Unformatted text preview: G(s) Angle condition
Odd number If angle condition is satisfied,
compute the corresponding K.
o In this example,
o For a point on root locus, gain K is obtained by
Magnitude Angle condition is not satisfied. Im Re Angle deficiency
2008/09 MECH466 : Automatic Control 7 2008/09 MECH466 : Automatic Control 8 2 Lead compensator design (cont’d)
To compensate angle deficiency,
design a lead compensator C(s)
C(s) satisfying How to select pole and zero?
Draw horizontal line PA
Draw line PO
Draw bisector PB
Draw Im Desired pole
A P Desired pole
Im Draw PC and PD
B O C
Re There are many ways to design such C(s)!
2008/09 MECH466 : Automatic Control 9 -p(=-5.4) -z(=-2.9)
p(=z(=Pole and zero of C(s) are shown in the figure.
2008/09 Comparison of root locus
G(s) 10 How to design the gain K? G(s)C(s)
Im MECH466 : Automatic Control Lead compensator
Im Open loop transfer function
Open Re Re Magnitude condition
Magnitude Improved stability!
2008/09 MECH466 : Automatic Control...
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This document was uploaded on 03/05/2014 for the course MECH 466 at University of British Columbia.
- Fall '08