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given my control system enter image description here

I have found the region of the complex space that satisfies my specifications, determining poles position in 0.5 +- 0.2i. enter image description here 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 ++

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  • $\begingroup$ 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 $\endgroup$
    – Damjan Dakic
    May 8, 2015 at 18:27
  • $\begingroup$ ok I will look at the link, thanks @DamjanDakic $\endgroup$
    – Daniel
    May 9, 2015 at 10:08

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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: $$ \begin{array}{cc} K_d=1 \\ K_p=1.16/4 \end{array}. $$

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