Fa2004 16.3338-10 Question #4: When/where is the locus on the real line? Locus points on the real line are to the left of an odd number of real axis poles and zeros [K positive Explanation a bit too detailed and not that relevan Question #5: Given that so is found to be on the locus, what gain is needed for that to become the closed-loop pole location? Need D(so)D(so) LLa(so)lNp(So)N(so) Since K=KpKc, sign of Kc depends on sign of Kp ◇eg, assume that∠La(so)=180°, then need Kc and Koto be same sign so that K>0
� � � � � � � � Fall 2004 16.333 8–10 • Question #4: When/where is the locus on the real line? – Locus points on the real line are to the left of an odd number of real axis poles and zeros [K positive]. – Explanation a bit too detailed and not that relevant • Question #5: Given that s0 is found to be on the locus, what gain is needed for that to become the closedloop pole location? – Need 1 K ≡ = Ld(s0) Dp(s0)Dc(s0) | | Np(s0)Nc(s0) – Since K = KpKc, sign of Kc depends on sign of Kp 3 e.g., assume that ∠Ld(s0) = 180◦, then need Kc and Kp to be same sign so that K > 0
Fa2004 16.3338-11 Root Locus Examples 工 igure 4: Basic Figure 5: Two poles Re Figure 6: Add zero Figure 7: Three poles Figure 8: Add zero Examples similar to control design process: add compensator dynamics to mod ify root locus and then chose gain to place CLP at desired location on the locus
Fall 2004 16.333 8–11 Root Locus Examples Figure 4: Basic Figure 5: Two poles Figure 6: Add zero Figure 7: Three poles Figure 8: Add zero Examples similar to control design process: add compensator dynamics to modify root locus and then chose gain to place CLP at desired location on the locus