Assignment 4 Solutions 2009

5 n4a4 gtfnd stepgtf holdon a1 n4a4 gtfnd stepgtf

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Unformatted text preview: single figure. What conclusio ns can you draw concerning the zero location? Is the location of the pole corresponding to t 2 = 5 important? Note that the zero is located at: z = 1 / a 3 Using the fo llowing mat lab m­file, TF=30; a=10; n=[2*a 2]; d=[conv([5 1],[1 1])]; g=tf(n,d); step(g,TF); hold on a=2; n=[4*a 4]; g=tf(n,d); step(g,TF); hold on a=0.5; n=[4*a 4]; g=tf(n,d); step(g,TF); hold on a=­1; n=[4*a 4]; g=tf(n,d); step(g,TF); We can generate the fo llowing figure: 4 3.5 3 a=10 2.5 2 1.5 a=2 a=0.5 1 0.5 a=­1 0 ­0.5 0 5 10 15 20 25 30 We can observe that if the zero is small (a is large), the response exhibit s an overshoot. For smaller but posit ive values o f a, the response is init ially in the direct ion o f the ult imate steady­ state. For negative values of a, the response shows the inverse (wrong­way) behavior. The locat ions o f the po les (as lo ng as they are stable) do not play a crit ical role in changing the qualitat ive response characterist ics. 4. A two­tank flow­surge system is given in the Figure, along wit h the block diagra m represent ing the approximate dynamic...
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