饱和时滞非线性系统的间接线性矩阵不等式抗饱和设计

Anti-windup design for saturated time-delay nonlinear systems: an indirect linear matrix inequality-based approach

中文关键词  一步抗饱和  时滞非线性系统  Takagi-Sugeno模糊模型  线性矩阵不等式  并行分布补偿

英文关键词  one-step anti-windup  time-delay nonlinear systems  Takagi-Sugeno fuzzy model  linear matrix inequality  parallel distributed compensation

中文摘要

      当时滞非线性系统具有执行器饱和时, 其稳定性无法得到保证. 为了寻找饱和时滞非线性系统的稳定控制 器, 本文阐述了一种间接线性矩阵不等式(LMI)一步抗饱和设计方法. 首先, 利用Takagi-Sugeno (T–S)模糊模型将一 类饱和时滞非线性系统精确重构, 引入输出反馈并行分布补偿系统得到闭环控制系统. 然后, 运用李雅普诺夫稳定 性理论, 导出闭环系统的稳定条件, 利用一个矩阵不等式的等价引理, 将闭环系统稳定条件间接的转化为两个 LMIs条件, 进而得到间接LMI抗饱和补偿算法, 同时给出了吸引域估计及其优化模型. 最后给出了应用此方案的一 个仿真实例.

英文摘要

      The stability of time-delay nonlinear systems cannot be guaranteed when it has actuator saturation. Motivated by looking for the stability controller of saturated time-delay nonlinear systems, one-step anti-windup design based on the indirect linear matrix inequality (LMI) approach is proposed in this paper. First, a class of saturated time-delay nonlinear systems can be reconstructed accurately by using Takagi-Sugeno (T–S) fuzzy model, and then the parallel distributed compensation system with output feedback is used to get the closed-loop control systems. Then, the stability conditions of the closed-loop systems are deduced by using Lyapunov stability theory, and the stability conditions of the closed-loop systems can be converted to two LMIs conditions indirectly by using an equivalent lemma of matrix inequality, then the anti-windup compensation algorithm based on indirect LMI approach is given, meanwhile, the attraction domain estimation and its optimization model are presented. Finally, a simulation example is given to illustrate the proposed method.