4 SAMPLED-DATA CONTROL SYSTEMS 
ical sampled-data systems is that physical plants and dynamical devices 
are basically analogue, or continuous, inform. For instance, in a control 
system, the actuator may be an electric motor which responds to a con- 
tinuous signal input and delivers a continuous output. If such a motor 
is incorporated into a sampled-data feedback control system, continuous 
signal at its input must somehow be reconstructed to obtain satisfactory 

Previous Extrapolated 
extrapolations. ih function 
ee Exact 
value 

nT 

(2+1)T 


Time 
Fia. 1.2. Data reconstruction process. 
operation. The devices which reconstruct continuous data from a 
sequence of samples or numbers are generally called data holds, extrapo- 
lators, desampling filters, or some similar descriptive name. They all 
have the same function and, from the practical viewpoint, they are made 
as simple as possible. In obtaining this physical simplicity, accuracy of 
extrapolation is often sacrificed. 
1.3 Open-loop Sampled-data Systems 
A sampled-data system is an interconnected group of dynamical 
elements in which the signal data appear at one or more points in the 
system as a sequence of numbers. Figure 1.3 shows the simplest form of 
Continuous Sampled | | | | Output 
input input Data Continuous 
reconstruction element 
Fia. 1.3. Typical open-cycle sampled-data system. 
open-cycle sampled-data system. As a result of a sampling operation, - 
the continuous input signal is converted into a sequence of numbers 
equally spaced in time by a sampling interval 7. The operation of 
sampling is shown schematically by a switch which is presumed to close 
momentarily at each sampling instant. The sequence of samples 
emerging from the switch is reconstructed into an approximation of the 
