106 s + a1 + a3 G3(s) = 100 (start as) (3+15(x + a)s + 100an + a.)) (s +100(a1 + a)) 100 (5+6+1) (571562+7)s +10c) (+100(e) ) Figure 1: Control system with a proportional-integral controller. Problem 3. Draw the Bode plot of the transfer function G3(s) that you found in the system setup section. Follow the instructions we explained in the class. (a) Determine the basic factors and corner frequencies. (b) Determine the slope, magnitude, and phase at a very low frequency. (c) Determine the phase and slope at corner frequencies. (d) Determine the phase and slope at a very high frequency. (e) Draw the Bode plot. Provide the details of your work. (30 points) 106 s + a1 + a3 G3(s) = 100 (start as) (3+15(x + a)s + 100an + a.)) (s +100(a1 + a)) 100 (5+6+1) (571562+7)s +10c) (+100(e) ) Figure 1: Control system with a proportional-integral controller. Problem 3. Draw the Bode plot of the transfer function G3(s) that you found in the system setup section. Follow the instructions we explained in the class. (a) Determine the basic factors and corner frequencies. (b) Determine the slope, magnitude, and phase at a very low frequency. (c) Determine the phase and slope at corner frequencies. (d) Determine the phase and slope at a very high frequency. (e) Draw the Bode plot. Provide the details of your work. (30 points)