# How can I find the transfer function from this Bode diagram?

I've been given this bode diagram :

I've been asked to find the transfer function only by using the bode diagram. It's the first time I'm doing this so here's what I thought.

The starting value is zero so the multiplying constant of the the transfer function has to be 1 and it is positive since the phase diagram starts from 0 degrees( it would start from 180 had it been negative)

From the fact that the starting degrees are 0 we derive that we have no pole or zero that is at the origin.

Also, the final degrees are -270 and the dBs are decreasing so I must have 3 poles.Am I correct?
Also ,I know that I can look at the curve , the dBs per decade at any point to see how many poles or zeros are acting. I can't get a good estimation though.It seems like it's 10 dBs per decade until the frequency reaches 10 rad/sec while I know it has to be a factor of 20 dBs. 60 dBs per dec mean 3 poles/zeros,40 dBs per dec mean 2 etc.

How do I know where the poles are if I can't tell where the angle of the curve changes? Is it clear and I can't see it?

By the way, I've been given the answer to check if I do it right in the end and it's as follows: $$G=\frac{500}{s^3+20s^2+200s+500}$$ Also p =

-8.2390 + 8.6072i, -8.2390 - 8.6072i, -3.5220 + 0.0000i

• If you have 3 poles, and the system is real, then 2 of them are complex conjugates (in the left semiplane), and the other is real (negative). Or the 3 are real. – Juancho May 25 '17 at 16:34