4. (10%) A control law is to be designed for the system in Problem 3 by using the ITAE criterion. Different parameters of w, in the ITAE criterion are considered here. (1) Choose wn such that the DC gain is equal to 1. M u(t) Figure 4: An inverted pendulum system. (i) Choose wn = 2 rad/sec. (11) Choose wn = 20 rad/sec. (a) Fill in the blanks in the following table based on the evaluation of the step responses. steady-state error rise time settling time overshoot Open-loop system Closed-loop() Closed-loop (ii) Closed-loop () (b) Plot and overlay the step responses of the three closed-loop control systems. (c) Discuss the signif cance of the choice of Wn in the ITAE characteristic equation. 4. (10%) A control law is to be designed for the system in Problem 3 by using the ITAE criterion. Different parameters of w, in the ITAE criterion are considered here. (1) Choose wn such that the DC gain is equal to 1. M u(t) Figure 4: An inverted pendulum system. (i) Choose wn = 2 rad/sec. (11) Choose wn = 20 rad/sec. (a) Fill in the blanks in the following table based on the evaluation of the step responses. steady-state error rise time settling time overshoot Open-loop system Closed-loop() Closed-loop (ii) Closed-loop () (b) Plot and overlay the step responses of the three closed-loop control systems. (c) Discuss the signif cance of the choice of Wn in the ITAE characteristic equation