永磁直线同步电机分数阶微分型边界层终端滑模控制

doi:10.19595/j.cnki.1000-6753.tces.220287

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摘要

针对永磁直线同步电机易受参数摄动、负载扰动等不确定因素的影响,提出一种分数阶微分型边界层非奇异快速终端滑模控制（FO-NFTSMC）策略。首先,采用NFTSMC方法来抑制不确定因素对系统的影响,保证了跟踪误差在有限时间快速收敛,避免了奇异性。其次,在系统不确定上界未知的情况下,将Riemann-Liouville分数阶微分定义和边界层技术结合,实现一种新的分数阶微分型边界层控制,不仅具有整数阶边界层的输出特性,还具备“大误差大增益,小误差小增益”的功能,化解了整数阶边界层控制中的“弱抖振”与“快收敛”之间的矛盾,使得系统全局快速收敛。最后,实验结果表明该策略提高了系统的跟踪精度与响应速度,对负载扰动和参数变化具有很强的抑制能力,同时有效地削弱抖振现象。

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关键词 ：永磁直线同步电机, 非奇异快速终端滑模控制, 分数阶微分型边界层, 抖振

Abstract：

Due to the advantages of high reliability, low cost and simple structure, permanent magnet linear synchronous motor(PMLSM) have been increasingly used in high-precision industrial servo applications. However, the lack of mechanical transmission in the structure makes it more susceptible to uncertainties such as parameter variations and load disturbance. To solve the above problem, a fractional order boundary layer nonsingular fast terminal sliding mode control(FO-NFTSMC) strategy is proposed.
Firstly, the dynamic model of PMLSM containing uncertainties is established. Then, the nonsingular fast terminal sliding mode control (NFTSMC) method is used to suppress the influence of uncertainties on the system, which ensures that the tracking error converges to zero in a finite time and avoids the singularity problem. In addition, the Riemann-Liouville fractional order differential definition and the boundary layer technique are combined to realize a new fractional order differential boundary layer control. The fractional order boundary layer has the output characteristics of the integer boundary layer and can also change the output value with the direction of change of the state trajectory, solving the contradiction between “Weak chattering” and “fast convergence” in the traditional integer order boundary layer control.
To highlight the superiority of the proposed method, the contrast experiments based on FO-NFTSMC method and IO-NFTSMC method are carried out on a linear motor system. When tracking a given step command, the actual trajectory based on the FO-NFTSMC deviates less from the given tracking trajectory and the steady-state error remains around 5 μm, while the deviation value of the IO-NFTSMC strategy is larger and the steady-state error remains around 10 μm. Therefore, the system based on the FO-NFTSMC has better tracking performance and weaker chattering. To further investigate the robustness of the PMLSM control system as affected by changes in motor mass and friction, a linear motor mounted with a 2 kg payload is allowed to track a given sine signal. The position tracking error of FO-NFTSMC has a smaller value compared to IO-NFTSMC, with a reduction of about 60%. In addition, the IO-NFTSMC strategy responds slower at the beginning of the system response, reaching steady state in about 0.1s, while the FO-NFTSMC ensures the convergence time of the system. Also, the load disturbance of 5N is suddenly added to the PMLSM system at nominal condition to verify the anti-interference ability of the system. The experimental result show that the error curves of both control strategies fluctuate significantly, with the fluctuation amplitude of FO-NFTSMC being smaller and remaining within 10 μm. While the tracking error curve of IO-NFTSMC strategy has a larger fluctuation amplitude, with the maximum magnitude reaching about 30μm. Finally, to verify the effect of different order of fractional-order boundary layer control on the system performance, an additional set of experiments were done to change only the fractional order condition, and experimental results showed that the 0.2 order-based control system has better dynamic performance.
The following conclusions can be drawn from the experimental analysis: 1) Compared with the IO-NFTSMC method, the FO-NFTSMC method improves the position tracking accuracy and robustness performance of the PMLSM system.2) Using the fractional order boundary layer control, the sliding mode chattering is reduced and the dynamic performance of PMLSM servo system is improved.3) Fractional order control systems have a wider range of parameter selection than integer-order control systems.

Key words： Permanent magnet linear synchronous Motor non-singular fast terminal sliding mode control fractional order differential boundary layer chattering

PACS:

TM359.4

基金资助:

国家自然科学基金项目（51875366）资助

通讯作者: 王丽梅女,1969年生,教授,博士生导师,研究方向为交流伺服驱动技术。E-mail：wanglm@sut.edu.cn

作者简介: 赵鑫宇男,1996年生,博士研究生,研究方向为永磁直驱伺服系统及其控制。E-mail：zhaoxy_sut@163.com

引用本文:

赵鑫宇, 王丽梅. 永磁直线同步电机分数阶微分型边界层终端滑模控制[J]. 电工技术学报, 0, (): 1-1. Zhao Xinyu, Wang Limei. Fractional Order Differential Boundary Layer Terminal Sliding Mode Control for Permanent Magnet Linear Synchronous Motor. Transactions of China Electrotechnical Society, 0, (): 1-1.

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