exam2_f10_sol

exam2_f10_sol - University of California, Davis Department...

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University of California, Davis Department of Chemical Engineering and Materials Science ECH 157 Process Dynamics and Control Ahmet Palazoglu EXAM 2 Fall 2010 (Open book and no notes) 1. (5 pts) The loop transfer function ( ) for a feedback system is given as: OL g ) 1 2 )( 1 ( 2 ) ( + + = s s s g OL Sketch the Bode and Nyquist diagrams for this system. Your sketch should show all key features of the diagram including the low frequency gain and the high frequency asymptotic behavior. Calculate the frequency at which the Nyquist diagram crosses the imaginary axis. The Bode diagram yields: 10 -2 10 -1 10 0 10 1 0 0.5 1 1.5 2 10 -2 10 -1 10 0 10 1 -200 -150 -100 -50 0 The Nyquist diagram looks like: -1 -0.5 0 0.5 1 1.5 2 -1.5 -1 -0.5 0 0.5 1 1.5 Nyquist Diagram Real Axis Imaginary Axis 1
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It starts at low frequencies from the steady-state gain which is 2. It is a second-order system so its phase shift is 180 0 , thus the sketch should remain in the lower half of the Complex Plane, asymptotically approaching the origin. Note that MATLAB also plots
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This note was uploaded on 04/01/2011 for the course ECH 157 taught by Professor Palagozu during the Spring '08 term at UC Davis.

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exam2_f10_sol - University of California, Davis Department...

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