Perfect Fourier Series Solution of Feedback Control System with a Piecewise-linear Element Subjected to Sinusoidal Input : An Example of Dead Zone Element

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  • 断片線形特性要素を含む閉ループ自動制御系の周期動作 : 不感帯要素の場合
  • ダンペン センケイ トクセイ ヨウソ オ フクム ヘイループ ジドウ セイギョケイ ノ シュウキ ドウサ

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Abstract

A method of obtaining generally a perfect Fourier series solution of the response of a feedback control system with a piecewise-linear element subjected to sinusoidal input is devised. The piecewise-linear characteristics treated in this paper are confined to those which are symmetrical and consist of three linear regions divided from each other by two given opposite values of input. The dead zone element, the element with saturation characteristics, and the relay-element without hysteresis are included among those with this kind of characteristics. The determination of the sought for Fourier coefficients is reduced to the solution of an infinite set of simultaneous linear equations, which can be transformed into new ones of improved convergency by means of an appropriate series transformation. As an numerical example, the results of analysis in the case of a dead zone element are given and compared with the results by means of the describing function method and those of the analog computer.

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