Control Flashcards
1st rule of root locus plotting
The root locus diagram is symmetrical about the real axis
2nd rule of root locus plotting
Loci start at open-loop poles and end at open-loop zeros
3rd rule of root locus plotting
If there is an excess of poles, the remaining loci tend
towards asymptotes
4th rule of root locus plotting
Asymptote angles =(2n + 1) · 180◦/excess of poles
5th rule of root locus plotting
scg = (sum of poles − sum of zeros)/ excess of poles
6th rule of root locus plotting
The real axis segments are at any point where the total number of poles and zeros to the right of the point is odd
7th rule of root locus plotting
Where loci arrive at or leave the real axis, they do so at 90◦
8th rule of root locus plotting
break in and break away points at dG(s)/ds = 0
9th rule of root locus plotting
The locus leaves a complex starting point at an angle
θ =sum of zero angles - sum of zero poles ± 180
10th rule of root locus plotting
The locus arrives at a complex ending point at an angle
θ = sum pole angles - sum of pole angles ± 180◦
11th rule of root locus plotting
Imaginary axis crossings are found by using a Routh array
12th rule of root locus plotting
The overall monic form gain for any point on the root locus is found by
gain = product of pole lengths/ product of zero lengths
if you have a zero row in a routh array what do you do
differentiate the previous row and continue as normal
what does a zero row in a routh array imply
A zero row indicates that some of the poles are symmetrical about the imaginary axis
if you have a zero element in the left hand column what do you do
Replace the zero with a vanishingly small number d and continue
