异步多率采样系统的H_∞控制

发布时间：2018-02-22 04:26

本文关键词： 异步多率采样系统提升技术 H_∞稳定性混杂系统网络控制系统时滞 LMI 离散重叠大系统分散控制　出处：《浙江大学》2017年博士论文　论文类型：学位论文

【摘要】：随着计算机和网络技术的不断发展,以多率采样为基础的数字网络控制系统发挥着越来越重要的作用,可以大大拓宽被控对象的时间和空间,实现控制的经济性、快速性和有效性。但是,由于控制设备的增加、控制策略的转变,也给多率采样系统的发展带来了极大的挑战,对采用网络控制所引起的新问题,亟需推广和改善现有的控制理论和方法,需要寻求更加严谨有效的解决方案。本论文在提升技术的使用策略和对象方面进行了完善和推广;对网络控制系统中产生的时滞,以及网络控制系统的随机性提出了更为严谨有效的分析和处理方法;最后从整体出发,对具有纵向拓扑结构的多率采样大系统如何实现结构限制下的分散控制进行了初步研究。本文的主要研究成果包括以下几个方面:1、针对线性异步多率采样系统,提出一个新的、更符合实际意义的异步采样系统的定义。然后对于这样的异步系统,采用平衡提升策略对其进行提升,即仅对不同频率的外部信号进行了提升,而对内部信号没有进行提升,从而避免产生因果约束以及系统维数的剧增,并将连续系统提升为具有快输入—慢输出特性的异步离散系统。然后设计此异步离散系统的基于状态观测器的异步H∞状态反馈控制器,可以证明此控制器亦可使原闭环系统镇定,并满足同样的H∞性能指标。所得到的稳定性条件是近似线性的,控制器参数可通过使用Matlab的LMI工具箱迭代求解。2、对于带有输入—输出时滞的异步系统的镇定问题,把连续时间系统的提升技术推广到带有多时滞的混杂系统,并给出能真正计算出等价离散系统算子矩阵的计算公式。不同于现有的辛对理论或状态扩维方法,通过构造一个Lyapunov-Krasovskii泛函,在时域内对所得的等价离散提升系统进行稳定性分析和静、动态输出反馈控制器设计,得到的稳定性条件是时滞相关的,并且在形式上接近线性不等式。可以证明,此控制器也可使原连续系统稳定,并满足同样的H∞性能指标。如果系统的采样和保持是周期的,提出多率异步系统扩维周期选择的规则,按照此规则扩维所得到的系统的维数远低于传统的扩维方法。之前得到的非周期系统两种反馈下的稳定性条件也相应地推广到扩维系统。3、对于带有Markov时滞的随机异步离散(DT)网络控制系统(NCSs),把随机采样和保持引入系统分析中,同时考虑采样器到控制器(S-C)以及控制器到执行器(C-A)的网络诱发时滞。这两个相互独立的时滞分别为两条不同的Markov链,但是,C-A前一时刻的时滞是通过S-C过程传递到控制器的。对于这样的复杂问题,基于一个更为严格的矩阵不等式,选择了一个恰当的Lyapunov-Krasovskii泛函进行系统稳定性分析和H∞控制器设计,得到时滞相关随机稳定条件。与现有文献相比,所得稳定性条件中的待定参数较少,维数较低,因此具有较小的保守性。通过矩阵松弛方法,可进一步将条件转化为线性矩阵不等式(LMI)。4、对于离散大型重叠系统的分散H∞控制问题,首先,基于包含原理,利用纵向拓扑结构变换矩阵对离散大型重叠系统进行扩维变换,从而实现了系统纵向分解;然后,构造了一个两部分状态反馈控制器,对没有完全分解的摄动部分进行了控制,对已分解的部分,设计基于状态观测器的H∞分散控制器;若系统分解过程满足收缩条件,则压缩转换后的控制器可使原系统稳定。此方法可推广到带有某些不确定项的离散重叠系统。
[Abstract]:With the development of computer and network technology, the multi rate digital sampling based network control system plays an increasingly important role, can greatly expand the object of time and space, to achieve economic control, rapid and effective. However, due to the increase of control equipment, control strategy transformation it has brought great challenges to the development of multi rate sampling system, new problems caused by the network control, control theory and methods to promote and improve the existing, need to seek the solution more effective. In this paper, using the method and object to enhance the technical aspects of the improvement and extension of network control; time delay system is generated, random and networked control system is proposed according to the analysis and processing method of effective; finally, starting from the whole, the multi rate with longitudinal topology How to realize the sampling system decentralized control structure constraints is studied. The main research results of this paper include the following aspects: 1, according to the linear asynchronous multi rate sampling system, put forward a new, more in line with the actual meaning of the definition of asynchronous sampling system. Then the asynchronous system that uses the balanced promotion strategy the promotion is only for external signals of different frequency were improved, and the internal signal of no improvement, so as to avoid causal constraints and increase the dimension of the systems, and the continuous system with fast slow to enhance the input output characteristics of asynchronous discrete systems. Based on asynchronous H via state feedback controller state observer then the design of asynchronous discrete system, it is proved that the controller can make the closed-loop system is asymptotically stable and satisfies the original, H 2 performance also obtained stable. The condition of the linear approximation, the controller parameters by using the toolbox of LMI iterative method for solving the.2 using Matlab, for the stabilization problem of asynchronous systems with input and output delays, the continuous time system technique is extended to hybrid systems with multiple time delays, and give can really calculate the calculation formula of equivalent discrete system operator matrix. Different from the existing theory of symplectic or state augmentation method, by constructing a Lyapunov-Krasovskii function in the time domain discrete lifting system equivalent to the stability analysis and design of static and dynamic output feedback controller, the stability condition is delay dependent, and close to linear inequality in form. This can be proved. The controller can make the continuous system stable, and meet the H 2 performance the same. If the system is periodic sampling and holding, proposed the multi rate asynchronous The system dimension expansion cycle selection rules, this rule system according to dimension dimension expansion are far lower than traditional methods. The augmented stability conditions of two kinds of feedback under non periodic systems obtained before the corresponding extension for.3 dimensional systems, discrete random asynchronous Markov with time delay network control system (DT) (NCSs), the random sampling and keep the introduction of system analysis, considering the sampler to the controller (S-C) and controller to actuator (C-A) of the network induced delay. The two independent delay were two different Markov chains, but the delay time C-A is transmitted to the controller through the front S-C process. For this complicated problem, based on a more strict matrix inequality, choose an appropriate Lyapunov-Krasovskii function for system stability analysis and controller design of H, get the delay dependent The stochastic stability condition. Compared with the existing literature, the stability condition of unknown parameters in small, low dimension, so it is less conservative. The matrix relaxation method, conditions may be further transformed into linear matrix inequalities (LMI).4, the discrete large overlap system decentralized H control problem, first of all, based on the inclusion principle the expansion of discrete Fourier transform, large overlap system using longitudinal topology transformation matrix, so the system realizes vertical decomposition; then, to construct a two part state feedback controller for not completely decomposition of the perturbation of control, has been part of the decomposition, design of robust H observer based decentralized controller if the system satisfies the decomposition process; the contraction condition, the controller can make the compression conversion of the original system stability. This method can be extended to some uncertain discrete system with overlapping items.

【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TP273

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