I am trying to sketch the bode phase plot for this transfer function:
$$H(s)=\frac{s-400}{(s+2)*(s+20)}$$
As far as I understand the phase diagram should start from 0 degrees as the poles are real and non zero. But as long as I plot the function on Wolfram Alpha I get a different result. As you can see the plot starts from 180 degrees.
Could someone please explain why?
This is because your DC gain is negative. Formally, when you compute $H(j\omega)$ for $\omega=0$, where $j:=\sqrt{-1}$, you obtain $H(0)=-10$, which corresponds in the complex plane to the vector with the magnitude $10$ and the phase $-\pi$ (or $\pi$, up to you).
Actually, this is why for systems with a negative DC gain, it is typically recommended to premultiply them by $-1$, and then proceed with control design, otherwise, the phase margin can be rather poor.