# Pole placement gains tuning

given my control system

I have found the region of the complex space that satisfies my specifications, determining poles position in 0.5 +- 0.2i. Now I want to find the gains that fix the desider pole (with matlab), but I have not understand well how to do it: anyone can suggest me an example on how to do that, with or without matlab? Thanks

Edit: in the first image the sum blocks are +-, not ++

• Sorry for not having enough time to type the complete answer, but this should help you in case noone else responds in the meantime: en.wikipedia.org/wiki/Full_state_feedback May 8, 2015 at 18:27
• ok I will look at the link, thanks @DamjanDakic May 9, 2015 at 10:08

I assume that you'd aim to place the poles in $$-0.5 \pm 0.2 \cdot i$$ for stability reasons.
In the s-domain, the transfer function is: $$\frac{\Phi_c}{\Phi}=\frac{K_p}{s^2+K_ds+K_p}.$$
Computing the closed-loop poles, hence the roots of the characteristics polynomial $$s^2+K_ds+K_p$$, gives you: $$\begin{array}{cc} K_d=1 \\ K_p=1.16/4 \end{array}.$$