基于线性矩阵不等式的磁悬浮轴承多目标控制系统设计

首先建立了磁悬浮轴承局部子系统线性Takagi- Sugeno(TS)模糊模型，利用单点模糊化、乘积推理和加权平均得到整个系统的非线性模型。针对以往非线性系统的单目标控制设计，提出了基于线性矩阵不等式(LMI)的多目标模糊控制系统的设计方法。该方法将闭环控制系统的稳定性、抗干扰性及极点配置的要求统一到1个线性矩阵不等式组中，通过求解线性矩阵不等式组获得满足要求的控制器参数，利用并行分布补偿控制(PDC)方法得到整个系统的非线性模糊状态反馈控制器，实现了系统同时满足多目标的要求，并且避免了设计过程的多次反复。应用于磁悬浮轴承非线性系统的控制中，通过实验验证了该设计方法的有效性。

A Design Method for the Magnetic Bearing Control System With Multi-objective Requirements via Linear Matrix Inequality Approach

Linear local Takagi-Sugeno(TS)-fuzzy models for magnetic bearing subsystem and nonlinear model for the overall system were given.Based on the TS-fuzzy model,a linear matrix inequality(LMI)-based design method for the fuzzy control of nonlinear systems with multi-objective requirements was presented.The method combines stable conditions of close-loop TS-fuzzy system,desired control performance and constraints on the control input into a framework of LMIs,and the parameters of controller can be obtained by convex programming techniques for LMIs.The fuzzy state feedback nonlinear controller for the overall system was obtained via parallel-distributed compensation(PDC) approaches,which can satisfy multi-objective requirements simultaneously,and the method avoided the repeat of design process.Through application in the magnetic bearing control system,the effect of this method is proved.