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

Hu Xi-heng

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Article Navigation > Applied Mathematics and Mechanics > 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.

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

Hu Xi-heng

Chongqing University, Chongqing

Received Date: 1981-12-15
Publish Date: 1982-08-15

Abstract

Abstract

A class of complex function of rational fraction type G(jω)=1+a₁jω+a₂(jω)²+…+a_m(jω)ⁿ/b₀+b₁jω+b₂jω+…+b_n(jω)ⁿ is frequently used to describe the dyna-mical properties of systems. It is however quite difficult to establish a mathematical model of this type on the basis of amplitude and phase frequency data collected from experiments conducted on the related physical system. Since the erection of mathematical model G(;o) would involve the solution of a set of nonlinear simultaneous equations and bis(i=0, 1,…,m,…,n)in. Up to now, these nonlinear equa-tiorjs have been considered to be very difficult to solve directly. In spite of the fact there are special computer programmes in certain software packages available to tackle this problem, it is by no means an easy task due to the complex procedures involved in picking up a set of initial values that should be close enough to the exact solutions. This paper proposes a simplified method of linearizing these nonlinear equations set so that direct solution is possible. The method can also be applied to systems with factors of(jω) and e^-jωra in G(jω). An illustration by a workable example is furnished at the end of this paper to show its versatility.

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References(13)

References

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