#### YukiWong

Joined Dec 5, 2011
27
Hi everybody ,

I got a transfer function which is 2/[s*(0.5s+1)] and figure below show the bode plot of the system. My quesiton is, why is the gain margin of this system is infinite?

Thank you very much.

#### thatoneguy

Joined Feb 19, 2009
6,359
The function simplifies to $$\frac{1}{s (0.25s + \frac{1}{2})}$$

No clue why it would be infinite, it should converge to 1

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#### t_n_k

Joined Mar 6, 2009
5,455
It is infinite - the total phase shift tends to exactly 180° as the frequency tends to infinity at which point the transfer gain is infinitesimal.

#### YukiWong

Joined Dec 5, 2011
27
It is infinite - the total phase shift tends to exactly 180° as the frequency tends to infinity at which point the transfer gain is infinitesimal.
thanks t_n_k,

erm, is that every second order system will cause infinity gain margin?

#### t_n_k

Joined Mar 6, 2009
5,455
thanks t_n_k,

erm, is that every second order system will cause infinity gain margin?
Consider a [2nd order?] transfer function like

$$G(s)=\frac{(10-s)}{s(s+5)}$$

Which has a non-infinite gain margin but has an unbounded step response.

Considered in isolation, gain margin of itself doesn't tell us much about system stability - so a system could have an infinite gain margin but be unstable or unbounded in transient response.

For instance the transfer function

$$G(s)=\frac{0.3}{{(s-0.001)}^2+0.09}$$

has infinite gain margin but has an unstable step response.

#### YukiWong

Joined Dec 5, 2011
27
Consider a [2nd order?] transfer function like

$$G(s)=\frac{(10-s)}{s(s+5)}$$

Which has a non-infinite gain margin but has an unbounded step response.

Considered in isolation, gain margin of itself doesn't tell us much about system stability - so a system could have an infinite gain margin but be unstable or unbounded in transient response.

For instance the transfer function

$$G(s)=\frac{0.3}{{(s-0.001)}^2+0.09}$$

has infinite gain margin but has an unstable step response.
thanks t_n_K, i got it