基于改进终端SMC和SMO的SRM瞬时转矩控制

凌辉; 杜钦君; 庞浩; 杨姝欣; 赵正阳; 李存贺

doi:10.13700/j.bh.1001-5965.2022.0021

基于改进终端SMC和SMO的SRM瞬时转矩控制

doi: 10.13700/j.bh.1001-5965.2022.0021

山东理工大学电气与电子工程学院，淄博 255022

基金项目: 国家自然科学基金(62076152)；山东省自然科学基金(ZR2020MF096)；山东省科技型中小企业创新能力提升工程项目(2021TSGC1109)

详细信息

通讯作者:
E-mail：duqinjun@sdut.edu.cn

中图分类号: TM352
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出版历程
- 收稿日期: 2022-01-17
- 录用日期: 2022-02-28
- 网络出版日期: 2022-03-12
- 整期出版日期: 2023-11-30

Instantaneous torque control of SRM based on improved terminal SMC and SMO

School of Electrical and Electronic Engineering，Shandong University of Technology，Zibo 255022，China

Funds: National Natural Science Foundation of China (62076152); Shandong Provincial Natural Science Foundation (ZR2020MF096); Innovation Ability Promotion Project of Science and Technology SMEs in Shandong Province (2021TSGC1109)

More Information

Corresponding author: E-mail：duqinjun@sdut.edu.cn

摘要

摘要:
针对开关磁阻电机(SRM)常规终端滑模控制器（SMC）响应速度慢和传统滑模观测器（SMO）存在的抖振问题，提出一种基于改进终端SMC和变速趋近律SMO的SRM瞬时转矩控制（DITC）方法。设计了电机速度误差可快速收敛的改进非奇异快速终端滑模面和可自适应调整趋近律速度的变速幂次趋近律，利用等效控制法，得出了连续非奇异控制律。通过Lyapunov函数证明了该系统的稳定性和有限时间收敛性。设计了变速趋近律SMO以实现SRM无位置传感器控制。采用双曲正切函数作为切换函数，并引入快速幂次趋近律作为SMO速度观测的趋近律，克服了传统SMO固定开关增益带来的抖振和收敛速度问题。通过Lyapunov函数证明了SMO运行的稳定性。仿真和实验验证了所提方法的有效性。结果表明：与常规终端SMC相比，改进终端SMC能够在0.07 s内实现对期望转速的跟踪，调节时间减少了0.04 s，并且系统稳定时转速波动降低了0.5 r/min，具有更好的响应速度和稳定性。在负载突增时，系统转速可在0.02 s内调节至给定值，恢复时间减少了0.05 s，具有更好的调节性能。变速趋近律SMO能够在0.01 s内实现转速估计误差的收敛，且误差波动维持在2 r/min以内，可实现电机转速和转子位置的准确估计。
- 开关磁阻电机 /
- 终端滑模控制器 /
- 滑模观测器 /
- 快速幂次趋近律 /
- 收敛速度 /
- 抖振
Abstract:
An instantaneous torque control method for switched reluctance motors (SRM) based on improved terminal sliding mode controller (SMC) and sliding mode observer (SMO) with variable speed reaching law was proposed to address the issues of slow response speed of conventional terminal sliding mode control system of SRM and system chattering of traditional sliding mode observer.Firstly, an improved nonsingular fast terminal sliding mode surface with fast convergence of motor speed error and a variable speed power reaching law with adaptive adjustment of reaching law speed were designed. The continuous nonsingular control law was obtained by using the equivalent control method. The stability and finite-time convergence of the system were proved by the Lyapunov function. Secondly, a sliding mode observer with variable speed reaching law was designed to realize sensorless control of SRM. In order to solve the chattering and convergence speed issues brought on by the fixed switching gain of the conventional sliding mode observer, the hyperbolic tangent function was employed as the switching function and the fast power reaching law was introduced as the reaching law of speed observation.The stability of the observer was proved by the Lyapunov function. Finally, the simulation and experiment verified the effectiveness of the proposed method. The results show that compared with the conventional terminal sliding mode control, the improved terminal sliding mode control system can realize the tracking of the desired speed in 0.07 s, the adjustment time is reduced by 0.04 s, and the speed fluctuation is reduced by 0.5 r/min when the system is stable, which has better response speed and stability. When the load suddenly increases, the system speed can be adjusted to a given value within 0.02 s, and the recovery time is reduced by 0.05 s, which has a better adjustment ability. The sliding mode observer with variable speed reaching law can realize the convergence of speed estimation error within 0.01 s, and the error fluctuation is maintained within 2 r/min, which can realize the accurate estimation of motor speed and rotor position.
- switched reluctance motor /
- terminal sliding mode controller /
- sliding mode observer /
- fast power reaching law /
- convergence speed /
- chattering

