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 : 続報, 要素特性の一般化と数学的基礎付け

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  • Perfect Fourier Series Solution of Feedback Control System with a Piecewise-linear Element Subjected to Sinusoidal Input : 2nd Report, Generalization and Mathematical Foundation
  • 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 ゾク

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In the foregoing reports, the author analysed exactly the periodic response to a sinusoidal input of the single-loop automatic control system including a piecewise-linear element of certain kind by means of new method utilizing the perfect Fourier series. In this report, however, the characteristics of the piecewise-linear element to be treated are generalized to such point that they are composed of two unsymmetrical or three symmetrical regions and their switching over conditions contain both hysteresis and jump. At the same time, the expression for the resulting output is changed from that referred to the cosine part of the fundamental harmonic to that referred to the fundamental harmonic itself, so that the relation to the describing function method is made much clearer. Lastly, the existence of the solution of the infinite set of simultaneous linear equations utilized in the way of the solving procedure and the convergency of the approximate solution by curtailment are both discussed to solidify the mathematical basis of our method.

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