区间观测器及其控制系统研究

发布时间：2019-04-10 10:26

【摘要】：近几十年来,观测器设计及其控制系统研究逐步成为了控制理论界的重要研究课题之一,并且在许多方面得到广泛的应用,如系统监控、过程辨识及故障检测等。然而,实际系统模型的完整信息不可获取,且存在外部干扰或噪声使得测量值不可靠,通过考虑用适当的区间来替代单一的测量值,相关学者提出了观测器设计新方法-区间观测器。不同于经典状态观测器设计要求观测器误差动态系统收敛到零,区间观测器只须设计观测器增益使得误差动态系统为非负的,且仅须设计误差动态系统矩阵为Metzler矩阵就可保证非负性。鉴于区间观测器设计具有重要的理论研究意义和实际应用价值,本文对其进行了深入的研究。本文主要的研究工作如下:1.针对一类线性连续系统,设计了Luenberger型区间观测器,该方法的特点是,先对线性系统进行初等变换得到系统的正实现,再对正系统设计Luenberger型区间观测器,其设计思路保证了观测器增益矩阵的存在性。与已有的区间观测器研究方法不同的是,本文还尝试利用正系统的比较原理针对线性离散系统设计了一类区间观测器,该设计方法有效地解决了观测器增益矩阵的存在性问题。2.鉴于已有的研究成果,在设计区间观测器过程中要求观测器误差动态系统矩阵为Metzler矩阵,从而成功设计区间观测器依赖于观测器增益矩阵的存在性。为此,本文首次以线性矩阵不等式的形式描述了Metzler矩阵,得到了区间观测器增益矩阵存在性判定条件,并通过对非线性系统的L2增益性能问题的讨论表明该方法的保守性更小。3.研究了线性参数变化系统的区间观测器设计问题,首先设计了时变区间观测器系统及系统增益调度控制器;其次,基于多胞LPV模型的线性参数变化系统结构特征,给出了有限个以线性矩阵不等式表述的镇定性条件。相比较于已有的研究成果针对仿射LPV模型的线性参数变化系统设计区间观测器,须给定满足Metzler矩阵的观测器增益矩阵,而本文所提出的方法可以同时进行设计观测器增益和增益调度控制器。最后,仿真数列表明本文所提方法的正确性和有效性。4.讨论了非线性切换系统的区间观测器设计问题,基于平均驻留时间控制策略,提出了一种新的非线性切换系统状态估计方法,同时基于区间观测器设计解决了非线性项满足Lipschitz条件的非线性切换系统的切换控制器设计问题。
[Abstract]:In recent decades, observer design and control system research has gradually become one of the important research topics in the field of control theory, and has been widely used in many fields, such as system monitoring, process identification and fault detection. However, the complete information of the actual system model is not available, and there is external interference or noise that makes the measurement unreliable. By considering the appropriate interval to replace the single measurement value, A new observer design method, interval observer, is proposed by relevant scholars. Unlike the classical state observer design, which requires the observer error dynamic system to converge to zero, the interval observer only needs to design the observer gain so that the error dynamic system is non-negative. The nonnegativity can be guaranteed only by designing the error dynamic system matrix as Metzler matrix. In view of the important theoretical significance and practical application value of interval observer design, this paper has carried on the in-depth research to it. The main research work of this paper is as follows: 1. A Luenberger type interval observer is designed for a class of linear continuous systems. The characteristic of this method is that the linear system is first transformed to obtain the positive realization of the system, and then the Luenberger type interval observer is designed for the positive system. The design method guarantees the existence of observer gain matrix. Different from the existing methods of interval observer research, this paper also attempts to design a class of interval observers for linear discrete-time systems by using the comparison principle of positive systems. The design method effectively solves the existence problem of observer gain matrix. 2. In view of the existing research results, the dynamic system matrix of observer error is required to be Metzler matrix in the process of designing interval observer, so the successful design of interval observer depends on the existence of observer gain matrix. In this paper, for the first time, the Metzler matrix is described in the form of linear matrix inequality (LMI), and the existence condition of the gain matrix of the interval observer is obtained. By discussing the L2 gain performance of nonlinear systems, it is shown that the conservatism of the proposed method is less conservative. 3. The problem of interval observer design for linear parameter-varying systems is studied. Firstly, the time-varying interval observer system and the gain scheduling controller of the system are designed. Secondly, based on the structural characteristics of the linear parameter-varying system of the multi-cell LPV model, a finite number of stability conditions expressed by linear matrix inequalities (LMIs) are given. Compared with the previous research results, to design interval observers for linear parameter-varying systems of affine LPV model, the observer gain matrix satisfying Metzler matrix must be given. The proposed method can be used to design observer gain and gain scheduling controller at the same time. Finally, the simulation sequence shows the correctness and effectiveness of the proposed method. 4. The problem of interval observer design for nonlinear switched systems is discussed. Based on the average resident time control strategy, a new state estimation method for nonlinear switched systems is proposed. At the same time, the problem of switching controller design for nonlinear switched systems with nonlinear terms satisfying Lipschitz condition is solved based on interval observer design.
【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP13

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