The effect of pole and zero locations on the transient response of sampled-data systems

The effect of the location of the poles and zeros of the transfer function of a sampled-data system on the location and magnitude of the maxima and minima of transient response resulting from a step function input is studied. Theorems are given relating to the necessary conditions for the production of monotonic and non-monotonic time response expressed in terms of pole and zero locations in the z-plane. It is shown that, under certain conditions of pole and zero locations, the normalized time-sequence response may well be approximated by a single dominant time term. A method is presented of ascertaining from the pole and zero location whether these conditions exist. On the basis of dominant term approximation, the methods of synthesis applied to second-order systems can be generally extended to general systems. The results of this investigation are directly applicable to the design problems in the field of pulsed networks and sampled-data control systems.