Real
Sampled Data Control Systems
Real sampled data control systems arise in the following way.
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An analog system is controlled
by a computer system.
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The computer puts out
a control signal using a D/A board
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The computer measures
the output of the system using an A/D board.
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The combination of the
D/A + System + A/D board can be represented by a system with a Z-Transform
Transfer Function. Click here
for that representation for a first order system. Click
here for a time-domain analysis of a first order system.
The net result is that you get a loop that has
only Z-Transform blocks in it. There are some things that we know
about the system and how to analyze it.
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The usual block diagram
algebra still works. The algebra is the same whether it is in the
z-domain or the s-domain.
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A closed loop transfer
function might be KG[z]/{1 + KG[z]}
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We interpret things differently.
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The stability
region is the interior of the unit circle in the z-plane.
A stable system has all of its poles inside the unit circle. In continuous
systems the stability region was the left half of the s-plane.
-
Some analysis techniquest
- like the Root Locus - will still work the same in the sense that the
same rules still apply - except for the business about the stability region.