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Unformatted text preview: ωn s + 2βωn s + ωn
s + (2βωn + Kd ωn )s + ωn (1 + Kp ) T (s) = This gives the following relationships:
ωn = ωn (1 + Kp )
2β ωn = 2βωn + Kd ωn Solving gives ωn = ωn
¯ 2βωn + Kd ωn = 2βωn + Kd ωn =
(1 + Kp ) and β =
2ωn (1 + Kp ) β+ Kd
2ωn (1 + K p ) . 6. In case the uncontrolled system G(s) in (3) has no damping and a resonance frequency
of 1 rad/s, compute the numerical values Kp and Kd of the PD-controller to triple the
undamped resonance frequency and bring the damping ratio up to 1/3. [10pt]
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This note was uploaded on 05/27/2010 for the course MAE MAT143B taught by Professor Linearcontrol during the Spring '10 term at UCSD.
- Spring '10