【作者】 刘昕；

【导师】 程平；

【作者基本信息】 武汉理工大学 ， 控制科学与工程， 2012， 硕士

【摘要】 非线性时滞系统的稳定分析与综合作为控制理论研究的热点,长期以来备受关注。T-S模糊模型方法因其自身的局部线性逼近特性,成为近些年来研究非线性时滞系统综合控制的一种重要方法。本文即是通过建立系统的T-S模糊模型,结合L函数方法和线性矩阵不等式(LMI)技术,研究了非线性时滞系统的稳定性、鲁棒模糊控制及H∞性能,主要内容及成果体现在以下几个方面：1)从实际应用的角度设定时变时滞的下界不严格为零,研究了一类带有非线性扰动的变区间连续时滞系统的稳定性。通过构造一类全新的带调节参数的L-K泛函,以线性矩阵不等式的形式,给出了全新的带调节参数的时滞相关型稳定性判据。并经数值仿真,验证了结论较小的保守性。2)将线性时滞系统控制中较完善的广义模型变换结合Moon不等式的处理方法推广到T-S模糊时滞系统,研究了一类不确定连续复合时滞系统的鲁棒控制。基于改进的带调节参数的L-K泛函,以LMI的形式,给出了全新的带调节参数的时滞相关型鲁棒镇定的充分条件及鲁棒状态反馈控制器的形式。在保证闭环稳定的基础上,可通过改变调节参数的值,增大时滞的范围,实现对控制器的间接调节。通过仿真实例,方法的有效性得以验证。3)在研究不确定连续复合时滞系统鲁棒控制的基础上,继续讨论了一类带有外界扰动的不确定复合时滞系统的鲁棒H∞控制,以LMI的形式,给出了全新的带调节参数的时滞相关型鲁棒H。镇定的充分条件及鲁棒H∞状态反馈控制器的形式。在保证闭环稳定的基础上,可通过改变调节参数的值,增大时滞的变化范围,减小系统的H∞指标,实现对控制器的间接调节。通过仿真实例,验证了所得结论的有效性。4)将连续时滞系统稳定控制研究中采用的技术合理应用于离散系统,研究了一类不确定离散复合时滞系统的鲁棒控制。通过引入前向差分变量y(k)对系统做变换,并借助积分与求和的关系,构造了一类充分利用时滞信息的新型的带调节参数的离散型L-K泛函,以LMI的形式,给出了全新的带调节参数的时滞相关型鲁棒镇定的充分条件及鲁棒状态反馈控制器的形式。在保证闭环稳定的基础上,可通过改变调节参数的值实现了对控制器的间接调节。所得结论通过仿真实例,验证了有效性。更多还原

【Abstract】 As the focus of control theory, the stability analysis and synthesis of nonlinear time-delay system have long been attached much importance. In recent years, T-S fuzzy model method for its own local linear approximation characteristics that have become an important method to study nonlinear time-delay system.Through the establishment of the T-S fuzzy model of the system, combined with the L function method and linear matrix inequalities technology, this article study the stability, robust fuzzy control and H∞performance of nonlinear time-delay systems, the main content and the results are embodied in the following aspects:1) From the perspective of practical application, this article sets time-varying delay the lower bound are not strictly zero, and study a class of interval time-varying delay system with nonlinear perturbation. By constructing a new kind of L-K functional with adjustable parameter, a new delay-dependent stability criteria with adjustable parameters are proposed via LMI approach. Some numerical examples have shown that the obtained results are less conservative.2) A combination of descriptor model transformation approach and Moon s inequality technique which is effective method to deal with the linear time-varying delay systems are extended to the T-S fuzzy time-varying delay systems,and study for a kind of uncertain continuous composite robust control of time-delay systems. Based on improved L-K functional with adjustable parameters, in the form of LMI, some new containing adjustable parameter of delay-dependent sufficient conditions for the robust stabilization are given, and the robust state-feedback controller is designed. On the basis of the closed-loop systems stable, the range of the time-delay can be widened and the indirect regulation on the controller can be realized by changing adjustable parameters. Through simulation examples, the effectiveness of the method is verified.3) Based on the results of uncertain systems with composite time-delay, H∞robust control problem is solved for the system with a disturbance outside,via LMI approach, a new containing adjustable parameters of delay-dependent robust stabilization of H∞sufficient conditions is given, and H∞robust state-feedback controller is designed. On the basis of the closed-loop systems stable, the range of the time-delay can be widened, the system H∞performance index can be reduced and the indirect regulation on the controller can be realized by changing adjustable parameters.The simulation example verify the effectiveness of the conclusion obtained.4) The technology used in the continuous delay-system stability control reasonably is applied to the research about robust control of a class of uncertain discrete system with composite time-delay. Using the forward difference function y(k) of the system to do the transformation, and with the help of integral and summation relationship,constructing a kind of new discrete L functional with adjustable parameters, that fully contains delay informations,in the form of LMI, some new containing adjustable parameter of delay-dependent sufficient conditions for the robust stabilization are given, and the robust state-feedback controller is designed.On the basis of the closed-loop systems stable, the indirect regulation on the controller can be realized by changing adjustable parameters. Through simulation examples, the effectiveness of the method is verified.更多还原