1

A robustness evaluation method for the robust control of electrical drive systems based on six-sigma methodology

基于六西格瑪方法的電氣驅動系統魯棒控制魯棒性評價方法

Nabil Farah; Gang Lei; Jianguo Zhu; Youguang Guo

N. Farah, G. Lei, J. Zhu and Y. Guo, "A robustness evaluation method for the robust control of electrical drive systems based on six-sigma methodology," in CES Transactions on Electrical Machines and Systems, doi: 10.30941/CESTEMS.2025.00011.

Abstract—Numerous uncertainties in practical production and operation can seriously affect the drive performance of permanent magnet synchronous machines (PMSMs). Various robust control methods have been developed to mitigate or eliminate the effects of these uncertainties. However, the robustness to uncertainties of electrical drive systems has not been clearly defined. No systemic procedures have been proposed to evaluate a control system's robustness (how robust it is). This paper proposes a systemic method for evaluating control systems' robustness to uncertainties. The concept and fundamental theory of robust control are illustrated by considering a simple uncertain feedback control system. The effects of uncertainties on the control performance and stability are analyzed and discussed. The concept of design for six-sigma (a robust design method) is employed to numerically evaluate the robustness levels of control systems. To show the effectiveness of the proposed robustness evaluation method, case studies are conducted for second-order systems, DC motor drive systems, and PMSM drive systems. Besides the conventional predictive control of PMSM drive, three different robust predictive control methods are evaluated in terms of two different parametric uncertainty ranges and three application requirements against parametric uncertainties.

摘要—實際生產和運行中的許多不確定性會嚴重影響永磁同步電機（PMSM）的驅動性能。為了減輕或消除這些不確定性的影響，人們開發了各種魯棒控制方法。然而，電氣驅動對不確定性的魯棒性尚未得到明確定義。目前還沒有提出評估控制系統魯棒性（魯棒性如何）的系統程序。本文提出了一種評估控制系統對不確定性的魯棒性的系統方法。通過考慮一個簡單的不確定反饋控制系統來說明魯棒控制的概念和基本理論。分析并討論了不確定性對控制性能和穩定性的影響。采用六西格瑪設計概念（一種魯棒設計方法）對控制系統的魯棒性水平進行了數值評估。為了證明所提出的魯棒性評估方法的有效性，對二階系統、直流電機驅動系統和 PMSM 驅動系統進行了案例研究。除了 PMSM 驅動器的傳統預測控制外，還針對參數不確定性的兩種不同參數不確定性范圍和三種應用要求評估了三種不同的魯棒預測控制方法。

2

Enhanced sensorless control of switched reluctance motors using inertial phase-locked loop for extended speed range

基于慣性鎖相環的開關磁阻電機增強型無傳感器控制及轉速范圍擴展

Zifeng Chen; Xijian Lin; Huayu Ji; Zehua Li; Hang Zhao; Dianxun Xiao

Z. Chen, X. Lin, H. Ji, Z. Li, H. Zhao and D. Xiao, "Enhanced sensorless control of switched reluctance motors using inertial phase-locked loop for extended speed range," in CES Transactions on Electrical Machines and Systems, doi: 10.30941/CESTEMS.2025.00013.

Abstract—Sensorless control of switched reluctance motors (SRMs) often requires a hybrid mode combining low-speed pulse injection methods and high-speed model-based estimation. However, pulse injection causes unwanted audible noises and torque ripples. This article proposes an enhanced model-based sensorless approach to extend downwards the speed range in which sensorless control can work without injection. An inertial phase-locked loop (IPLL) based on a stator flux observer is introduced for position estimation. Compared to the conventional phase-locked loop scheme, the IPLL offers a more robust disturbance rejection capability and thus reduces the flux model errors at lower speeds. Experimental results substantiate the feasibility of the extended low-speed operation using the model-based sensorless control approach.

摘要—開關磁阻電機（SRM）的無傳感器控制通常需要結合低速脈沖注入方法和高速基于模型的估計的混合模式。然而，脈沖注入會導致不必要的可聽噪音和扭矩波動。本文提出了一種增強的基于模型的無傳感器方法，用于無傳感器控制在沒有注入的情況下，向下擴展速度范圍。介紹了一種基于定子磁鏈觀測器的慣性鎖相環（IPLL）用于位置估計。與傳統的鎖相環方案相比，IPLL提供了更魯棒的干擾抑制能力，從而減少了低速下的通量模型誤差。實驗結果證實了使用基于模型的無傳感器控制方法進行擴展低速運行的可行性。

3

Additional magnetic field of dual-parallel rotor permanent magnet synchronous motor and its influence on electromagnetic torque

雙并聯轉子永磁同步電機附加磁場及其對電磁轉矩的影響

Yang Chen; Dajun Tao; Baojun Ge

Y. Chen, D. Tao and B. Ge, "Additional magnetic field of dual-parallel rotor permanent magnet synchronous motor and its influence on electromagnetic torque," in CES Transactions on Electrical Machines and Systems, doi: 10.30941/CESTEMS.2025.00015.

Abstract—The coupling effect of dual-parallel rotor connected stator permanent magnet synchronous motor not only affects the magnetic field in the coupling area, but also generates an additional magnetic field in the uncoupled area. The characteristics of the additional magnetic field and its influence on electromagnetic torque are studied in this paper. The topology and parameters of motor are described briefly. The existence of additional magnetic field is proved by the simulation models under two boundary conditions, and its characteristics and source are analyzed. The analytical model is established, and the influence of key parameters on the additional magnetic field is discussed. On this basis, the influence of the additional magnetic field on the electromagnetic torque of the motor is studied, and the analytical expression of the additional torque is constructed. The fluctuation rule is analyzed, and the additional magnetic field separation model is proposed. The theoretical analysis and simulation results reveal and improve the internal mechanism of reducing motor torque ripple by optimizing the duty angle and coupling distance. Finally, a prototype test platform is built to verify the correctness of the proposed theory and the accuracy of the simulation model.

摘要—雙并聯轉子定子永磁同步電機的耦合效應不僅會影響耦合區域的磁場，還會在未耦合區域產生附加磁場。本文研究了附加磁場的特性及其對電磁轉矩的影響。本文簡要介紹了電機的拓撲結構和參數。通過兩個邊界條件下的仿真模型證明了附加磁場的存在，并分析了其特性和來源。建立了分析模型，并討論了關鍵參數對附加磁場的影響。在此基礎上，研究了附加磁場對電機電磁轉矩的影響，并構建了附加轉矩的解析表達式。分析了波動規律，提出了附加磁場分離模型。理論分析和仿真結果揭示并改進了通過優化占空比和耦合距離降低電機轉矩紋波的內部機理。最后，建立了一個原型測試平臺，以驗證所提理論的正確性和仿真模型的準確性。

《中國電工技術學會電機與系統學報（英文）》(CES TEMS)是中國電工技術學會和中國科學院電工研究所共同主辦、IEEE PELS學會技術支持的英文學術期刊。期刊發表國內外有關高性能電機系統、電機驅動、電力電子、可再生能源系統、電氣化交通等研發及應用領域中原創、前沿學術論文。中國工程院院士馬偉明擔任主編，IEEE 副主席 Don Tan 博士為國際主編。目前已被ESCI、EI、Scopus、 Inspec、Google scholar、IEEE Xplore、中國科學引文數據庫(CSCD) 核心版、DOAJ、CSTPCD、知網、萬方、維普等數據庫收錄。

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