note8 - MEEN 364 Notes for session on October 27, 2004....

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MEEN 364 Notes from Session on October 27, 2004 304 Fermier Hall, 6:00~7:00 pm 1 Notes for session on October 27, 2004. 1. The unit step response of the system described by the following block diagram is shown below it. Determine the values of the gains k 1 , k 2 , and the other pole of the plant, b . Also obtain the peak, rise, and settling time for 1% criterion. ( 2 (2 1 2 k sbs ++ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 Step Response Time (sec) Amplitude d c b a
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MEEN 364 Notes from Session on October 27, 2004 304 Fermier Hall, 6:00~7:00 pm 2 Solution: The transfer function is given by: ( 2 (2 1 12 1 2 () ( )2 22 k Ys TF R s sb s kk k s b s b kk == + ++ = ++ ++ (1) Since R(s) = 1 / s (unit step input), the steady state value of the output is: 1 0 lim 2 s k S S TF b kk + (2) From the figure for the step response, SS = 1, so, equation (2) becomes: 1 21 2 b k += (3) Now we compare equation (1) with the standard expression for the transfer function of a second order system, given in problem 1.a: 2 1 2 nn k k an db w zw + =+ (4)
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This note was uploaded on 04/18/2010 for the course MEEN 364 taught by Professor Staff during the Spring '08 term at Texas A&M.

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note8 - MEEN 364 Notes for session on October 27, 2004....

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