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Sketch Bode plot & assess the stability for the control system having open loop transfer function G(S)H(S)=120(S+2)(S+10)
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G(S)H(S)=120(S+2)(S+10)

Arrange the above equation in time control form,

G(S)H(S)=120(2(1+0.5S) 10(1+0.1S))

G(S)H(S)=6(1+(S2)(1+S10)

Comparing with standard form of time constant,

K=6

Mo pole at origin.

Simple pole at 1(1+(S+2), wc1=2 rad/sec

Simple pole at 1(1+(S+10), wc2=10 rad/sec

Magnitude plot:

For k=6, 20log6=15.563 dB

Phase angle plot:

G(jw)H(jw)=6/(1+j(w/2)(1+j(w/10)

=<6+j0)<1+j(w/2)(<1+j(w/10)

The table for phase angle will be:

enter image description here

From Bode plot as shown in the figure:

GM=∞; PM=58

Hence the system is stable.

enter image description here

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