I have a plant, Gp = 100/s(1+s/100)^2

I need to compensate this plant using lag compensation to give a phase margin of 45 and a Kv 0...
So I know that my compensator will be of form:

Gc = Kc(1+s/b)/(1+s/a).

I know Kc = 2.

Now, I made some assumptions:

a < b < c < 100, where c = crossover frequency in rad/s and a, b are respective frequencies at which the lag compensator comes into affect. I solve a system of 3 equations from:

|GcGp|= 1 @ c

phase GcGp @c = -3pi/4 (using Taylor series arctan approximations)

and

d/dw[phase] @ c = 0.

Solving the 3 equations, I came up with nonsense results-- ie values for a,b, and c that violated the assumed relationships between a,b,c,100. So, I know the assumption is wrong--but I do not understand how one knows what the 'right' assumption is regarding the lag compensation parameters and the cross over frequency and the double pole at 100.

Yes, this is a homework -- and I'm not looking for a direct answer--but rather a hint in knowing--or rather how to know what the relationships of a,b, c and 100 are? Or can this only be done by trial and error? Tim Wescott has been quite helpful in the past with giving me clues--and hoping he or someone else here will again. My thanks in advance to any/all.

My next best guess is a < c < b < 100-- but I REALLY don't want to solve 3 more nasty simultaneuos equations again only to discover the assumption is bad. How do you determine a 'best' assumption? My original assumption was modeled after an in class example the teacher worked.

Thanks,

Bo

I need to compensate this plant using lag compensation to give a phase margin of 45 and a Kv 0...

Gc = Kc(1+s/b)/(1+s/a).

I know Kc = 2.

Now, I made some assumptions:

a < b < c < 100, where c = crossover frequency in rad/s and a, b are respective frequencies at which the lag compensator comes into affect. I solve a system of 3 equations from:

|GcGp|= 1 @ c

phase GcGp @c = -3pi/4 (using Taylor series arctan approximations)

and

d/dw[phase] @ c = 0.

Solving the 3 equations, I came up with nonsense results-- ie values for a,b, and c that violated the assumed relationships between a,b,c,100. So, I know the assumption is wrong--but I do not understand how one knows what the 'right' assumption is regarding the lag compensation parameters and the cross over frequency and the double pole at 100.

Yes, this is a homework -- and I'm not looking for a direct answer--but rather a hint in knowing--or rather how to know what the relationships of a,b, c and 100 are? Or can this only be done by trial and error? Tim Wescott has been quite helpful in the past with giving me clues--and hoping he or someone else here will again. My thanks in advance to any/all.

My next best guess is a < c < b < 100-- but I REALLY don't want to solve 3 more nasty simultaneuos equations again only to discover the assumption is bad. How do you determine a 'best' assumption? My original assumption was modeled after an in class example the teacher worked.

Thanks,

Bo