数控机床用磁悬浮系统非线性时变滑模变结构控制

为实现数控机床横梁磁悬浮系统悬浮气隙的精确控制，采用了非线性时变滑模变结构控制策略。首先,通过设计一种带有指数项的滑模面，使系统在任意初始状态下的状态变量都直接处于系统的滑模面上，实现对参数摄动和外部干扰的全局鲁棒性;然后，在此基础上设计了一种时变滑模控制器，并通过李亚普诺夫定理证明了该控制律的稳定性。仿真实验结果表明，非线性时变滑模变结构控制方法在保证系统全局稳定的前提下提高了滑模面的收敛速度，有效地削弱了抖振。

Nonlinear Time-varying Sliding Mode Control for NC Machine Magnetic Levitation Systems

In order to reach high-precision air gap of electromagnetic levitation grip a novel time-varying sliding mode was proposed. At first, a new exponential time-varying sliding surface was designed and guaranteed the sliding mode occurrence from beginning to end. The global robustness of parameter perturbation and external disturbance was realized. After that a control law of time-varying sliding mode was designed based on the sliding surface of exponential term and its stability was proved by the Lyapunov stability principle. Simulation results demonstrate that the time-varying term is introduced to improve the convergence speed of the sliding surface in the context of ensuring global stability of the system and to eliminate system chattering effectively.