Students enrolled in 481, please complete problems 1-9. Students enrolled in 581, please complete problems 1-10. Also, please indicate which section you are registered for in the name of the file

you submit. Ⓒ(s) = 0+ Input Controller -K(s + a) s+b 10(1) M₂ M₂ Figure 1 Ta(s) xx Figure 2 8 Pendulum Model -1 M₂L (M₂+ M₂)8 M₂L 52 Ⓒ(s)/n1. Consider the problem of controlling an inverted pendulum on a moving base, as shown in Figure 1. The design objective in this problem is to balance the pendulum in (get 0 (t) 0) in the presence of disturbance inputs. Let M₁ = 10 kg, M₁ = 100 kg, L = 1 m, g = 9.81 m/s², a = 5, and b = 10. The design specifications, assuming a unit step disturbance are (a) settling time of T ≤ 10 s, (b) percent overshoot of P.O. < 40%, and (c) steady-state tracking error less than 0.1° in the presence of the disturbance. In order to carry out the design process, create one script that Computes the closed-loop transfer function from disturbance to output with K as an adjustable parameter. 1/nR(s) Controller Ge(s) Vehicle 0.3(s+0.05) (s² + 1600) (s² +0.05s + 16)(s +70) Sensor 0.5 Figure 3 Y(s) · Draws the Bode plot of the closed-loop system. • Automatically computes the maximum frequency response value Mp and reso- nant frequency w... Next, create another script that - Derives and w, from Mpw and wr . Estimates the settling time and percentage overshoot from ( and wn. Finally, plot the response (t) to a unit step disturbance with the choice of K you determine using your scripts. As a design starting point, you can compute the minimum K to meet the steady-state error specification. C