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Sketch Bode plot & assess the stability for the control system having open loop transfer function G(S)H(S)=$\frac{120}{(S+2)(S+10)}$
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written 8.0 years ago by |
G(S)H(S)=$\frac{120}{(S+2)(S+10)}$
Arrange the above equation in time control form,
G(S)H(S)=$\frac{120}{(2(1+0.5S)}$ 10(1+0.1S))
G(S)H(S)=$\frac{6}{(1+(\frac{S}{2}) (1+\frac{S}{10})}$
Comparing with standard form of time constant,
K=6
Mo pole at origin.
Simple pole at $\frac{1}{(1+(S+2)}$, $w_c1$=2 rad/sec
Simple pole at $\frac{1}{(1+(S+10)}$, $w_c2$=10 rad/sec
Magnitude plot:
For k=6, 20log6=15.563 dB
Phase angle plot:
G(jw)H(jw)=$\frac{6/(1+j(w/2)}{(1+j(w/10)}$
=$\frac{\lt6+j0)}{\lt1+j(w/2)(\lt1+j(w/10)}$
The table for phase angle will be:
From Bode plot as shown in the figure:
GM=∞; PM=58
Hence the system is stable.