Extra Credit. A closed-loop feedback system is shown below, where the system transfer functions

1

are,G₁ (s) = 3s + 1 and

Find the steady state error when input, R(s) =

s² (s+4)*

S²

Y(s)

* Mason's gain formula:

G₂(s) =

R(s)

Y(s)

R(S) A(S)

=

Pk= the kth forward-path gain

G₁

-ΣP, (s)A, (s)

G₂

A(s) = 1- (sum of all individual loop gains) + (sum of products of gains of all 2 loops that do not touch

each other) - (sum of products of gains of all possible three loops that do not touch each other) + ...

Ak(s) = A for part of SFG that does not touch k-th forward path.