quiz2sol

# quiz2sol - George W Woodruff School of Mechanical...

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1 George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology ME6403 Digital Control Systems Quiz #2 February 18, 2010 (Atlanta Main Campus), February 25 th 2010 (DL) NAME (PRINT) Problem 1 (20 points): Consider the block diagram shown below. The parameters for a first-order Butterworth low-pass filter are given as 5 . 0 , 25 . 0 , 25 . 0 1 1 0 a b b . Determine the first 5 values of y ( k ) (i.e., k =0,1,2,3,4) for ) 2 ( , 2 ) ( , 1 ) 1 ( , 0 ) 0 ( k k x x x . Assume zero initial condition for the filter. Use a calculator. ) ( k x + 1 z 1 b 1 z 1 a ) ( k y 0 b ) 1 ( ) ( ) 1 ( ) ( 1 0 1 k x b k x b k y a k y y(0)=0 y(1)= 0.25000000000000 y(2)= 0.87500000000000 y(3)= 1.43750000000000 y(4)= 1.71875000000000 Problem 2 (25 points=15+10) : Consider the following digital control system where 2 ) 1 ( 5 . 0 ) ( z z z G . ) ( z G + - K (1) Sketch the root-locus plot of this system. For simplicity, you do NOT need to determine break-in/break-away points. The open loop systems has two poles at 1 and one zero at 0.5.

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2 -1 -0.5 0 0.5 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Root Locus Real Axis Imaginary Axis (2) Find the range of gain K that maintains the stability of the closed-loop system.
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## This note was uploaded on 05/10/2010 for the course ME 6403 taught by Professor Staff during the Spring '08 term at Georgia Tech.

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quiz2sol - George W Woodruff School of Mechanical...

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