ELEC$3521$ HOMEWORK II

Due date: $\frac{14}{01}\frac{?}{2024}$

Q$1)$

In MT $2$ you are asked to plot the root locus plot of a system with characteristic equation

$s^2+s+1+Ks=0$

But to plot root locus we must reformulate the characteristic equation in the form $1+G(s)=0$ where $G(s)$ will include $K$ as a gain in the numerator.

$s^2+s+1+Ks=01+\frac{Ks}{s^2+s+1}=0$

Using MATLAB plot the root locus for

$G(s)=\frac{Ks}{s^2+s+1}$

Indicating BA$/$BI points and value of $K$ at those points of $K$ for stability, range of $K$ for an overdamped system.

Q$2)$

Using MATLAB plot the Bode Magnitude and Bode Phase plot for

$G(j)=\frac{(\frac{j}{0\mathrm{.}5}+1)}{(j{)}^2((\frac{j}{2}{)}^2+0\mathrm{.}1j+1)}$

Q$3)$

Problem B$-7-25$ from textbook.

Q$4)$

Problem B$-7-27$ from textbook.