Choosing a system to control

I have to do a multi-part project for my Linear Control Systems course, and to do that, I need to choose a system (a third order one
or higher). I have no idea what to choose. Can anyone suggest a source to find such system? Any sort of system (mechanical, electrical, etc.) would do as long as I can find its differential equations.
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How about a linearized version of a servo controlled hydraulic actuator. K/(s*(s^2+2*æ*ù*s+ ù^2)) 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: http://www.engin.umich.edu/group/ctm/examples/motor2/PID2.html 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.
Peter Nachtwey
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pnachtwey wrote:

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.
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Tim Wescott
Wescott Design Services
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Hmmm, all the text books I see are like that. I haven't seen one start with; 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.
Peter Nachtwey
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pnachtwey wrote:

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 course.
(So, Homayoon -- make a career of this and you won't get stale!).
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Tim Wescott
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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.
Homayoon.
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Homayoon wrote:

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 resonance.
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Tim Wescott
Wescott Design Services
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Homayoon wrote:

Are you doing to do it in hardware or on paper?
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On Apr 25, 4:38 am, Freelance Embedded Systems Engineer

On paper, or more probably on computer.
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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.
Peter Nachtwey
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wrote:

On paper, or more probably on computer.
This may be old-fashioned (I certainly am) but you'll learn a lot of valuable stuff if you build a real thing and try to control it.
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