Quote:
Originally Posted by AustinSchuh
I've recently switched formulations to what we used this and last year, and I think the new formulation is easier to understand.
If you have an un-augmented plant dx/dt = Ax + Bu, you can augment it by adding a "voltage error state".
d[x; voltage_error]/dt = [A, B; 0, 0] x + [B; 0] u
You then design the controller to control the original Ax + Bu (u =K * (R - X), design an observer to observe the augmented X, and then use a controller which is really [K, 1].
We switched over last year because it was easier to think about the new controller. In the end, both it and Delta U controllers will do the same thing.
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Thank you for your fast reply!
Are the A and B matrices here the same as in this pdf?
https://www.chiefdelphi.com/forums/a...1&d=1419983380
Quote:
Originally Posted by AustinSchuh
Yes. It's just another way to add integral into the mix. I like it because if your model is performing correctly, you won't get any integral windup. The trick is that it lets the applied voltage diverge from the voltage that the robot appears to be moving with by observing it in the observer.
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I am a bit confused here. I integrated both sides of the equation and got:
u = constant * integral of position error + constant * integral of velocity error + constant * integral of voltage error
Isn't that a PI control + integral control of the voltage? This controller as far as I know should have integral windup. What am I missing?
Quote:
Originally Posted by AustinSchuh
I defined a cost function to minimize the error between the trajectory every cycle and a feed-forward based goal (this made the goal feasabile), and used that to define a Kff.
The equation to minimize is:
(B * U - (R(n+1) - A R(n)))^T * Q * (B * U - (R(n+1) - A R(n)))
This means that you have 3 goals running around. The un-profiled goal, the profiled goal and the R that the feed-forwards is asking you to go to. I'd recommend you read the code to see how we kept track of it all, and I'm happy to answer questions from there.
The end result was that our model defined the feed-forwards constants, so it was free We also were able to gain schedule the feed-forwards terms for free as well.
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WOW!
This is really smart!
I want to make sure I got it, Q is weight matrix and you are looking for the u vector to minimize the expression? In which way are you minimizing it? My current Idea is to set the derivative of the expression to zero and solve for u. Is that correct?
Did you get to this expression by claiming that R(n+1) = AR(n) + Bu where u is the correct feed forward?
Can you explain how did you observe the voltage?
Quote:
Originally Posted by AustinSchuh
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This looks very interesting, why did you choose this way instead of all the other available methods?
Also how does your students understand this paper? There are lot of things that needs to be known in order the understand it.
Who teaches your students all this stuff?
My team don't have any control's mentor and we are not sure if to move to model based control or not. Our main problem with it is that there are a lot of things that need to be taught and it's very hard to maintain the knowledge if we don't have any mentor that knows this. Do you have any advice?
Thank you very much!