为了提高磁悬浮平台直线同步电动机悬浮系统的性能，提出了一种分数阶反步控制策略。基于磁悬浮直线同步电动机（MLLSM）悬浮系统的运行机理，建立了其数学模型和状态空间方程；针对MLLSM悬浮系统的强非线性，通过非线性坐标映射对其进行输入输出反馈线性化处理；引入了分数阶理论构造分数阶虚拟稳定函数来提高系统的收敛速度和控制精度；设计了分数阶反步控制器，构造Lyapunov函数证明系统稳定性。仿真结果表明，分数阶反步控制能够提高悬浮系统响应速度，有效抑制不确定性扰动对悬浮系统的影响。

A fractional order backstepping control strategy is proposed to enhance the performance of the linear synchronous motor suspension system for magnetic levitation platform. Based on the operating mechanism of the magnetic levitation linear synchronous motor (MLLSM) suspension system, its mathematical model and state space equation are established. Aiming at the strong nonlinearity of the MLLSM suspension system, input output feedback linearization is performed through nonlinear coordinate mapping. And to improve the convergence speed and control accuracy of the suspension system, fractional order theory is introduced to construct fractional order virtual stability functions. Fractional order backstepping controller is designed and Lyapunov function is constructed to prove the stability of the system. Simulation results show that the fractional order backstepping control can improve the response speed of the suspension system and effectively suppress the impact of uncertain disturbances on the suspension system.

国家自然科学基金项目（51575363）