Not process plants, no, but it's certainly common in servo applications
where the whole point of the system is to follow the command -- and
which is reflected by calling the input a command, and not a set point.
If nothing else, wouldn't you find it in servo valves (or whatever
they're called)? Perhaps it's there, masquerading under the name "feed
Control system and signal processing consulting
Example plant: With disturbance z2
1,570587 v1'' + 1,262046 v1' + v1 = v2
Damping d = 0,503517
Example 1: With derivative action
Example 2: Witout derivative action
If just using PID control there is no chance to find a better solution
without derivative action!
* http://home.arcor.de/janch/_control/20100613-derivative-action /
Under damped systems should have a derivative gain to dampen the
system response. If you want to place all the poles there needs to be
one controller gain for each pole open loop pole. The integrator gain
doesn't count because it comes with its own pole. In JCH's example
the system has two poles and they are imaginary. Therefore the system
is under damped so two gains are necessary, the P and D gains.
Not always. For example cascaded loop with an inner velocity loop and
an outer position loop. The inner velocity loop may be just a simple
PI controller because the error is in velocity units. The P gain in a
velocity loop does about the same thing as the D gain in the position
loop which uses error in position units.
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