(Solved): 2. Consider the root locus diagram shown below. (a) t what value of Kc does the closed loop sy ...

2. Consider the root locus diagram shown below. (a) $\Lambda \mathrm{t}$ what value of $K_c$ does the closed loop system most closely resemble a second order critically damped system? (b) When $K_c=4$, derive a second order underdamped system that approximately governs the closed loop response. (c) Find the ultimate gain of this system. (d) Tune a proportional controller using the Ziegler-Nichols tuning rules.