## 留言板

 引用本文: 胡锡恒. 一类含幅、相等式的非线性方程组的线性化及其应用[J]. 应用数学和力学, 1982, 3(4): 519-527.
Hu Xi-heng. The Linearization of Certain Class of Nonlinear Simultaneous Equation Set Containing Amplitude and Phase Frequency Characteristics and Application[J]. Applied Mathematics and Mechanics, 1982, 3(4): 519-527.
 Citation: Hu Xi-heng. The Linearization of Certain Class of Nonlinear Simultaneous Equation Set Containing Amplitude and Phase Frequency Characteristics and Application[J]. Applied Mathematics and Mechanics, 1982, 3(4): 519-527.

## The Linearization of Certain Class of Nonlinear Simultaneous Equation Set Containing Amplitude and Phase Frequency Characteristics and Application

• 摘要: 一类有理分式复函数G(jω)=1+a1jω+a2(jω)2+…+am(jω)n/b0+b1jω+b2jω+…+bn(jω)n常被用来描述系统的性能.当其有关的幅值(模)和相角(幅角)的数据能获取时,可以对G(jω)进行综合.诸未知系数ai及bi(i=0,1,…,m,…,n)将通过解一类含幅、相等式的非线性代数方程组i i=1,2,…,r.确解的初值[9].本文通过简单的数学处理,将这类非线性方程组完全线性化为同维的线性方程组,从而得以直接解.此法还可以推广到分母含纯(jω)因子和e-jωi0因子的系统.文章最后通过例子简介了这种方法在控制工程领域的应用.
•  [1] Omega,J.M.and Rheirboldt,W.C,,Iterative Solution of Nonlinear Equations in Several Trariables,Academic Press,New York(1970). [2] 王德人,《非线性方程组解法与最优化方法》,人民教育出版社,(1979). [3] 冯康等,《数值计算方法》,国防工业出版社(1978),359-366,379-389. [4] Broyden,C,G,,Dennis,J.E,and More,J,J.,On the local superlinear convergence of Ouasi-Newton methods,J.Inst.Maths,Applies.,12,13(1973). [5] Fielding,K,Algorithm 387,Function minimization and linear search,CACM,13(1970),509-510. [6] 张启人,大系统模型降阶理论,信息与控制,9,4(1980).2-25. [7] Bosley,M,7,and Lees,F.P.,A survey of simple transfer-function derivations from high order state-variable models,Automatics,g(1972),765-775. [8] 周其鉴,李祖枢,数学模型简化及其在工程系统中的应用,重庆大学学报,4(1980). [9] Shieh,L.S,,Datta-Barua,M,and Yates,R,E,,A method for modelling transfer [10] function using dominant frequency-response data and its applications,Int.J.Systems [11] Sci,10.10(1979).1097-1114. [12] Marshall,S.A,,The design of reduced-order syste m,Int,J.Control,,31,4(1980).677-690. [13] 松原正一,等価むな时间につへこ,计测と制御,3.6(1964).440-446.

##### 计量
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##### 出版历程
• 收稿日期:  1981-12-15
• 刊出日期:  1982-08-15

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