(Solved): 4) Consider a unity negative feedback control system. The forward path is a cascade of a PD contro ...

4) Consider a unity negative feedback control system. The forward path is a cascade of a PD controller $$C(s)=K_P+K_{D}s$$ and a plant (or process) $$G(s)=\frac{10}{s^2+10}$$. i) Recast the system's characteristic equation in the Evans form $$1+KL(s)=0$$. Assume $$K=K_D$$ and $$K_P/K_D=6$$, hence determine $$L(s)$$. ii) Make hand sketch of the corresponding root locus for $$0?K<?$$ then use Matlab to generate an accurate root locus plot. iii) On your Matlab plot, also plot the admissible pole locations of designs that meet the specifications: $$5\%$$ settling time $$?1\mathrm{s}$$ and overshoot $$?5\%$$. iv) Use the Matlab function 'rlocfind' to determine $$K=K_D$$ required for the system to satisfy these specs. State the corresponding pole closed-loop pole locations. v) Use the Matlab function 'step' to plot the corresponding closed-loop system unit step response. Call the Matlab function 'stepinfo' to check if the specs have actually been met (type 'help stepinfo' to learn more about the output generated by this function).