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Lecture_F11_ECH157_Root_locus

# Lecture_F11_ECH157_Root_locus - rlocus(h this will plot the...

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Plotting root locus using M ATLAB If the open-loop transfer function G OL ( s ) is of the form k N ( s ) D ( s ) where k is a parameter that we can vary, then the closed-loop transfer function between the set-point and the output is G OL ( s ) = k N ( s ) D ( s ) 1 + k N ( s ) D ( s ) (1) And the characteristic equation becomes 1 + k N ( s ) D ( s ) = 0 D ( s ) + k · N ( s ) = 0 (2) For different values of k , the roots of the characteristic equation are in general different. And we can generate a plot showing how the roots move in the complex plane as k changes and this plot is the root locus. In M ATLAB , root locus can be easily generated. For example, if G OL ( s ) = k s + 2 s 2 + 5 s + 2 , then you can do the following in M ATLAB to plot the root locus: h = tf([1 2],[1 5 20]); % this is where you specify the % coefficients of N(s) and D(s)
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Unformatted text preview: rlocus(h); % this will plot the root locus And M ATLAB will then generate the root locus:-12-10-8-6-4-2 2-4-3-2-1 1 2 3 4 System: h Gain: 3.73 Pole: -4.36 - 2.9i Damping: 0.833 Overshoot (%): 0.887 Frequency (rad/sec): 5.24 Root Locus Real Axis Imaginary Axis where points with “ × ” represent the open-loop poles and points with “ ◦ ” represent the open-loop zeros. Clicking on any point of the trajectory, you will see a datatip with information about the system when the root is at that particular location and the corresponding value of k . For more information, please see http://www.mathworks.com/help/toolbox/control/ref/rlocus-root-locus.html...
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