hwsln-421-s06-03

hwsln-421-s06-03 - ECE 421, Spring 2006 Solutions to HW...

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Unformatted text preview: ECE 421, Spring 2006 Solutions to HW Assignment #3 Problem B-5-1 Assume that the thermometer is modeled by a f rst-order system with output c ( t ) representing the thermometer reading and the input r ( t ) representing actual temperature, and the relationship C ( s ) R ( s ) = 1 T s + 1 (1) Settling time for the step input is T s = 1 minute or T s = 60 seconds. The settling time to get within 2% of the f nal value is de f ned to be four time constants. Therefore, T s = 60 = 4 T T = 15 sec (2) or T s = 1 = 4 T T = 0 . 25 min (3) If the temperature is changing linearly with time, that is modeled as a ramp input, in this case with a slope of 10. For a unit ramp input (slope = 1 ), the steady-state error is equal to the value of the time constant T . This error is scaled by the slope of the input, so the steady-state error is e ss = 10 deg / min . 25 min = 2 . 5 deg (4) or e ss = 10 deg / min (1 / 60) min / sec 15 sec = 2 . 5 deg (5) Problem B-5-2 G ( s ) = 1 s ( s + 1) = 2 n s ( s + 2...
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hwsln-421-s06-03 - ECE 421, Spring 2006 Solutions to HW...

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