Find the value of “K” to limit steady state error to 10, when input to system is {1+10t+20t2}. Here ‘t’ is the time.

G(S)H(S)=$\frac{k}{(S^2 (S+2)(S+3))}$, r(t)=1+10t+20t^2

=1+10t+40$\frac{t_2}{2}$

Input is the combination of all the three type, step of magnitude $A_1$=1, Ramp of magnitude $A_2$=10 and parabolic of magnitude $A_3$=40.

Position error $k_p$=\lim_(S\to 0)$G(S) H(S) =$\lim_(S\to 0)\frac{k}{(S^2 (S+2)(S+3))}$=$\frac{k}{0}k_p$=∞ Velocity error,$k_v$=$\lim_(S\to 0)$ S G(S) H(S)

=$\lim_(S\to 0)$ $\frac{(S.k)}{(S^2 (S+2)(S+3))}$

=$\frac{k}{0}$ …