Chapter 10
10.8 Evans Root Locus Construction Rule #6: Angles of Departures/Arrivals at Complex Poles/Zeros
This Rule deals with angles of departure (arrival) from/to complex poles (zeros).
Rule 6: If G(s) has a pole p of multiplicity r, then r branches of the root locus depart from p. The angle of departure of these root loci from p are described by this equation:
|
θdep= ∠[G(s)(s−p)r]s=p+(2k+1)⋅180∘r k=0,1,2,...,r−1 Equation 10-13 |
Similarly, if G(s) has a zero z of multiplicity r, then r branches of the root locus arrive at z. The angle of arrival of these root loci to z are described by this equation:
| θarr=−∠[G(s)(s−z)r]s=z+(2k+1)⋅180∘rk=0,1,2,...,r−1
Equation 10-14 |
See examples in the next section for illustration of this rule.