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图 1 SRM-DITC系统框图

Figure 1. Block diagram of SRM-DITC system

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图 2 不对称半桥的开关状态

Figure 2. Switching states of asymmetrical half bridge

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图 3 扇区划分

Figure 3. Sector division

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图 4 磁链特性曲线

Figure 4. Characteristic curve of magnetic chain

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图 5 变速趋近律滑模观测器原理

Figure 5. Principle of sliding mode observer with variable speed convergence law

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图 6 基于改进终端滑模控制器和变速趋近律滑模观测器的SRM瞬时转矩控制系统

Figure 6. Instantaneous torque control system of SRM based on improved terminal sliding model controller and SMO with variable speed convergence law

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图 7 转速曲线对比

Figure 7. Comparison of rotate speed curves

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图 8 转速误差曲线对比

Figure 8. Comparison of rotate speed error curves

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图 9 稳态转矩曲线对比

Figure 9. Comparison of steady state torque curves

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图 10 突加负载时转速曲线对比

Figure 10. Comparison of rotate speed curves under sudden load

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图 11 突加负载时转矩曲线对比

Figure 11. Comparison of torque curves under sudden load

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图 12 传统滑模观测器转速估计曲线

Figure 12. Speed estimation curve of traditional SMO

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图 13 变速趋近律滑模观测器转速估计曲线

Figure 13. Speed estimation curve of SMO with variable speed convergence law

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图 14 变速趋近律滑模观测器位置估计曲线

Figure 14. Position estimation curve of SMO with variable speed convergence law

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图 15 变速趋近律滑模观测器位置估计误差

Figure 15. Error of position estimation of SMO with variable speed convergence law

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图 16 实验平台

Figure 16. Experimental platform

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图 17 电机加速的瞬态过程

Figure 17. Transient process of motor acceleration

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图 18 转子位置波形

Figure 18. Rotor position waveform

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表 1 电压矢量表

Table 1. Voltage vector table

区间	ΔT >内滞环上限	ΔT >外滞环上限	ΔT <内滞环下限	ΔT <外滞环下限
N=1	(−1,0,1,−1)	(−1,1,1,−1)	(−1,0,0,−1)	(−1,−1,0,−1)
N=2	(−1,−1,1,−1)		(−1,−1,0,−1)
N=3	(−1,−1,0,1)	(−1,−1,1,1)	(−1,−1,0,0)	(−1,−1,−1,0)
N=4	(−1,−1,−1,1)		(−1,−1,−1,0)
N=5	(1,−1,−1,0)	(1,−1,−1,1)	(0,−1,1,0)	(0,−1,−1,−1)
N=6	(1,−1,−1,−1)		(0,−1,−1,−1)
N=7	(0,1,−1,−1)	(1,1,−1,−1)	(0,0,−1,−1)	(−1,0,−1,−1)
N=8	(−1,1,−1,−1)		(−1,0,−1,−1)
注：ΔT为转矩误差。

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表 2 电机参数

Table 2. Motor parameters

参数	数值
额定功率/kW	1.5
额定转速/(r·min⁻¹)	1500
额定转矩/(N·m)	9.55
转动惯量/(kg·m²)	0.0082
摩擦系数/((N·m)(rad·s⁻¹)⁻¹)	0.01
开通角/(°)	35
关断角/(°)	57.5

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