(Solved): 5.9 Put the characteristic equation of the system shown in Fig. 5.51 [ [n root-locus form with resp ...

5.9 Put the characteristic equation of the system shown in Fig. 5.51 [ [n root-locus form with respect to the parameter \( \alpha \), and identify the corresponding \( L(s), a(s) \), and \( b(s) \). Sketch the root locus with respect to the parameter \( \alpha \), estimate the closed-loop pole locations, and sketch the corresponding step responses when \( \alpha=0,0.5 \), and 2 . Use Matlab to check the accuracy of your approximate step responses. 3) FPE 5.9. Sketch the root locus by hand first and mark the closed-loop system pole locations for the given alphas; use Matlab to check your answer. Calculate and sketch the unit step responses for the tree given alphas using Matlab only and plot the results in a single figure for easy comparison. Is the step response behavior as expected for the pole locations? Explain.