基于LMI的模糊控制器设计

对于许多实际的非线性系统,状态变量往往不能获取或难于测量。因此设计模糊状态观测器来估计状态变量是非常必要的。针对T-S模糊模型近似描述的非线性系统,提出了一种基于线性矩阵不等式(LMI)的具有区域极点配置功能的模糊控制器和模糊状态观测器的设计方法。首先利用并行分布补偿(PDC)设计思想和基于线性矩阵不等式(LMI)的极点配置理论,将闭环系统的全局渐进稳定性要求,性能指标及控制量约束条件统一到线性矩阵不等式框架内。然后求解线性矩阵不等式族获得控制器和观测器参数。最后将该设计方法应用于倒立摆的平衡控制中,通过仿真曲线可以看出该方法设计的控制器可使倒立摆稳定并满足指定的性能指标,因此该设计方法是有效的。

Design of Fuzzy Controller Based on LMI

In practice, the states of the nonlinear systems are usually unobservable, so it is necessary to design a fuzzy observer in order to estimate the state variable. A method of designing fuzzy controllers and fuzzy state observers with pole placement constraints for nonlinear systems approximately expressed by Takagi-Sugeno (T-S) fuzzy dynamic model was proposed. Firstly, based on the concept of the parallel distributed compensation (PDC) and the theory of pole placement, the method combined condition which guarantees global asymptotic stability of the whole system, satisfied desired performance and constrainted on the control input into a framework of linear matrix inequalities (LMIs), and then, the parameters of controller and observer could be obtained by convex programming techniques for LMIs. Finally, the design method was verified by designing a PDC controller for an inverted pendulum using the proposed method and the results are soundness. So the method is efficiency.