一类线性时变系统的状态观测器设计方法
发布时间：2018-12-28 15:26
【摘要】：该论文主要研究控制领域中的线性时变系统的状态观测器设计问题,其目的在于经由状态重构解决实际工程中系统状态量由于种种原因无法完全或部分获得的问题。区别于在状态观测器理论方面已经趋于成熟的线性定常系统,线性时变系统的研究相对困难并且具有挑战性,所发表出的理论成果较少,并且更接近于实际工程,故而是近几年的研究热点。下面阐述该论文的主要研究内容。该论文的设计思路是对于原有的线性时变系统,首先对其进行线性非奇异变换以使得变换后的系统具有某种特殊形式,而后对变换后的系统进行状态观测器设计,并最终达到重构原有系统状态的设计要求。针对此思路能够得知设计工作主要划分为两个部分,即线性非奇异变换以及状态观测器设计。首先,该论文提出线性时变系统基于方块展开的状态观测器设计。线性非奇异变换后的系统中系数矩阵皆为分块形式,并且其中包含较多的零阵以及单位阵。而后对变换后的系统进行全维,降维以及Luenberger状态函数观测器设计,给出各自的动态方程,系数矩阵求解方法以及算法步骤等。其次,该论文提出线性时变系统基于行展开的状态观测器设计。线性非奇异变换矩阵由原有系统能观测性矩阵中线性无关的行经过运算得到。变换后的系统仍为分块形式,不同点在于其各个子块中均包含较多的零元。而后对变换后的系统进行全维状态观测器设计。上述基于一种设计思路,两种设计方法得到的各个状态观测器均由仿真验证其可行性以及有效性。并且针对两种设计方法该论文给出对比,从而在具体实际工程中能够加以选择。最后,该论文还对线性时变系统中闭环系统的分离原理问题进行了初步研究,得到该论文所设计出的状态观测器均符合分离原理的结论。该论文主要研究成果是对线性时变系统的状态观测器设计此研究课题在理论层面上的推进与添补。所设计出的状态观测器其优点在于可以避免求解复杂的矩阵微分方程,并且将部分运算转化到线性定常系统中。这样极大地降低与简化了计算复杂度以及计算量。故而也有其实际工程层面的意义。
[Abstract]:This paper focuses on the design of state observer for linear time-varying systems in the field of control. The purpose of this paper is to solve the problem that the system state variables can not be obtained completely or partially in practical engineering because of various reasons. Different from the linear time-invariant systems which have become mature in the theory of state observer, the study of linear time-varying systems is relatively difficult and challenging, and the published theoretical results are less and closer to the actual engineering. Therefore, it is a hot research topic in recent years. The main research contents of this paper are described below. The design idea of this paper is to design the original linear time-varying system by linear nonsingular transformation to make the transformed system have some special form, and then to design the state observer for the transformed system. Finally, the design requirements of reconstructing the original system state are achieved. According to this idea, the design work can be divided into two parts: linear nonsingular transformation and state observer design. Firstly, the design of state observer for linear time-varying systems based on block expansion is proposed. In the linear nonsingular transformation system, the coefficient matrices are all partitioned, and they contain more zero matrices and unit matrices. Then, the full dimension, reduced order and Luenberger state function observer are designed for the transformed system, and their dynamic equations, coefficient matrix solutions and algorithm steps are given. Secondly, this paper presents the design of state observer based on row expansion for linear time-varying systems. The linear nonsingular transformation matrix is derived from the linear independent rows in the observability matrix of the original system. The transformed system is still in block form, the difference is that each subblock of the system contains more zeros. Then the full-order state observer is designed for the transformed system. Based on a design idea, the feasibility and validity of each state observer obtained by the two design methods are verified by simulation. Two design methods are compared in this paper, so that they can be selected in practical projects. Finally, the separation principle of closed-loop systems in linear time-varying systems is studied preliminarily, and it is concluded that the state observers designed in this paper are in accordance with the separation principle. The main achievement of this paper is the design of state observer for linear time-varying systems. The advantage of the designed state observer is that it can avoid solving complex matrix differential equations and transform partial operations into linear time-invariant systems. This greatly reduces and simplifies the computational complexity and computational complexity. Therefore, it also has its practical engineering significance.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP13
本文编号：2394124
[Abstract]:This paper focuses on the design of state observer for linear time-varying systems in the field of control. The purpose of this paper is to solve the problem that the system state variables can not be obtained completely or partially in practical engineering because of various reasons. Different from the linear time-invariant systems which have become mature in the theory of state observer, the study of linear time-varying systems is relatively difficult and challenging, and the published theoretical results are less and closer to the actual engineering. Therefore, it is a hot research topic in recent years. The main research contents of this paper are described below. The design idea of this paper is to design the original linear time-varying system by linear nonsingular transformation to make the transformed system have some special form, and then to design the state observer for the transformed system. Finally, the design requirements of reconstructing the original system state are achieved. According to this idea, the design work can be divided into two parts: linear nonsingular transformation and state observer design. Firstly, the design of state observer for linear time-varying systems based on block expansion is proposed. In the linear nonsingular transformation system, the coefficient matrices are all partitioned, and they contain more zero matrices and unit matrices. Then, the full dimension, reduced order and Luenberger state function observer are designed for the transformed system, and their dynamic equations, coefficient matrix solutions and algorithm steps are given. Secondly, this paper presents the design of state observer based on row expansion for linear time-varying systems. The linear nonsingular transformation matrix is derived from the linear independent rows in the observability matrix of the original system. The transformed system is still in block form, the difference is that each subblock of the system contains more zeros. Then the full-order state observer is designed for the transformed system. Based on a design idea, the feasibility and validity of each state observer obtained by the two design methods are verified by simulation. Two design methods are compared in this paper, so that they can be selected in practical projects. Finally, the separation principle of closed-loop systems in linear time-varying systems is studied preliminarily, and it is concluded that the state observers designed in this paper are in accordance with the separation principle. The main achievement of this paper is the design of state observer for linear time-varying systems. The advantage of the designed state observer is that it can avoid solving complex matrix differential equations and transform partial operations into linear time-invariant systems. This greatly reduces and simplifies the computational complexity and computational complexity. Therefore, it also has its practical engineering significance.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP13
【参考文献】
相关期刊论文 前1条
1 段广仁,吴爱国;广义线性系统的干扰解耦观测器设计[J];控制理论与应用;2005年01期
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