(Solved): Use MATLAB to solve this problem. Use MATLAB to solve this problem. (a) Plot the root-locus of the s ...

Use MATLAB to solve this problem. (a) Plot the root-locus of the system: $$L(s)=\frac{K}{s(s+1)(s+a)}$$ for $$a=0,\frac{1}{2},1$$, and 2. Compare it with the root-locus of: $$L(s)=\frac{K}{s(s+1)}$$ Use the same coordinate ranges in all plots. Observe that an extra pole tends to shift the root-locus to the right, and the larger the extra pole, the greater the effect. (b) Plot the root-locus of the system: $$L(s)=\frac{K(s+b)}{s(s+1{)}^2}$$ for $$b=10,5,1$$, and $$0.5$$. Compare it with the root-locus of: $$L(s)=\frac{K}{s(s+1{)}^2}$$ Use the same coordinate ranges in all plots. Observe that an extra zero tends to shift the root-locus to the left, and the larger the extra zero, the greater the effect.