Rules for Sketching the Root Locus 1.Number of Branches: The number of branches of root locus = the number of closed loop poles. 2.Symmetry: The root locus is symmetrical with respect to the real axis. Open Loop TF: K=0 Re Im -2 0 K=1 Characteristic Equ. : 3.Real-axis Segments: On the real axis the root locus exists only in the segment where the number of finite open-loop poles/zeros on the right-hand side of the segment is odd. 4.Starting and ending points: The root locus starts at the open-loop poles and ends at the open-loop zeros, including those zeros at infinity.

Rules for Sketching the Root Locus (cont’d) 6.Asymptotes: The root locus approaches straight lines as asymptotes as the root locus approaches infinity. In particular, the asymptotes have the following angles (θ) and intercept on the real axis (σ). Where n is an add number and  is the number of the infinite zeros 5.Breakaway and Break-in Points: The breakaway and break-in points are the real roots of or Where N(s) and D(s) are the numerator and denominator of G(s)H(s).

Determine whether or not each of the following sketches can be a root locus.