Answer Happy

Problem 3 Sketch the Nyquist diagram for the system of Problem 2, showing important features, including: region of stability, starting point, ending point, crossings of the real axis. Problem 4 In the system of Problem 2 the gain K is set at K = 24. For this value of K, and with a unit step reference input Yr(s) = 1/s, sketch the unit step response. Show the following features of the unit step response: - Steady state output y(0) - Overshoot - Oscillation frequency (if any) Hint: The root locus of Problem 3 gives a hint of the locations of the dominant poles. Or you can calculate them using the result of Problem 2. -

Problem 1 A certain plant has the following state-space description *1 = 12 12 = 10:01 - 3x2 + u y = 21 (a) Determine G(s), the transfer function of the plant. Hint: Since this system appears in the following problems, it is recommended that you calculate the transfer function by two different methods. (b) The forward loop of the closed-loop system F(8) H(8) 1+ F(8) comprises the plant of part (a) and PI compensator. Thus the forward loop transfer function is F(s) K18+K2 + K2G(s) Determine the region in the K2, K1 plane (if any) in which the closed-loop system is stable. Problem 2 The system of Problem 1 is operated with Ki = K2=K Sketch the root locus of the poles of the closed-loop system, showing important features, including: segments on the real axis, asymptotes for large values of K, and crossing(s) of the imaginary axis.