week8 Solution0.pdf - University of Wollongong MECH321...

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1 2 2 University of Wollongong MECH321 Autumn 2016 - Tutorial 8 Solution Consider a remotely controlled pick up arm for collecting waste bags. The tip position of the hydraulic arm is controlled through a feedback control system, where a proportional controller is employed as the controller. 1 D e s ir e d C o n t r o lle r Hydraulic A r m R e a l arm p o s it ion H 1 ( s ) H 2 ( s ) G ( s ) arm p o s it ion G ( s ) = S e n s o r 6 1 , H 1 ( s ) = 3 , H 2 ( s ) = ( 3s + 1 )( s + 1 ) 9 (a) (20%) Determine the expressions for the magnitude and phase angle of the op e n-lo op transfer function. Answer: Open-loop tran s f er function is given by, Magnitude given by, P ( s ) = 2 (3 s + 1)( s + 1) 2 | P ( j ω ) | = ( j 3 ω + 1)( j ω + 1) = | 2 | | ( j 3 ω + 1) || ( j ω + 1) | 2 = 9 ω + 1 ω + 1 1 Picture adapted from ”M odern Control Systems”, 10E, page 569, Dorf & Bishop.
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