Exact analysis of a first-order relay control system with a white noise disturbance
- 21 May 1980
- journal article
- research article
- Published by Taylor & Francis in International Journal of Control
- Vol. 31 (5) , 841-867
- https://doi.org/10.1080/00207178008961087
Abstract
For a control system consisting of a first-order plant and a relay in a closed loop, and with a gaussian white noise disturbance added to the plant input, the Fokker-Planck equation is applied to find the first and second probability density functions of the plant output. Closed-form expressions are then obtained for the autocorrelations, cross-correlations, spectral densities and cross-spectral densities of all the system signals. The results may be used to test the assumptions made in approximate methods of analysis of stochastic bang-bang control systems.Keywords
This publication has 2 references indexed in Scilit:
- Analysis of nonlinear stochastic systems by means of the Fokker–Planck equation†International Journal of Control, 1969
- Analysis of a Nonlinear First-Order System with a White Noise InputJournal of Applied Physics, 1961