Root Locus Examples - Michigan State University
Root Locus Examples
(graphed using MatLab)
|MatLab Program: |[pic] |
|num = [1] | |
|poles = [0;-1+j;-1-j;-3] | |
|den = poly(poles) | |
|rlocus(num,den) | |
|Notes: | |
|n=4 poles, m=0 zeros | |
|asymptotes at ±45,±135 | |
|asymptote cg @ | |
|(-3-1-1+0)/4 = -1.25 | |
|Angle of Departure, θd | |
|([pic]+ arctan(0.5) + 90 + 135) = 180 | |
|[pic] = -71.6 deg | |
|MatLab Program: |[pic] |
|num = [1] | |
|poles=[0;-1+4*j;-1-4*j;-2] | |
|den = poly(poles) | |
|rlocus(num,den) | |
|Notes: | |
|n = 4 poles, m = 0 zeros | |
|asymptotes at ±45,±135 | |
|asymptote cg @ | |
|(-2-1-1+0)/4 = -1.0 | |
|Angle of Departure, [pic] | |
|([pic]+ arctan(4) + (180-arctan(4)) + 90) = 180 | |
|[pic] = -90 deg | |
|MatLab Program: |[pic] |
|zeros = [-1+3*j;-1-3*j] | |
|num = poly(zeros) | |
|poles = [0;-1+2*j;-1-2*j;-2] | |
|den = poly(poles) | |
|rlocus(num,den) | |
|Notes: | |
|n = 4 poles, m = 2 zeros | |
|asymptotes at ±90 degrees | |
|asymptote cg @ | |
|[(-2-1-1+0)-(-1-1)]/2 = -1.0 | |
|Angle of Departure, [pic] | |
|[([pic]+ arctan(2)+(180-arctan(2))+ 90) - | |
|(-90+90) ] = 180 => [pic] = -90 deg | |
|Angle of Arrival, [pic] | |
|[(90 + arctan(3)+(180-arctan(3))+ 90) - | |
|(-([pic]+90) ] = 180 => [pic] = 90 deg | |
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