I need help finding the gain \$K\$ so that the phase margin for the system equals 50 degrees.
$$F(s) = K$$
$$G(s) = \dfrac{1}{(s+1)^2}$$
\$v\$ is a process disturbance sinusoid with amplitude 2.5 and freq 0.5 rad/s. Image below.
Now I need to find K so that the phase margin = 50 deg. I tried:
\$\varphi_m = 180\$ deg \$+ \arg G(i\omega_c) + \arg F(i\omega_c) = 50\$ deg
and solve for \$\omega_c\$ but I can't really figure out how to. Do I have to account for the disturbance as well? If so, why? why not?