Transient analysis of sampled-data control systems

RECENTLY, studies of sampled-data control systems have been published1,2 which furnish exact and approximate expressions for the closed-loop transient response to an arbitrary external disturbance. However, the computations required are exceedingly tedious, even for the simplest type of system. Alternatively, a locus plotted in the frequency domain has been proposed by Linvill,1 to permit studies to be made of closed-loop stability (in accordance with Nyquist´s criterion). Here again the computations are tedious. It is further pointed out that the Nyquist plot obtained in this manner applies only at the sampling instants and, as such, the well-known techniques pertaining to relative stability of continuous systems do not readily apply, although absolute stability is well defined by this technique. Consequently, in most practical situations, the designer has found it expedient to resort to analogue computer studies to determine how the transient response depends upon such factors as the sampling frequency or the velocity constant of the proposed system. The purpose of this paper is to furnish a set of dimensionless curves, based upon computer studies, which are of a sufficiently generalized nature to permit approximate design criteria to be established for a wide variety of system transfer functions.