I have difficulty to find the angles in the point from which poles go away from real-axis. The transfer function L(s) of open-loop is:

$$ L(s) = \frac{\mu_r(s+10)}{s^2(s+100)} $$


$C(s) = \frac{\mu_r(s+10)}{(s+100)}$ and $G(s) = \frac{1}{s^2}$

The generic formula for calculating the departure angle for a pole $p_i$ with multiplicity of $h_i$ is

$\alpha_{i,k} = \frac{1}{h_i}[180°(2k+1)- \sum_{j=1}^{n}\tilde{\phi_j}+\sum_{j=1}^{m}\tilde{\theta_j}]$

$k \in \{0,1,...,h_i-1\}$

$\tilde{\theta_j}$ angle of the line between pole $p_i$ and zero $z_j$

$\tilde{\phi_j}$ angle of the line between pole $p_i$ and pole $p_j$

For example the only break-away point is located in -40. If I use the formula I'll find that the angles are 90° and -90° but that don't correspond to the root locus plot on Matlab.

I'm sorry for my English, I did the better I could do.


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