Consider the feedback control system with the following

transfer functions:

$G_p=G_d=\frac{1}{5s+1},G_m=\frac{1}{s+1},G_v=\frac{1}{2s+1}$ and $G_c=k_c$

Show that the closed$-$loop system produces unstable responses

if controller gain $Kc$ is too large.

Tips

$$ Specify $K_c$

$$ Determined the roots of the cubic polynomial in $s($using standard root$-$finding techniques$)$

$$ Perform the partial fraction expansion.

$$ Determine the inverse Laplace transform

$$ Determine $y(t)$