A determine the minimum value of the gain k when gcs k so

Question

The heading control of the traditional bi-wing aircraft, shown in Figure DP10.2 (a), is represented by the block diagram of Figure DP 10.2(b).

(a) Determine the minimum value of the gain K when G_c(s) = K, so that the steady-state effect of a unit step disturbance T_d(s) = 1/sis less than or equal to 5% of the unit step (y(∞) = 0.05).

(b) Determine whether the system using the gain of part (a) is stable.

(c) Design a compensator using one stage of lead compensation, so that the phase margin is 30°.

(d) Design a two-stage lead compensator so that the phase margin is 55°.

(e) Compare the bandwidth of the systems of parts (c) and (d).

(f) Plot the step response y(t) for the systems of parts (c) and (d) and compare percent overshoot settling time (with a 2% criterion), and peak time.