A Determination of the Errors in the State Vector arising from the Impulse Representation of a Finite Pulse Width Sampled-data System†

Abstract

This paper describes the practical problem of determining errors in the State vector resulting from the representation of a finite pulse width sampler by an impulse sampler in a sampled-data control system. It is shown that the response of the impulse sampling system is the limit of the response of the corresponding finite pulse width system with on associated gain factor, as the pulse width tends to zero. Conditions for the convergence of the errors in the state vector and the asymptotic equivalence of the two systems are; considered. Results show that this representation is only valid as long as the pulse width is small enough, otherwise the representation may result in appreciable errors.