For the following models, the error signal is defined as

Chapter , Problem 10.13

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For the following models, the error signal is defined as e(t) = r(t) - c(t). Obtain the steady-state error, if any, for the given input. If it is not possible to determine the response, state the reason.

a.                          \(\frac{C(s)}{R(s)}=\frac{1}{3 s+1} \quad r(t)=6 t\)

b.                          \(\frac{C(s)}{R(s)}=\frac{5}{3 s+1} \quad r(t)=6 t\)

c.                           \(\frac{C(s)}{R(s)}=\frac{4}{3 s^2+5 s+4} \quad r(t)=12 t\)

d.                           \(\frac{C(s)}{R(s)}=\frac{10}{2 s^2+4 s+5} \quad r(t)=8 t\)

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