Magnitude Condition of 3 Real Poles and 1 Real Zero
Applet below show how the closed loop poles can be approximately found by locating the zeros of the characteristic eqn. In the applet the magnitude of the characteristic equation is plotted as a contour plot with the lowest magnitudes being white and black. The resolution
of the minimum can be changed by changing rs.
To find the closed loop for K = 7 for a system with open loop poles at
-0.5, -1.0, 1.5 and open loop zero at -3.0, set the following
(0.5, 1.0, 1.5, 3.0, 7.0, sr, si, 6) then adjust sr, si to find
where the angle condition is satisfied. For sr = -0.37, si = 1.82;
K = 7.06 and f = -180.3°. For
sr = -2.266, si = 0.0; K = ~ 7 and f = -540°.
The CL poles are ~-2.266, ~-0.37 ± ~j1.82. In this plot the
location of the minimum is limited but it is in general agreement
with that obtained from sr, si.
Gif image showing how applet should appear is shown below.
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COPYRIGHT © 2006 Cuthbert Nyack.