4.1. Inverted Pendulum Modeling Consider an inverted single link arm of length l carrying; a mass m, acceleration due to gravity g and input torque T applied at the base as shown in Figure 1 Figure 1: Inverted Pendulum What are the poles of the system? Answer\". 31,2 = 3|: 1% (5] Remark: The pole locations are not dependent on the pendulum mass m! What are the zeros of the system? Answer\". The system has zeros at s : oo, 00. What is the magnitude response, |Pg(jw}|, of the system? What is the phase response, APOMUJ), of the system? _ * . . 2 _ Hint. Draw the picture to help you With the phase of s as?\" (s + ns pjw. Then, Law) 2 z (32 EMF\"). What is the DC gain of the system