Question 4.2. For the ball and beam outer loop shown in Fig. 4.5, using the PD controller (4.10) and the ball and beam plant model P943) given by (4.7), calculate the transfer function from Xd(s) to X (3) Question 4.3. Find the expression for the Laplace transform of the tracking error E(s) : X c1(3) X (s) when Xd(s) = %. Based on your answer, calculate the steady state tracking error. For what values of the control gains Kc and 2 will the steady state tracking spec in (4.8) be satised? Question 4.4. Find the values of C and w\" to meet the specications given in (4.8). Question 4.5. Based on your answer to your previous question, nd the gains Kc and z to meet the specica tions given in (4.8)