Abstract
In this paper, sufficient conditions for the chaos in pulse-width modulated (PWM) feedback systems are investigated by using Shiraiwa-Kurata's Theorem.
The PWM has such characteristic that its output is a pulse whose width depends on an absolute value of its input at the sampling instant. Since the maximum pulse width is equal to the sampling period, the saturation of the pulse width occurs when the absolute value of the input is large. This nonlinear characteristic causes various nonlinear phenomena such as limit cycle, chaotic behavior, and so on. Baillieul et al studied the chaos in PWM feedback systems. In their paper, however, conditions for the linear elements are strict, and the relationship between the chaos and the sampling period has not been investigated. This paper makes it clear the relationship between the chaos and the sampling period. That is, it is proven that PWM feedback systems are chaotic for any sufficiently large sampling period if the linear elements have at least one unstable mode and if a certain inequality is satisfied.
