03-03-2016, 04:50 PM
Stability of Digital Control Systems
Introduction
One of the most important requirements in the performance of control systems is stability. This is true whether the system has continuous data,, digital data, or a combination of the two kinds of signals. As in the case of continuous time signals there are methods for determining the general closed-loop behaviour.
The two methods of determining absolute stability are the Jury method and the Routh-Hurwitz criterion, the latter is essentially the same as for continuous systems. The root-locus technique is a graphical approach for determining general closed-loop behaviour without solving the system equations.
5.2 Jury’s Stability Test Consider characteristic equation:
F(z) = anzn+an_iZn_1 + ^-a^ + aQ, where an>0
Rule 1: There are n-branches corresponding to the number of open-loop poles Each
open-loop serves as a beginning and each open-loop zero, as an end of a continuous path traversed by a closed-loop poie.
Rule 2: As K becomes large (n-m) branches become asymptotic to straight lines that
intersect at z=a, and whose angle with respect to real-axis are given by,