Pole Placement and State feedback

[@amrali8215]

You are an amazing professor thank you so much

[@richard_pates]

Thanks for the feedback - I'm glad you found some use for these videos!

[@mohamedelaminenehar333]

😊😊 thank u sir

[@adricat59]

Hi. I believe that there is a mistake in the third-order Butterworth polynomial expression.

[@richard_pates]

Yes, you're right! The final w_c^2 is meant to be a w_c^3, so it should be s^3+2w_cs^2+2w_c^2s+w_c^3... Good spot - glad you're paying attention! Thanks!

[@adricat59]

@@richard_pates Thank you for your response! May I ask you what are the real benefits for employing the Butterworth configuration for pole placement? I am getting better results by defining instead a first-order and second-order characteristic equations. The three poles are still in the semi-circle, but I can play with the damping of the complex conjugate poles, and get better response characteristics.

[@richard_pates]

@@adricat59 The honest answer is not many as far as I know. The motivation for the butterworth configuration comes from the butterworth filter. This is the filter with transfer function y(s)=G(s)u(s), where G(s)=1/(butterworth polynomial). The motivation here is that this G(s) should give a very smooth response to input signals that satisfy u(jw)

[@adricat59]

@@richard_pates Thank you very much for the response and the time invested on it, Richard. It was very useful. By the way, I found very interesting your videos and the way you present them. Have a good day :-)