A proposed z-plane criterion to expedite transient-performance analyses

A simple and insightful performance criterion is described with reference t o the position of a pair of complex-conjugate poles in the z-plane, Introdu ced as the half-cycle decay factor, this criterion is a relative stability measure that is determined directly in the z-plane without reference to a c orresponding damping ratio in the s-plane, Use of the proposed criterion ex pedites various analysis and design procedures, and this property is illust rated. The utilization is presented with several control system application s, One example presents a time-scaling procedure as required to implement a n observer-the complex-pole pairs are mol ed in a manner that maintains the half-cycle decay factor for each complex pair at a fixed value, Other exam ples are considered in which the system model is characterized by a single pair (or single dominant pair) of complex-conjugate poles. In this situatio n specific conditions are described for which the half-cycle decay factor c an be employed in expressions to evaluate percent overshoot and settling ti me in response to a step input. Finally, it is shown that the concept can b e applied in either the z-plane or the s-plane using either discrete-time m odels or continuous models, respectively.