Delta算子切换系统的容错控制

发布时间：2018-06-21 15:54

本文选题：容错控制 + Delta算子　；参考：《南京航空航天大学》2016年博士论文

【摘要】：切换系统是控制理论研究的一个热门的类别,有关切换系统的研究成果也颇丰富。但是,仍有许多相关的问题没有被完全解决,比如切换系统的容错控制问题。在数字控制领域,Delta算子比移位算子更优越,因此Delta算子系统的相关研究逐渐为广大学者所接受。每个模态都描述为Delta算子系统的切换系统叫做Delta算子切换系统。尽管近些年Delta算子切换系统得到了一些学者的重视,但是其控制理论还有较大的发展空间。在出现故障的实际的切换系统中,除了要求所设计控制器和切换律使得系统稳定外,还需要其他性能,比如:外部扰动对系统被调输出较小的影响、瞬态性能等。本文主要研究Delta算子切换系统的容错控制问题,主要研究内容如下:(1)针对一类具有执行器故障的不确定Delta算子切换系统,研究了保成本鲁棒H_∞可靠控制问题。分别基于任意切换和状态切换方法,设计了状态反馈控制器和切换律使得闭环切换系统具有指定的H_∞性能且给出了闭环保成本函数的一个上界。在设计过程中,出现了不确定矩阵相乘的现象,提出了针对这种现象的处理方法。(2)研究了具有执行器故障的Delta算子切换系统的非脆弱可靠(35)-镇定问题,所得的研究成果以LMI的形式给出。首先,为了确定在(35)-镇定过程中的Delta算子切换系统的每一个模态的衰减率,提出了一阶LMI区域理论。其次,针对非脆弱可靠控制问题中出现了不确定矩阵相乘的现象,提出了对应的处理方法。基于上面所提的两种方法和平均驻留时间方法,设计了状态反馈控制器和切换律,使得闭环Delta算子切换系统的每一个模态的极点均位于指定的圆盘内,且其是指数稳定的。(3)基于模态依赖平均驻留时间方法,研究了一类具有执行器故障的Delta算子切换线性系统的可靠保成本控制问题。首先,基于模态依赖平均驻留时间方法,分析了非线性Delta算子切换系统的渐近稳定性和指数稳定性准则。然后,基于该准则,设计了可靠控制器和切换律,以镇定所给定具有执行器故障的Delta算子切换系统,并且给出了闭环成本函数的一个上界。(4)解决了Delta算子切换系统的故障检测及容错控制问题。基于状态切换方法,设计了观测器/控制器和切换律,使得切换系统故障能够被检测出来且闭环切换系统具有指定的H_∞性能。(5)研究了基于动态输出反馈的具有传感器故障的Delta算子切换系统的容错控制问题,应用了两种状态切换方法,所得的结果均以LMI形式给出。首先,应用了Lyapunov-Metlzer方法。所选的Metlzer矩阵的非零元素被用于切换控制器和切换律的设计中。其次,应用了凸组合方法设计切换控制器和切换律。两种方法所设计的控制器和切换律,均能够保证闭环切换系统的渐近稳定性。在凸组合方法的应用中,出现了不确定矩阵相乘现象。针对此现象,提出了一种有效的处理方法。(6)基于状态切换方法,研究了具有执行器故障的Delta算子切换系统的具有圆盘极点约束的可靠H_∞控制问题。分别应用Lyapunov-Metlzer和凸组合方法设计了状态反馈控制器和切换律,使得闭环切换系统的每一个模态的极点均位于指定的圆盘内,且其具有指定的H_∞性能。
[Abstract]:Switching systems are a hot category in the study of control theory, and there are plenty of research achievements on switching systems. However, there are still many related problems that are not completely solved, such as the fault tolerant control problem of switched systems. In the digital control field, the Delta operator is superior to the shift operator, so the related research of the Delta operator system is run by. The switching system described as Delta operator system is called Delta operator switching system. Although the Delta operator switching system has been paid attention to by some scholars in recent years, the control theory has great development space. As the system and switching law make the system stable, other properties are needed, such as the effect of the external disturbance on the output of the system, and the transient performance. This paper mainly studies the fault tolerant control problem of the Delta operator switching system. The main research contents are as follows: (1) for a class of uncertain Delta operator switching systems with actuator failures, Based on the arbitrary switching and state switching method, the state feedback controller and the switching law are designed to make the closed loop switched system have the specified H_ infinity performance and give a upper bound of the closed environmental cost function. In the design process, the phenomenon of the uncertainty matrix multiplication is presented in the design process. The method of dealing with this phenomenon. (2) the non fragile reliable (35) - stabilization problem of the Delta operator switching system with actuator failures is studied. The results obtained are given in the form of LMI. First, in order to determine the attenuation rate of each mode of the Delta operator switching system in the (35) - stabilization process, the first order LMI region is proposed. Secondly, in view of the phenomenon that the uncertainty matrix multiplies in the non fragile reliable control problem, the corresponding processing method is proposed. Based on the two methods mentioned above and the mean standing time method, the state feedback controller and the switching law are designed, which make the poles of each mode of the closed loop Delta subunit switching system all located in the finger. In the fixed disk, and it is exponentially stable. (3) based on the modal dependent mean standing time method, the reliability guaranteed cost control problem of a class of Delta operator switched linear systems with actuator failures is studied. First, the asymptotic stability of the nonlinear Delta operator switching system is analyzed based on the modal dependent mean standing time method. Then, based on the criterion, a reliable controller and switching law are designed to stabilize the Delta operator switching system with a given actuator fault, and a upper bound of the closed loop cost function is given. (4) the problem of fault detection and fault tolerance of the Delta operator switching system is solved. Based on the state switching method, the system is set up. Considering the observer / controller and the switching law, the switching system fault can be detected and the closed loop switched system has the specified H_ infinity performance. (5) the fault tolerant control problem of the Delta operator switching system with sensor fault based on dynamic output feedback is studied. The two state switching methods are applied, and the results are all LMI First, the Lyapunov-Metlzer method is applied. The non zero element of the selected Metlzer matrix is used in the design of switching controllers and switching laws. Secondly, a convex combination method is used to design the switching controller and the switching law. The controller and the switching law designed by the two methods can ensure the asymptotic stability of the closed loop switching system. In the application of the convex combination method, there is an uncertain matrix multiplication phenomenon. An effective method is proposed for this phenomenon. (6) based on the state switching method, a reliable H_ infinity control problem with the disk pole constraint for the Delta operator switching system with actuator failures is studied. The application of Lyapunov-Metlzer and convex respectively is applied respectively. The combination method designs the state feedback controller and the switching law, making the poles of each mode in the closed loop system all located in the specified disk, and it has the specified H_ infinity performance.
【学位授予单位】：南京航空航天大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP13

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