The following is an openloop bode plot of au unknown plant I

The following is an open-loop bode plot of au unknown plant: Is this system minimum phase? Show how you determined this. What are the gain and phase margins? Is the closed loop system stable?

Solution

Ans)

From the bode plot initial phase is 0^o and it decreses to -270^o as frequency increases

Each pole on the left half of \'s\' plane contributes -90^o phase nad -20 dB /decade decrease in gain after cuttoff

So from the bode plot we can say this system has 3poles on the left half of \'s\' plane which contributes a

phase of 3*-90=-270^o Which can be cross checked from bode plot which also gives -270^o as \'w\' increases

Gain also satisfies that 3*-20dB/decade =-60 db /decade (3 poles)

So from all this we can now understand that there are 3 poles in the system on left half of \'s\' plane hence

system is \'minimum phase system\' as there are no poles or zero\'s in right half of \'s\' plane

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b)

Gain margin is obtained by looking at gain at frequency(i.e w=10 rad/s from graph) when phase=-180^o i.e-18 dB from the graph

Phase margin is obtained by phase at frequency(w=20 rad/sec) when gain crosses 0dB i.e -50 deg from graph

As both phase margin and gain margin <0 i.e negative Hence closed loop system is unstable