diff --git a/Figures/perfconp.pdf b/Figures/perfconp.pdf new file mode 100644 index 0000000..15518cb Binary files /dev/null and b/Figures/perfconp.pdf differ diff --git a/Figures/perfconp.png b/Figures/perfconp.png new file mode 100644 index 0000000..f9cebf1 Binary files /dev/null and b/Figures/perfconp.png differ diff --git a/Figures/perfconp.svg b/Figures/perfconp.svg new file mode 100644 index 0000000..87408bf --- /dev/null +++ b/Figures/perfconp.svg @@ -0,0 +1,568 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/rotating_frame.org b/rotating_frame.org index 77b66bb..e90f1b5 100644 --- a/rotating_frame.org +++ b/rotating_frame.org @@ -1092,19 +1092,64 @@ However, when we look at the poles of the closed loop with a diagonal controller | -1.1837+0.0041777i | | -1.1837-0.0041777i | -*** TODO Close loop performance -First we compute the close loop transfer functions. +*** Close loop performance +First, we create the closed loop systems. Then, we plot the transfer function from the reference signals $[\epsilon_u, \epsilon_v]$ to the output $[d_u, d_v]$ (figure [[fig:perfcomp]]). #+begin_src matlab :results none :exports code - Gcl = feedback(Gvc, K); - Gtcl = feedback(Gtvc, K); + K.InputName = 'e'; + K.OutputName = 'u'; + + Gtvc.InputName = 'u'; + Gtvc.OutputName = 'y'; + + Gvc.InputName = 'u'; + Gvc.OutputName = 'y'; + + Sum = sumblk('e = r-y', 2); + + Tvc = connect(Gvc, K, Sum, 'r', 'y'); + Ttvc = connect(Gtvc, K, Sum, 'r', 'y'); #+end_src - #+begin_src matlab :results none :exports code + freqs = logspace(-2, 2, 1000); + figure; - bode(Gcl, Gtcl) + ax1 = subplot(1,2,1); + hold on; + plot(freqs, abs(squeeze(freqresp(Tvc(1, 1), freqs, 'Hz')))); + plot(freqs, abs(squeeze(freqresp(Ttvc(1, 1), freqs, 'Hz')))); + hold off; + xlim([freqs(1), freqs(end)]); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + xlabel('Frequency [Hz]'); ylabel('Magnitude [m/N]'); + legend({'w = 0 [rpm]', 'w = 60 [rpm]'}, 'Location', 'southwest') + title('$G_{r_u \to d_u}$') + + ax2 = subplot(1,2,2); + hold on; + plot(freqs, abs(squeeze(freqresp(Tvc(1, 2), freqs, 'Hz')))); + plot(freqs, abs(squeeze(freqresp(Ttvc(1, 2), freqs, 'Hz')))); + hold off; + xlim([freqs(1), freqs(end)]); + ylim([1e-5, 1]); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + xlabel('Frequency [Hz]'); + title('$G_{r_u \to d_v}$') + + linkaxes([ax1,ax2],'x'); #+end_src +#+HEADER: :tangle no :exports results :results file :noweb yes +#+HEADER: :var filepath="Figures/perfconp.png" :var figsize="full-tall" +#+begin_src matlab + <> +#+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