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jtucker
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Homework Statement
1. The first part of the problem was to find a transfer function. Output is the displacement of the mass (mass of pinion is negligible)
2.The next thing to do was find the poles, which I believe means set the denominator=0 and solve for s.
3. The next thing to do was find the damping ratio (z) and natural frequency (Wn)
4. Here is where I am stuck:
Determine values of k and b such that the following are met:
m=0.1kg
r=0.01m
600msec<=rise time (tr)<=800msec
and %OS <= 10%
Homework Equations
The transfer function I came up with:
1. G(s)=(1/mr)/(s^2+b/m*s+k/m)
Poles I found:
2. Poles=(-b/m +- sqrt((b/m)^2-4(k/m)))/2
3. z and Wn I found:
z=b/(m*2*sqrt(k/m))
Wn =sqrt(k/m)
The Attempt at a Solution
4. To attempt to find values I used:
Tr~1.8/Wn
substituting into rise time equation (4) above I came up with
0.50625<=k<=0.9
I also concluded that z must be >= 0.6 for the overshoot condition.
and solving (2) for b I have
b>=0.12 *sqrt(k/m)
I have tried rearranging these equations every way I can think of to come up with a solution. I have also tried making graphs by hand and using Matlab (though I'm not great with Matlab). The thing I am running into is that there seems to be any number of solutions that will work, but I am assuming that I am wrong and that there should only be one valid solution.
Any help will be greatly appreciated, I've spent many hours trying to figure this out!
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