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基于非线性磁悬浮系统的奇异摄动特点,研究了一种精确几何积分流形控制方法,使磁悬浮系统的稳态流形能够无误差地跟踪给定设计流形。将复杂奇异摄动磁悬浮系统按照不同时间尺度分解为降阶系统和边界层,以线性降阶系统设计流形为例,推算出稳定慢控制的具体形式并说明参数稳定范围,结合稳定边界层的快控制,最终推算出磁悬浮系统的复合控制规律。仿真和实验均证明该控制算法能够保证降阶系统的流形无误差地跟踪给定的设计流形。利用该算法能够使磁悬浮系统无误差地跟踪任意给定的设计流形,从而提高磁悬浮系统的动态特性。输出流形与设计流形的一致性还可以用来简化系统模型,降低磁悬浮车辆系统动力学分析的复杂程度。
Based on the singular perturbation characteristics of nonlinear maglev system, a precise geometrically integrated manifold control method is studied, which enables the steady state manifold of a maglev system to track a given design manifold without error. The complex singularly perturbed maglev system is decomposed into the reduced-order system and the boundary layer according to different time scales. Taking the linear decentralized system design manifold as an example, the specific form of steady slow control is deduced and the stable range of parameters is described. Combining with the stable boundary layer Fast control, the final calculation of the magnetic levitation system compound control law. Simulations and experiments show that the proposed control algorithm can ensure that manifolds of reduced order systems can track a given design manifold without error. The algorithm can make the magnetic levitation system track any given design manifold without error, so as to improve the dynamic characteristics of the levitation system. The consistency of the output manifold with the design manifold can also be used to simplify the system model and reduce the complexity of the dynamic analysis of the system.