自励振動する制御系に対する正規性白色雑音による影響

抄録

This paper is concerned with the problem of the influence of Gaussian white noise on a selfoscillating control system.
Two possible methods of analysis are applied to a nonlinear feedback control system containing a saturating element. One is the averaging method and the other is the statistical equivalent linearization method which has been used widely for nonlinear control systems with random inputs or disturbances.
The results obtained by these methods are quite different.
Namely, according to the statistical equivalent linearization method, the variance will jump and the limit cycle will cease to exist.
However, by the averaging method, neither the jump phenomenon in the variance nor the cessation of limit cycle is predicted. An analog computer simulation confirms the conclusion of the averaging method.
The difference between the two methods lies in the domain of linearization.
In the averaging method, the system is linearized around the limit cycle, but in the statistical equivalent linearization method, the system is linearized roughly in the larger domain.
Though the both are approximation techniques, the averaging method is more suitable for the analysis of this type of system.