Research Article
Root Locus Practical Sketching Rules for Fractional-Order Systems
Table 1
Practical rules for RL sketching of FO systems as defined in (
11).
| | Fractional-order case, (11) |
| Rule 1 | RL is symmetrical about the real axis. | Rule 2 | If , 1, 3, 5, …, then the number of branches is . | Rule 3 | Mark all open-loop poles and zeros on the s-plane. | Rule 4 | If necessary, use the angle condition (1) to determine the open-loop poles that have RL branches departing from them. | Rule 5 | Compute the asymptotes centroid, , and angle, , according to the following expressions: , . | Rule 6 | Points in the real axis belong to the RL if, for all poles and zeros seen to the right, is an integer odd number. | Rule 7 | Find the intersection of the RL with the imaginary axis making in the characteristic equation and solving it in order to determine and . | Rule 8 | Compute the breakaway and break-in points using the characteristic equation and determining . | Rule 9 | Determine the departure and arrival angles using the angle condition (1). |
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