328 
Digital controller, multirate (see Multi- 
rate digital controller) 
sampled-data, 3 
speed-up with multirate techniques, 
244-248 
Digitally controlled systems, effect of 
disturbances on, 192-195 
Dominant poles in sampled-data sys- 
tems, 109-110 
Double-rate sampling, 203-206 
Early feedback sampled-data systems, 
equivalent digital controller, 173— 
178 
state variable, 173 
Error-sampled feedback systems, 5-7, 
90-105 
Extrapolation, exponential, 49-50 
Gregory-Newton formula, 32 
polynomial, 31-34 
(See also Data hold) 
Extrapolator, data (see Data hold) 
polynomial, 43-49 
Porter-Stoneman, 44—49 
Fail-safe systems (see Bypass digital 
controllers) 
Feedback sampled-data systems, 5-7, 
90-105 
with digital element, 92-93 
error-sampled, 90-91 
stability of, 93-105 
(See also Sampled-data-system de- 
sign; Sampled-data systems) 
Final-value theorem, 61-63 
Finite pulse-width sampling, 14, 21-23, 
255-256 
Finite settling-time systems, 178-181 
(See also Minimal prototype response 
functions; Minimum prototype 
response functions; Ripple-free 
sampled-data systems) 
First-order data hold, 37-44, 127-129 
approximation by continuous ele- 
ment, 127-129 
SAMPLED-DATA CONTROL SYSTEMS 
First-order data hold, frequency re- 
sponse of, 38-39 
open-cycle implementation of, 43-44 
partial-velocity (see Partial-velocity 
first-order data hold) 
partial-velocity correction, 40-42 
transfer function of, 38 
Frequency response of sampled-data 
systems, 110-115 
periodicity of, 111-112 
relation to pulse transfer locus, 114— 
115 
Generating function (see z transform) 
Generating triangle for polygonal ap- 
proximation, 287-288 
Gregory-Newton extrapolation for- 
mula, 32 
Hidden oscillations in sampled-data 
systems, 93-94, 136, 199, 217-218 
Higher-order data hold (see Data hold) 
Implementation of pulse transfer func- 
tions, 75-77, 1389-148, 195-197 
of digital controllers, 195-197 
using pulsed networks, 139-1438 
Impulse modulation, 19 
Impulse sampling, 19-23 
Impulse sequence, frequency spectrum 
of, 20 
Laplace transform of, 23-26 
Infinite series, evaluation by sampling 
techniques, 308-311 
Initial-value theorem, 61-62 
Integrated-square error, minimization 
of, in sampled-data systems, 179-— 
181 
Inverse Laplace transform, approxima- 
tion by sampling techniques, 295- 
301 
table of z forms, 298 
Inversion of z transforms (see z trans- 
form) 
