Problem 4. At Mach 0.6, an experimental aircraft has the unstable phugoid eigenvalues 0.04 0.12 and stable short period eigenvalues -4.3 5.7). Wind tunnel testing reveals that the elevator-to-pitch transfer function has one zero located at -0.2. Assume that a proportional feedback control (KP) is used to control the pitch. (a) Sketch (by hand) the root locus by determining the center, asymptotes, and departure angles. Check your sketch using Matlab's root locus command. (You do not have to include the Matlab code and plots.) (b) Using your root locus sketch, discuss the relationship between the values of the proportional gain Kp and the stability of the closed-loop.