双边闭环泛函的T-S模糊系统事件触发滑模控制

Event-triggered Sliding Mode Control for T-S Fuzzy Systems via Two-side Looped Functionals

  • 摘要: 针对非线性系统存在的外部干扰、参数不确定性以及通信资源浪费等问题,提出了基于双边闭环泛函的Takagi-Sugeno(T-S)模糊系统的事件触发滑模控制(ETSMC)方法。本文以永磁同步电机(PMSM)为控制对象,首先建立T-S模糊模型,将非线性系统状态空间方程转化为低阶子系统;针对子系统设计线性滑模面和事件触发方案,引入双边闭环泛函进行稳定性分析,可通过分割相邻2次采样时间间隔,完整包含整个数据信息,可有效减少对李雅普诺夫泛函正定性的约束,进而降低稳定性判据的保守性,最终得出系统稳定的充分条件;再根据稳定性条件得出控制器增益,设计ETSMC并进行可达性分析;最终控制目标是在外部干扰与参数不确定性下,实现PMSM的鲁棒镇定,同时减少通信资源消耗。结果表明,所提方法可使PMSM快速稳定,有效节约通信资源。

     

    Abstract: To address the issues of external disturbances, parametric uncertainties, and communication resource waste in nonlinear systems, we propose an event-triggered sliding mode control (ETSMC) method for Takagi-Sugeno (T-S) fuzzy systems based on two-side looped functionals. Taking a permanent magnet synchronous motor (PMSM) as the control object, a T-S fuzzy model is first established to transform the state-space equation of the nonlinear system into low-order subsystems. A linear sliding surface and an event-triggered scheme are designed for the subsystem, and two-side looped functionals are introduced for stability analysis. Specifically, the two-side looped functionals can completely include all data information by dividing the interval between two adjacent sampling times, which can effectively reduce the constraint on the positive definiteness of the Lyapunov functional and thus significantly lower the conservatism of the stability criteria, ultimately deriving sufficient conditions to ensure stability. Furthermore, the controller gain is obtained based on the stability conditions, and the ETSMC is designed with reachability analysis of the system. The ultimate control objective is to achieve robust stabilization of the PMSM under external disturbances and parametric uncertainties, while reducing the consumption of communication resources. Simulation results verify that the proposed method can stabilize the PMSM rapidly and effectively save communication resources.

     

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