前提匹配的T-S模糊时滞系统稳定性分析和控制器设计
发布时间：2018-09-13 13:19
【摘要】：众所周知,时滞现象广泛存在于各个工程领域当中。时滞的存在不仅是导致系统不稳定的重要因素之一,还会影响系统的性能。而且目前很多的工程领域涉及到的复杂的系统都是非线性的,所以,对非线性时滞系统稳定性的研究尤为重要,这也正是现代控制理论研究的热点问题之一。特别地,可以以任意精度逼近一个非线性系统的Takagi-Sugeno(T-S)模糊模型提出后,把专家的实践经验和线性系统的理论知识相结合,得到了研究复杂非线性时滞系统行之有效的方法;这个方法也受到了国内外学者的普遍关注。随着线性矩阵不等式(LMI)理论的提出,可以把复杂非线性时滞系统稳定性的研究转化为求解一系列线性矩阵不等式的问题,进一步推动了T-S模糊时滞系统的发展。因此,对时滞T-S系统稳定性的研究,不仅具有重要的理论意义,更具有重要的实际意义。正是基于这样的背景之下,本文选择了模糊时滞系统稳定性和控制器设计方面的研究。目前,从相关文献的研究中可以得出,主流的方法依然使用的是时域分析法:本文就是基于T-S模糊模型,建立适当的李雅普诺夫泛函(LKF),在对李氏泛函求导之后,通过积分不等式的放缩和矩阵不等式的变换,将其转化成一系列线性矩阵不等式的形式,采用求解线性矩阵不等式的方法得到时滞T-S系统稳定性的充分条件以及控制器设计的相关准则。现在已有报道的文献中,基于状态反馈的T-S模糊时滞系统稳定性的相关研究比较多,在降低保守性方面也取得了丰硕的成果;但静态输出反馈(SOF)和动态输出反馈(DOF)领域研究的文献有限,在降低保守性方面也没有特别好的处理方法;同时,也没有一套系统的方法既能够降低状态反馈的保守性,又能降低输出反馈的保守性。所以,本文重点研究了三类问题:一是定常时滞T-S系统的状态反馈和静态输出反馈的稳定性和控制器设计问题;二是具有反馈记忆的常时滞T-S系统的状态反馈和静态输出反馈的稳定性和控制器设计问题;三是时变时滞T-S系统的动态输出反馈镇定和动态输出反馈H_∞控制器设计问题。对于以上问题,本文在定理证明过程中引入了调节矩阵L,通过对L矩阵中某些参数的设定,对稳定性条件进行调节,以达到降低保守性的目的。对于状态反馈问题,在转化成线性矩阵不等式的过程中,采用了基于引理9的方法;对于输出反馈问题,在矩阵不等式变换的过程中,引入了调节参数β,通过对β值的恰当选取,得到保守性更低的稳定条件。最后,对于常时滞T-S系统稳定性的研究,本文通过具体实例得出了相关定理的结果,并与现有很多文献的结果进行了对比说明;针对一些复杂实例进行了仿真,同时描绘出了相关的闭环系统和开环系统的状态响应曲线。对于时变时滞T-S系统动态输出反馈稳定性的研究,本文则是通过具体的案例进行了仿真,得出了仿真结果的图表;同时也绘制出了闭环系统和开环系统的状态响应曲线进行比较。通过案例分析结果的对比和仿真图表的比较,得出了以下一些结论:(1)时域分析法,即基于T-S模糊模型,运用李雅普诺夫稳定判据、通过不等式放缩与变换、最终转化成一系列LMIs进行求解,是解决复杂非线性系统稳定性和控制器设计问题非常有效的方法。(2)在稳定性分析的过程中,引入调节矩阵L,设置L中合适的参数值,在某种程度上可以降低保守性;同时,这个方法也具有很好的通用性。(3)对于状态反馈的时滞T-S系统,基于引理9的处理方法可以简化获取LMIs形式稳定条件的过程,同时也能降低保守性。(4)在研究输出反馈问题(包括静态和动态)时,引入恰当的参数β,也可以有效降低保守性。
[Abstract]:As we all know, time-delay phenomenon exists widely in various engineering fields. The existence of time-delay is not only one of the important factors that lead to the instability of the system, but also affects the performance of the system. Especially, the Takagi-Sugeno (T-S) fuzzy model of a nonlinear system can be approximated with arbitrary accuracy. By combining the expert's practical experience with the theoretical knowledge of the linear system, an effective method for studying the complex nonlinear time-delay system is obtained. With the development of linear matrix inequality (LMI) theory, the stability of complex nonlinear time-delay systems can be transformed into solving a series of linear matrix inequalities, which further promotes the development of T-S fuzzy time-delay systems. Based on this background, this paper chooses to study the stability of fuzzy time-delay systems and the design of controllers. At present, from the research of related literature, it can be concluded that the mainstream method is still using the time-domain analysis method: this paper is based on T-S fuzzy. After deriving the LKF, the integral inequality is reduced and transformed into a series of linear matrix inequalities. By solving the linear matrix inequalities, the sufficient conditions for the stability of T-S systems with time-delay and the controller design are obtained. There are many studies on the stability of T-S fuzzy time-delay systems based on state feedback, and plentiful results have been achieved in reducing the conservatism. However, the research on static output feedback (SOF) and dynamic output feedback (DOF) is limited, and there is no special research on reducing the conservatism. There is no systematic method to reduce the conservatism of state feedback and output feedback. Therefore, this paper focuses on three types of problems: the stability of state feedback and static output feedback of T-S systems with time-delay and the design of controllers; and the stability of feedback and output feedback with feedback memory. Stability and controller design of state feedback and static output feedback for T-S systems with constant delays; dynamic output feedback stabilization and H_uuuuuuuuuuuuuuuuuuuuu For the state feedback problem, the method based on lemma 9 is adopted in the process of transforming it into linear matrix inequalities; for the output feedback problem, the adjustment parameter beta is introduced in the process of matrix inequality transformation, and the appropriate selection of the value beta is obtained. Finally, for the stability study of T-S systems with constant time-delay, the results of the relevant theorems are obtained through specific examples, and compared with the results of many existing literatures. For the study of dynamic output feedback stability of T-S systems with time-varying delays, the simulation results are obtained through a specific case, and the state response curves of closed-loop and open-loop systems are compared. Some conclusions are drawn as follows: (1) Time domain analysis method, which is based on T-S fuzzy model, applies Lyapunov stability criterion, transforms inequality into a series of LMIs to solve the problem. It is a very effective method to solve the stability and controller design problems of complex nonlinear systems. (2) In the process of stability analysis, Lyapunov stability criterion is used. By introducing the adjusting matrix L and setting the appropriate parameter value in L, conservatism can be reduced to a certain extent. At the same time, this method also has good generality. (3) For the state feedback T-S system with time delay, the processing method based on lemma 9 can simplify the process of obtaining the LMIs form stability conditions, and also can reduce the conservatism. (4) In the study of transmission. When the feedback problem (including static and dynamic) is introduced, the proper parameter beta can also effectively reduce the conservatism.
