compensator19 - [ ] 2 1 180 0, 1, 2, a i i n m + = = -K...

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Compensators Q UESTION 19 For the closed–loop system in Figure 19 with ( 29 1 C G s = and ( 29 2 1 G s s = , sketch the Root Locus Diagram. Qualitatively describe the closed–loop system stability and transient characteristics for 0 < K < ∞. Turn in your Matlab code. G(s) KG C (s) U(s) R(s) + - Y(s) E(s) Figure 19 There are m = 0 finite open–loop zeros There are n = 2 finite open–loop poles located at 0 and 0 There are n = 2 branches and n m = 2 branches go to infinity The Root Locus is on the real axis only at 0 The asymptote real–axis intercept is [ ] [ ] 0 0 0 0 a n m σ + - = = - The asymptote angles are
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Unformatted text preview: [ ] 2 1 180 0, 1, 2, a i i n m + = = -K There are n m = 2 distinct asymptotes with angles 90 , 90 a =-The closedloop characteristic equation is ( 29 ( 29 2 1 C KG s G s s K + = + = Solving, s K j = . Therefore, the closedloop system response is always undamped and the closedloop system is always marginally stable. Compensators The Root Locus Diagram is given below.-0.2-0.15-0.1-0.05 0.05 0.1 0.15-1.5-1-0.5 0.5 1 1.5 Real Axis Imaginary Axis 2...
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compensator19 - [ ] 2 1 180 0, 1, 2, a i i n m + = = -K...

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