2.171 Quiz #2 Nov. 20, 2006 This quiz is open-book. You may also refer to two 8 1/2” by 11” sheets of notes. There is one problem; all seven sections of the problem will count equally. Problem 1 This problem considers a continuous-time system with a transfer function 2 a H ( s ) = . (1) s 2 − a 2 This might model the linearized behavior of a magnetic suspension. Note that both poles are real-axis, with one in the right-half plane. a) Calculate the zero order hold equivalent H eq ( z ) for this system with a sampling time T . b) Show that for a = 40, T = 0 . 001 sec, H eq ( z ) becomes 8 × 10 − 4 ( z + 1) H eq ( z ) = z 2 − 2 . 0016 z + 1 . (2) Please use this transfer function for all subsequent work even if your answer does not agree with it. Clearly state if this is the case, and then use the answer we are providing above. Plot the poles and zeros of this system on the z-plane. Do the poles map as z = e sT ? c)
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