ECE535_10S_hw5

ECE535_10S_hw5 - ECE 535 DISCRETE TIME SYSTEMS SPRING 2010...

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Unformatted text preview: ECE 535 DISCRETE TIME SYSTEMS SPRING 2010 HOMEWORK ASSIGNMENT #5 Due: 31 March 2010 1. Design using Ragazzinis method a compensator for G ( s ) = 1 ( s + 0 . 1)( s + 3) that yields a second order system whose step response shows less than 5% overshoot, 1% settling time less than 2 sec., and has zero steady state error to step inputs. Let T = 0 . 2 sec. Do this two ways. (a) First, specify your desired closed loop transfer function to be H ( z ) = ZOH ( 2 n s 2 + 2 n s + 2 n ) with and n chosen appropriately. (b) Second, specify H ( z ) so that its poles are the same as those of H ( z ) in (a), but so that its zero is the same as the zero of the ZOH-equivalent of G ( s ). Be sure to adjust the numerator of H ( z ) so that its DC gain equals one (why?). How does this controller compare to that in (a)? You should find that one controller has lower order than the other. Plot the step responses of both controllers, and show that they meet the given speci- fications....
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ECE535_10S_hw5 - ECE 535 DISCRETE TIME SYSTEMS SPRING 2010...

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