Time-Dependent Probability Distribution of the Non-Stationary Response of Nonlinear Control Systems

DOI DOI Web Site Web Site Web Site

Bibliographic Information

Other Title
  • 正規性定常突変不規則入力をうける非線形制御系の応答の確率分布について
  • セイキセイ テイジョウトツヘン フキソク ニュウリョク オ ウケル ヒセンケイ セイギョケイ ノ オウトウ ノ カクリツ ブンプ ニ ツイテ

Search this article

Description

To evaluate the probability density function of the response of nonlinear control systems with a stationary random input, an analytical method by means of solving the combined Fokker-Planck equation with the equation of a control system was established by the authors. If a time-invariant nonlinear control system is excited by a suddenly applied stationary random input, the response becomes a non-stationary random time series and the probability density function depends on time. Unfortunately, it is almost impossible to solve the Fokker-Planck equation in the case where the probability density function depends on time. In this paper, an approximate method is presented. The nonlinear transfer characteristic contained in the system is replaced by an equivalent linear one with piecewise linear segments, in the sense of the least square value. The form of probability density function is also replaced by the form of connected Gaussian type probability density function. Under these conceptions, a numerical calculation is carried out. Detail illustrations are shown by several examples.

Journal

Details 詳細情報について

Report a problem

Back to top