复杂线性系统建模求解的矩阵方法.pdfVIP

复杂线性系统建模求解的矩阵方法 ——论信控类主流课程中建模现代化 西安电子科技大学（710071 ）陈怀琛 屈胜利 陈的电子邮址：hchchen1934@163.com , 电话：029 屈的电子邮址：slqu@ , 电话：029 摘要：“根据各组成部分的特性求出系统特性”是贯穿在信控类专业许多主流课程中的核 心内容。在电路中是网络阻抗的计算；在信号与系统课程中是对信号流图的分析；在数字信号 处理中是对滤波器结构和特性的讨论；在自动控制课程中则是对复杂系统结构图简化方法的研 究；…等等。讲解这个内容和实际计算在各门课程中都是难点，而学生并未学到前后一致而通 用的方法。本文导出了具有普遍意义矩阵建模公式，可以藉计算机的帮助，快速准确地解决这 个问题。比起各课程中原有的方法，都有很大的优越性。 关键词：信号流图，梅森公式，矩阵建模，线性系统，MATLAB ，信号处理，数字滤波 器，网络结构图，系统结构图，传递函数，系统函数，零极增益，状态空间， Modeling and Solution of Complex Linear Systems using Matrices —On the modernization of modeling in the main courses of information and control area Chen, Huaichen, Qu, Shengli Xidian University, Xi’an, 710071 P.R.China Abstract “find out the system attribute according to the attributes of the parts organizing the system” is always a very important topic in many main information and control courses. In Circuit course it is the calculation of inpedence of complex networks. In Signal and System Course it is the analysis of Signal Flow graph. In Signal Processing Course it is the discussion of complex filter structure with its system function. In Automatic Control Course it is the reduction of structure diagram of complex systems. The theory and calculation are always one of the most difficult points in these courses. But after spending a lot of time, students do not get a general and unified method after learning all these courses. In this paper, A general model for these linear systems using matrices is deduced. According to this model, with the aid of computing software, this problem can be solved very quickly and precisely. It is much superior to all the other methods given in the previous courses. Keywords: signal flow graph, Mason’s formula, matrices modeling, linear systems, MATLAB, signal processing, digital filters, n