The block diagram of a typical feedback control system was presented in Figur and redrawn Figure:                            Use the transfer functions given in Section 4.4.5 and the baseline...

The block diagram of a typical feedback control system was presented in Figur and redrawn Figure:

Use the transfer functions given in Section 4.4.5 and the baseline parameter values unless stated otherwise.

a.       Find the magnitude and phase of each component G_C(s), G_A(s), G_P(s), and G_T(s) at the open-loop system phase crossover frequency ω₀=0.9936 rad/s. Compare the results to the magnitude and phase of the open-loop transfer function G_OL(s)=G_C(s)G_A(s)G_P(s)G_T(s) at the same frequency.

b.      Input to the open-loop system (feedback path broken at summer) is r(t)=sin ω₀t. Generate graphs of e(t)=r(t), along with u_C(t), u_A(t), y(t), and u_T(t). Comment on the stability of the closed-loop system.

c.       Graph the step response of the closed-loop system.

d.      Repeat parts (a), (b), and (c) using K_C=(K_C)_max=2.62.