# Help in control systems with feedfoward

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Hi I am doing a HW assignment for my control systems and I just need some clarifications on some concepts so i can solve the problem. This is the current problem I am working on.

36) (Homework 4 Problem 2 – Feedforward Control) Consider an unstable process
G(S) = Y(S)/U(S) = 8/(s-2)
Y s G s driven by a controller C(s)=U(s)/E(s) where E(s)=R(s)-Y(s). That is
the process is stabilized by embedding it within a unity negative feedback loop. Assume
that the initial conditions of G(s) are all zero (that is, you may use a transfer function
block when simulating G(s) in Simulink).
36.1) Design a simple proportional controller C(s)=K > 0 to make the loop stable. For
instance, does K=0.5 do the job? Verify by Simulink simulation that indeed the loop is
stable. Show also a case of instability as K has an incorrect value, such as K=0.1.
36.2) Assume that in the system of 36.1 the output y(t) needs to be able to track a ramp
signal r(t) = 4t for t ≥ 0 (that is, R(s) = 2/s
2 ) with zero error (either all the time, if
possible, or at least at steady-state). Without changing the feedback loop, as designed in
36.1, add a feedforward signal rff(t) to the command r(t) in order to achieve y(t) ≈ r(t).
Find Rff(s) analytically so that Y(s)=(R(s)+Rff(s))·KG(s)/(1+KG(s))=R(s). Then find what
Rff(s) means in the time domain (that is, find the signal rff(t) and decide how to

I have done the first part correct and that part was easy but the second part I am a little confused on. I know that for the feed foward to make sure we have no error that it must be stable itself so it can have no poles in the RHP. And I know that there are two conditions for the feed foward to work. The first is that the system be stable and the second is that F(s) = inverse of the Process G(s). So with that the problem I am having is the G(S) and taking the inverse. I get F(s) = (s-2)/8 and when I do that and try to run it I dont think that it is a proper transfer function. So when that didn't work I tried to convert it back into the time domain take the inverse and then convert it back into the laplace domain and I got the transfer function F(s) = 8/(s+2) but I'm not sure if I am doing that right. once I do that I created the system function using mason formula and then solve for K when my system would be stable but I didnt get the correct answer. Any help would be appreciated. Thank you

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There's a forum on PF dedicated to homework, so, in the future, you should post your problems there instead.

With that said, it's this:
$$F(s) \frac{KG(s)}{1 + KG(s)} = 1 \Leftrightarrow F(s) = \frac{1 + KG(s)}{KG(s)}$$
you want. Not:
$$F(s) G(s) = 1 \Leftrightarrow F(s) = \frac{1}{G(s)}$$
Can you see why?