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Given the flexibility
of the digital computer, digital control algorithms need not
be restricted to discrete versions of analog designs. In particular,
it is possible to formulate controllers that, under ideal conditions,
will produce the desired closed loop response. This set of notes
introduces some of these digital controller design methodologies.
You will need to be familiar with sampled
data systems and the associated mathematics to be able to
follow the notes.
The schematic
of a conventional sampled data control system is shown below:
where the position of the samplers
are depicted explicitly. Since this is a standard set up, we
do not need to show the samplers. Instead, we can make use of
the following simplified block diagram
W(z),
E(z), U(z) and Y(z) are respectively, the
set-point, the error, the controller output and the controlled
output. D(z) represents the digital controller, while
the block HGp(z) refers to the z-transform
of the zero-order-hold device in series with the process being
controlled.
The zero-order-hold
has the Laplace transform
Thus 
Now, we are in a position to
start designing digital controllers.
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