K 2 K Increasing K 6 K 2 K Increasing □= roots of the closed-lo 00 p K stem X= poles of th open-loop system K 2022-2-3 2 6
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et is a root of the characteristic equation Then for this root the angle condition can be written as K =-∠s1-∠(s1+2)=-180 s(s+2 =51 s+2 2022-2-3 7
2022-2-3 7 Let is a root of the characteristic equation. Then for this root, the angle condition can be written as 1 1 1 2 180 2 s s K s s s s
The gain condition may be used to find the required value of at the root as K KG()= =1(48) S+2 S or K=sN(+2)9 Another example for the root locus of a system for varying a parameter other than gain is introduced Consider a system shown in the figure below 2022-2-3 8
2022-2-3 8 The gain condition may be used to find the required value of at the root as 1 1 1 1 2 2 s s K K KG s s s s s K s1 s1 2 Another example for the root locus of a system for varying a parameter other than gain is introduced. Consider a system shown in the figure below. or (4.8) (4.9)
Another introduced. Consider a system shown in the figure below. example for the root locus of a system for varying a parameter other than gain Is jVK -八R G(5) R(→○ K s(s +a) s1+八K 2022-2-3 9
2022-2-3 9 Another introduced. Consider a system shown in the figure below. example for the root locus of a system for varying a parameter other than gain is
4.3 The root locus construction procedure for General system E(s) R()一 G(s) Y(s) H(S) For the general feedback control system shown above, the closed-loop transfer function is given by T()=-G(s) 1+GH(S) (4.10 2022-2-3 10
2022-2-3 10 4.3 The Root Locus Construction Procedure for General System For the general feedback control system shown above, the closed-loop transfer function is given by 1 G s T s GH s (4.10)