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[摘要]
【目的】六相混合励磁磁通切换直线电动机(SHEFSLM)悬浮系统具有非线性、强耦合与参数时变特性。虽然SHEFSLM应用模块化结构,能够有效改善磁路不平衡问题,但外部扰动与直线电机固有的端部效应,仍给悬浮系统控制带来严峻挑战。为此,本文针对SHEFSLM悬浮系统提出一种变指数滑模控制(VESMC)策略。【方法】首先,基于SHEFSLM悬浮系统的磁链方程、电压方程与运动方程,推导得到电磁推力方程、悬浮力方程与系统状态方程。其次,构造滑模面并设计一种新型变指数趋近律。该趋近律能够自适应调节收敛速度,使系统状态远离滑模面时快速收敛、靠近滑模面时平稳趋近,提升系统稳定性并有效抑制抖振。随后,采用李雅普诺夫函数证明闭环系统稳定性,系统收敛时间由控制器参数决定。最后,通过仿真对所提VESMC、滑模控制(SMC)和比例积分(PI)控制进行对比分析。【结果】仿真结果表明,相较于SMC与PI控制,本文所提VESMC的空载起动调节时间分别缩短68%和73.3%;突加阶跃扰动时,系统恢复时间分别缩短68%和85.5%;在抑制端部效应方面,VESMC的控制性能优于另外两种控制策略。【结论】在面对扰动时,VESMC表现出更强的鲁棒性,有效削弱了SMC固有的抖振现象,提升了系统稳定性和动态性能,具有稳态误差小,调节时间和恢复时间短的优点,可有效提高磁悬浮系统的控制性能,并满足系统控制需求。
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[Abstract]
[Objective] The maglev system of the six-phase hybrid excitation flux switching linear motor (SHEFSLM) is nonlinear, strongly coupled and parameter-varying. Although the modular structure adopted by the SHEFSLM can effectively mitigate the magnetic circuit imbalance, external disturbances together with the inherent end effects of linear motors still bring severe challenges to the control of maglev system. To tackle these control performance problems, a variable exponential sliding mode control (VESMC) strategy is proposed for SHEFSLM maglev system. [Methods] Firstly, the electromagnetic thrust equation, levitation force equation and system state equation were derived based on the flux linkage equation, voltage equation and mechanical motion equation of the SHEFSLM maglev system. Secondly, a sliding mode surface was constructed, and a novel variable exponential reaching law was proposed. This reaching law was capable of adaptively adjusting the convergence rate, which enabled rapid convergence when the operating point was far away from the sliding surface and smooth convergence in the vicinity of the sliding surface. Hence, superior system stability was guaranteed and chattering was effectively suppressed. Subsequently, the stability of the closed-loop system was verified via the Lyapunov function, and the convergence time was determined by the controller parameters. Finally, simulation comparisons among the proposed VESMC, sliding mode control (SMC) and proportional-integral (PI) control were carried out. [Results] Simulation results indicated that compared with SMC and PI control, the VESMC proposed in this paper reduced the settling time of no-load startup by 68% and 73.3%, respectively. Under sudden step disturbances, the recovery time was shortened by 68% and 85.5%, respectively. In suppressing end effects, VESMC exhibited better performance than the other two control strategies. [Conclusion] In the presence of disturbances, VESMC exhibits stronger robustness, effectively attenuates the chattering inherent in sliding mode control, and improves the stability and dynamic performance of the system. It offers the advantages of small steady-state error, short settling time, and short recovery time, thereby effectively enhancing the control performance of the maglev system and meeting the control requirements.
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