基于磁场非线性的中低速磁悬浮鲁棒自适应控制

Robust Adaptive Control of Medium-low Speed Maglev Based on Magnetic Nonlinearity

摘要:

为了保障磁悬浮列车的悬浮稳定性，研究了中低速磁悬浮列车在磁场非线性和轨道不平顺激扰下的悬浮控制问题。首先，基于有限元方法分析了动态和静态磁场特性，建立了考虑磁饱和及涡流效应的悬浮力模型，并以该悬浮力模型为基础建立了单个悬浮单元的数学模型；然后，提出了一种鲁棒自适应控制方法，在广义（比例?积分）PI控制框架下，设计了自适应律灵活调节控制参数，并采用李雅普诺夫方法证明了闭环系统内所有信号均是最终一致有界的；最后，在整车动力学模型上进行多种工况的仿真分析，验证了所提出控制方法的有效性。结果表明，在正弦和随机激扰下，鲁棒自适应控制的气隙跟踪误差都降低70%以上；在竖曲线工况下，相较于传统（比例?积分?微分）PID控制，同一个悬浮模块的前后悬浮点最大气隙跟踪误差的差值分别从1.571 8 mm和1.227 8 mm下降到0.195 2 mm和0.396 2 mm。

Abstract:

In order to ensure the suspension stability of maglev trains， we investigate the suspension control problem of medium-low speed maglev vehicles under the disturbances of nonlinear magnetic fields and track irregularity in this paper. Firstly， the dynamic and static magnetic field characteristics are analyzed based on the finite element method， and a suspension force model considering magnetic saturation and eddy current effects is established. A mathematical model of a single suspension unit is built on the basis of the suspension force model. Then， a robust adaptive control method is proposed， which flexibly adjusts the control parameters through the adaptive law in the framework of generalized PI control. The Lyapunov method is used to prove that all signals in the closed-loop system are ultimately uniformly bounded. Finally， simulations under various operating conditions are conducted on the whole vehicle dynamics model to verify the effectiveness of the proposed control method. It is shown that air gap tracking errors under the robust adaptive control are both reduced by over 70% under sine and random disturbances， and compared with the traditional PID control， the maximum differences of air gap tracking errors between the front and rear suspension points of the same suspension module decrease from 1.571 8 mm and 1.227 8 mm to 0.195 2 mm and 0.396 2 mm respectively under the condition of vertical curves.