≥ 1, N = 1, 2, ..., n, 得到表达式

 (7)

step 2:对于任意的h, 存在NM, MZ, 使不等式成立.

step 3:得到异步电机中立型系统方程式为

 (8)
2 中立型电流控制器设计

 (9)

 (10)

 (11)

, 则不等式变为

 (12)

step 1:解线性矩阵不等式(11)得正定矩阵PxQxRx以及矩阵.

step 2:判断Riccati不等式(29)是否有解, 若有解, 则即为反馈控制器增益矩阵; 若无解, 则需要重新返回step 1求解.

3 稳定性分析

step 1:针对标准型中立型系统[15]

 (13)

 (14)

 (15)

step 2:观测器设计完成后, 下一步设计基于观测状态的反馈控制器u(t)=Kx(t), 使得下面闭环系统方程稳定:

 (16)

 (17)

step 3:考虑如下与方程(17)具有相同零极点的中立型系统方程:

 (18)

step 4:为了证明系统方程式(18)的稳定性, 本文设计了一种李亚普诺夫泛函[16], 其表达式为

 (19)

 (20)
 (21)

 (22)

 (23)

 (24)

step 5:由Razumikhin型定理[17], 得到系统方程(18)渐近稳定, 而系统方程(18)渐近稳定的充分必要条件是系统方程(17)渐近稳定.

 (25)
 (26)

 (27)

 (28)

4 实验研究

 图 1 基于中立型的异步电机电流环结构

 图 2 基于中立型电流控制器的异步电机仿真原理图

 图 3 基于中立型控制方法的异步电机仿真波形
 图 4 基于传统PI控制方法的异步电机仿真波形

 图 5 考虑延时后传统PI方法的电流转矩分量和励磁分量跟随曲线

 图 6 异步电机传真速度响应波形

 图 7 电力电子与电气传动综合实验台
 图 8 两种控制方法的异步电机实验波形

5 结论

1) 中立型电流控制器(NDS-ACR)通过软件编程实现, 参数自动整定, 效率高, 时效性好, 研究意义明显.

2) 基于中立型的异步电机数学建模中包含数字延迟项, 系统描述精确, 通过模型求解来解决数字延迟影响异步电机调速控制系统性能的问题.

3) 与采用传统控制方法的异步电机调速系统相比, 采用中立型电流控制器的系统具有转速调节时间范围大、系统响应速度快、鲁棒性好的优势.

4) 异步电机调速系统中使用中立型电流控制方法, 消除了两相定子电流间的交叉耦合, 解耦效果明显, 定子电流转矩分量和励磁分量波动较小, 控制效果好, 具有良好的应用前景.

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