How about a linearized version of a servo controlled hydraulic
Where K is the gain in m/s per % control output. K=0.01 would be a
good place to start.
æ is the damping factor. æ=0.2
ù is the natural frequency ù=2*ð*20hz or 125.66 rad/s
The system actually has two underdamped poles and the third is due to
integrating velocity to get position. If you need more poles then
add the response of the valve.
If you want a motor system then try this:
If you want to make it more difficult then assume the shaft twists to
the load response is springy.
I think you should also work in identifying the system so you can
calculate the gains. Controlling a system without first getting a
model of the plant requires a lot of trial and error.
I suspect that he's only assigned to do the pie-in-the-sky part, where
you assume that reality matches your first cut at a model.
Let's not disillusion him until it's too late for him to to change his
major to business administration or medieval English lit or something.
Hmmm, all the text books I see are like that. I haven't seen one
Chapter 1. System Identification.
I think the first two suggestions you made on another post are good
and will make Homayoon really understand the system. The first
problem is more of a dead time problem. The ring and the solenoid
wouldn't require near as much thought. It is too much like what I had
suggested. The main problem is that the damping factor is very low.
If I interpret what you said correctly it would be linear. We have
controlled solenoids moving masses, they just require a fast loop time
but other than that they were easy.
I should have pointed out the essential difference in the reality of the
two systems, which is that your example is one where the resonance can
be brought inside the loop (at least that's what I gather from earlier
threads on the topic), while with the resonance problems that I've dealt
with the resonance is high enough that any attempts to bring it inside
the loop eventually get tripped up by manufacturing or environmentally
induced variations -- so you have to notch it out, and the
resonance-notch system become the limiting factor on your loop bandwidth.
But explaining that gets way beyond what they teach in a linear systems
(So, Homayoon -- make a career of this and you won't get stale!).
Thank you guys; All of you. I think I'll go with one of Peter's
suggestions, because the equations are already there and I don't feel
like doing the modeling myself. Of course, I don't know anything about
hydraulic actuators or DC motors (neither much about heat transfer and
tanks) but I try to figure things out.
The first two parts of my assignment are 1. drawing an SFG and writing
the state equations, and 2. calculating the step and impulse
responses. I guess I'll be assigned controller desgin soon enough.
Again, thank you everyone.
A bar of aluminum, at least twice as long as it is thick, insulated
along its length and heated at one end. Control the temperature at the
other. No one will argue about insufficient order.
A pair of tanks, interconnected by a largish pipe at the bottom, with a
smallish uncontrolled outflow from the far-end tank and a controlled
inflow from the near-end one. Hold the level of the far-end tank
constant (don't forget to model the sloshing between the two tanks -- it
gives you two states).
A speaker-coil motor pushing on a hollow ring with a mass at the other
end of the ring. Control the position of the mass without exciting the
Tim, really did have the best suggestions because you would need to
learn how to model the plant. Once you know the trick it will take
only a few minutes to control a 3 pole system using a computer. To
make this more challenging, you should add dead time to the systems
you are trying to control. Once you learn 'the trick' you should then
apply it to many different systems and build a table with how the PID
gains should be calculated for each type of system, integrating ( type
1 ), non-integrating ( type 0 ), and one, two, three and four pole
systems. All of these would be done with dead time or without. When
simulating you should show effects of feedback resolution. You
should also calculate the gains using the ideal model but then
randomly change the model parameters change by a certain percentage.
This will give you an idea of how robust your tuning method is. If
you think about it you only need to do 8 simulations if there are
three model parameters such as a gain, damping factor and natural
frequency with the model parameters set to the minimum or maximum
extreme. This provide an idea of how the system will behave as the
load changes. etc.
Now you have a worthy project because tuning a 3 or 4 pole system is
simply too easy once you know 'the trick'. My advice is to start with
a type 0 single pole system to learn 'the trick' first. Then the rest
are just variations on the same theme.
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