(Solved): Exercise 2: Use Octave to plot the System's Root Locus. Using the Octave command rlocus(G,increment ...

Exercise 2: Use Octave to plot the System's Root Locus. Using the Octave command rlocus(G,increment, Kmin,Kmax) plot the following root-loci for $\mathrm{K}=0$ to 30 increment of 0.1 1. Examples $\mathrm{RD}=1$ a) $\mathrm{G}(\mathrm{s})=\frac{3}{s?1}$, b) $G(s)=\frac{s+3}{(s?1)(s+2)}$ c) $G(s)=\frac{(s+3)(s+1)}{(s?1){\left(s^2+4\right)}^{?}}$ 2. Examples $\mathrm{RD}=2$ a) $\mathrm{G}(\mathrm{s})=\frac{3}{(s+1)(s+2{)}^{?}}$, b) $G(s)=\frac{(s+3)}{(s+1){\left(s^2+2s+4\right)}^{?}}$ c) $\mathrm{G}(\mathrm{s})=\frac{(s+3)(s+1)}{s(s+1)\left(s^2+2s+4\right)}$ Exercise 3: Controller Design for a system with $\mathrm{RD}=3$. Design a control law C(s) for the following system and calculate the Zeigler-Nichols ultimate gain of the system: $G(s)=\frac{2}{(s+1)\left(s^2+s+8\right)}$