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z7Z(P4if@r^8i$TZl$r@fV@5AuI6_Qx+nUG+WnA_%;-uSV2zpw1F`==&+~c?5!m4A` z5A5Q^cj-^R4e6W`zri4@8ob!J&ya zXgc@|s3zZ?Mvvx6IdN-xCu;UNrj=HYFa>1I)2E`(s8Yo8$xlyUl@eSqJ{p*q z0vrNPk8+Cw*Uuszog%g!%P$ADKc$5G+M>A^Xpa;zK@@3e$Z|yqMolTQ=;#q2-yg8gDbFY zbbas}yv2-y0^*2gm%L06W;`Z}_^l5#J6*R(*9YyJB8ElK;yw}3-2?`QT9kLI%L=s4(*ak|*W++&H z^UI(A^!I=Gm;ds|KmGH6_?v(J`#=Bb_y6}_yMeru|M> +#+end_src + +#+NAME: fig:perfcomp +#+CAPTION: Close loop performance for $\omega = 0$ and $\omega = 60 rpm$ +#+RESULTS: +[[file:Figures/perfconp.png]] + *** Effect of rotation speed We first identify the system (voice coil and light mass) for multiple rotation speed. Then we compute the bode plot of the diagonal element (figure [[fig:Guu_ws]]) and of the coupling element (figure [[fig:Guv_ws]]). @@ -1112,7 +1157,7 @@ Then we compute the bode plot of the diagonal element (figure [[fig:Guu_ws]]) an As the rotation frequency increases: - one pole goes to lower frequencies while the other goes to higher frequencies - one zero appears between the two poles -- the zero disappears when $\omega > \sqrt{\frac{k}{m}}$ and the low frequency pole becomes unstable (positive real part) +- [ ] the zero disappears when $\omega > \sqrt{\frac{k}{m}}$ and the low frequency pole becomes unstable (positive real part) To stabilize the unstable pole, we need a control bandwidth of at least twice of frequency of the unstable pole. @@ -1214,7 +1259,6 @@ To stabilize the unstable pole, we need a control bandwidth of at least twice of [[file:Figures/Guv_ws.png]] ** TODO Plant Control - MIMO approach - ** test #+begin_src matlab :exports none :results silent