模糊时滞系统的状态反馈控制器设计与稳定性分析

在保证闭环系统稳定的基础上,为进一步改进系统的动态性能,将模糊T-S模型方法应用到非线性连续时滞系统的控制器设计中,提出了一种带调节因子的状态反馈控制器的设计方法.首先给出变时滞非线性系统的模糊T-S模型,然后设计出基于观测器的状态反馈控制器,并利用Lyapunov-Razum ikhin稳定性理论给出模糊闭环系统一致渐近稳定的充分条件,最后通过求解一系列线性矩阵不等式得到状态反馈增益矩阵和观测增益矩阵.通过对卡车倒车控制的实验仿真,表明当调节因子选取适当时,闭环系统的超调量和震荡次数都有明显减少,选取不当时,超调量和震荡次数都有所增加.因此,通过改变调节因子的值,可以对闭环系统的动态性能进行适当调节.此外,通过引入特殊矩阵,使得判据中含有较少的约束不等式,从而减弱了结论的保守性.

Design and stability analysis of state feedback controller for fuzzy time-delay systems

On the basis of guaranteeing closed loop systems stability,in order to improve the dynamic performance,the T-S fuzzy model approach is extended to the controller design for continuous nonlinear systems with time delay,and a method of designing state feedback controller with adjustable parameter is proposed.The T-S fuzzy model for nonlinear systems with time-varying delay is given firstly.Then observer-based state feedback controller is designed,and sufficient stability conditions for the closed loop systems are proposed by using the Lyapunov-Razumikhin theorem.Lastly,the fuzzy state feedback gain and observer gain are derived through the numerical solution of a set of obtained linear matrix inequalities(LMIs).The experiment simulation based on the backing up control of truck-trailer model shows that: when adjustable parameter is properly chosen,the overshoot and oscillation will be weakened,otherwise,will be strengthened.Therefore,by taking different adjustable parameter,the dynamic performance of the closed loop system can be adjusted properly.Less restriction inequalities,in addition,are needed in the stability criterion by introducing a special matrix,which makes the result less conservative.