【学位授予单位】：西华大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP13
[Abstract]:As we all know, time-delay phenomenon exists widely in various engineering fields. The existence of time-delay is not only one of the important factors that lead to the instability of the system, but also affects the performance of the system. Especially, the Takagi-Sugeno (T-S) fuzzy model of a nonlinear system can be approximated with arbitrary accuracy. By combining the expert's practical experience with the theoretical knowledge of the linear system, an effective method for studying the complex nonlinear time-delay system is obtained. With the development of linear matrix inequality (LMI) theory, the stability of complex nonlinear time-delay systems can be transformed into solving a series of linear matrix inequalities, which further promotes the development of T-S fuzzy time-delay systems. Based on this background, this paper chooses to study the stability of fuzzy time-delay systems and the design of controllers. At present, from the research of related literature, it can be concluded that the mainstream method is still using the time-domain analysis method: this paper is based on T-S fuzzy. After deriving the LKF, the integral inequality is reduced and transformed into a series of linear matrix inequalities. By solving the linear matrix inequalities, the sufficient conditions for the stability of T-S systems with time-delay and the controller design are obtained. There are many studies on the stability of T-S fuzzy time-delay systems based on state feedback, and plentiful results have been achieved in reducing the conservatism. However, the research on static output feedback (SOF) and dynamic output feedback (DOF) is limited, and there is no special research on reducing the conservatism. There is no systematic method to reduce the conservatism of state feedback and output feedback. Therefore, this paper focuses on three types of problems: the stability of state feedback and static output feedback of T-S systems with time-delay and the design of controllers; and the stability of feedback and output feedback with feedback memory. Stability and controller design of state feedback and static output feedback for T-S systems with constant delays; dynamic output feedback stabilization and H_uuuuuuuuuuuuuuuuuuuuu For the state feedback problem, the method based on lemma 9 is adopted in the process of transforming it into linear matrix inequalities; for the output feedback problem, the adjustment parameter beta is introduced in the process of matrix inequality transformation, and the appropriate selection of the value beta is obtained. Finally, for the stability study of T-S systems with constant time-delay, the results of the relevant theorems are obtained through specific examples, and compared with the results of many existing literatures. For the study of dynamic output feedback stability of T-S systems with time-varying delays, the simulation results are obtained through a specific case, and the state response curves of closed-loop and open-loop systems are compared. Some conclusions are drawn as follows: (1) Time domain analysis method, which is based on T-S fuzzy model, applies Lyapunov stability criterion, transforms inequality into a series of LMIs to solve the problem. It is a very effective method to solve the stability and controller design problems of complex nonlinear systems. (2) In the process of stability analysis, Lyapunov stability criterion is used. By introducing the adjusting matrix L and setting the appropriate parameter value in L, conservatism can be reduced to a certain extent. At the same time, this method also has good generality. (3) For the state feedback T-S system with time delay, the processing method based on lemma 9 can simplify the process of obtaining the LMIs form stability conditions, and also can reduce the conservatism. (4) In the study of transmission. When the feedback problem (including static and dynamic) is introduced, the proper parameter beta can also effectively reduce the conservatism.
【学位授予单位】：西华大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP13
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