Update link to journal and matlab scripts
This commit is contained in:
247
matlab/index.org
247
matlab/index.org
@@ -167,10 +167,10 @@ exportFig('figs/weight_formula.pdf', 'width', 'wide', 'height', 'normal');
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[[file:figs/weight_formula.png]]
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#+begin_src matlab
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n = 2; w0 = 2*pi*10; G0 = 1/10; G1 = 1000; Gc = 0.45;
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n = 3; w0 = 2*pi*10; G0 = 1000; G1 = 0.1; Gc = 0.45;
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W1 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
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n = 3; w0 = 2*pi*10; G0 = 1000; G1 = 0.1; Gc = 0.45;
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n = 2; w0 = 2*pi*10; G0 = 1/10; G1 = 1000; Gc = 0.45;
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W2 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
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#+end_src
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@@ -249,6 +249,28 @@ H1 = 1 - H2;
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** Obtained Complementary Filters
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The obtained complementary filters are shown on figure [[fig:hinf_filters_results]].
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#+begin_src matlab :results output replace :exports results :tangle no
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zpk(H1)
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zpk(H2)
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#+end_src
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#+RESULTS:
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#+begin_example
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zpk(H1)
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ans =
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(s+1.289e05) (s+153.6) (s+3.842)^3
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-------------------------------------------------------
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(s+1.29e05) (s^2 + 102.1s + 2733) (s^2 + 69.45s + 3272)
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zpk(H2)
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ans =
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125.61 (s+3358)^2 (s^2 + 46.61s + 813.8)
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-------------------------------------------------------
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(s+1.29e05) (s^2 + 102.1s + 2733) (s^2 + 69.45s + 3272)
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#+end_example
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#+begin_src matlab :exports none
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figure;
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tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
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@@ -1315,45 +1337,67 @@ exportFig('figs/hinf_comp_H1_H2_syn.pdf', 'width', 'wide', 'height', 'normal');
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[[file:figs/hinf_comp_H1_H2_syn.png]]
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** Using Feedback architecture
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#+begin_src matlab
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n = 2; w0 = 2*pi*11; G0 = 1/10; G1 = 1000; Gc = 1/2;
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n = 3; w0 = 2*pi*10; G0 = 1000; G1 = 0.1; Gc = 0.45;
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W1 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
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n = 3; w0 = 2*pi*10; G0 = 1000; G1 = 0.1; Gc = 1/2;
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n = 2; w0 = 2*pi*10; G0 = 1/10; G1 = 1000; Gc = 0.45;
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W2 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
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#+end_src
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Let's first synthesize $H_1(s)$:
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#+begin_src matlab
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P = [W1 -W1;
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0 W2;
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1 -1];
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P = [ W1 0 1;
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-W1 W2 -1];
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#+end_src
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#+begin_src matlab :results output replace :exports both
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[K, ~, gamma, ~] = hinfsyn(P, 1, 1,'TOLGAM', 0.001, 'METHOD', 'lmi', 'DISPLAY', 'on');
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[L, ~, gamma, ~] = hinfsyn(P, 1, 1,'TOLGAM', 0.001, 'METHOD', 'lmi', 'DISPLAY', 'on');
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#+end_src
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#+begin_src matlab
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H1 = inv(1 + K);
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H1 = inv(1 + L);
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H2 = 1 - H1;
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#+end_src
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#+begin_src matlab :results output replace :exports results :tangle no
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zpk(H1)
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zpk(H2)
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#+end_src
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#+RESULTS:
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#+begin_example
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zpk(H1)
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ans =
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(s+2.115e07) (s+153.6) (s+4.613) (s^2 + 6.858s + 12.03)
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--------------------------------------------------------
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(s+2.117e07) (s^2 + 102.1s + 2732) (s^2 + 69.43s + 3271)
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zpk(H2)
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ans =
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20455 (s+3425) (s+3318) (s^2 + 46.58s + 813.2)
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--------------------------------------------------------
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(s+2.117e07) (s^2 + 102.1s + 2732) (s^2 + 69.43s + 3271)
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#+end_example
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#+begin_src matlab :exports none
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freqs = logspace(-2, 4, 1000);
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(H1, freqs, 'Hz'))), '-', 'DisplayName', '$H_1$');
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plot(freqs, abs(squeeze(freqresp(H2, freqs, 'Hz'))), '-', 'DisplayName', '$H_2$');
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set(gca,'ColorOrderIndex',1);
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plot(freqs, 1./abs(squeeze(freqresp(W1, freqs, 'Hz'))), '--', 'DisplayName', '$|W_1|^{-1}$');
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plot(freqs, 1./abs(squeeze(freqresp(W2, freqs, 'Hz'))), '--', 'DisplayName', '$|W_2|^{-1}$');
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set(gca,'ColorOrderIndex',1);
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plot(freqs, abs(squeeze(freqresp(H1, freqs, 'Hz'))), '-', 'DisplayName', '$|H_1|$');
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plot(freqs, abs(squeeze(freqresp(H2, freqs, 'Hz'))), '-', 'DisplayName', '$|H_2|$');
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plot(freqs, abs(squeeze(freqresp(L, freqs, 'Hz'))), 'k--', 'DisplayName', '$|L|$');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Magnitude');
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legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 2);
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legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 3);
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#+end_src
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** Adding feature in the filters
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@@ -1999,6 +2043,183 @@ There is no difference between " open-loop" shaping and "close-loop" shaping:
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- same obtained filter orders
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#+end_important
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** Integral Action
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*** Test
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#+begin_src matlab
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freqs = logspace(-2, 3, 1000);
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#+end_src
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\begin{equation}
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W_1(s) = \frac{W_{10}(s)}{s}
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\end{equation}
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with $W_{10}(0) \neq 0$
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#+begin_src matlab
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W10 = 0.1*(s+125.7)^2/(s+1.257)^2*(s + 0.0001)/(1 + s/1000);
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W1 = W10/s;
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#+end_src
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#+begin_src matlab
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n = 2; w0 = 2*pi*10; G0 = 1/10; G1 = 1000; Gc = 0.5;
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W2 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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set(gca,'ColorOrderIndex',1)
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plot(freqs, 1./abs(squeeze(freqresp(W1, freqs, 'Hz'))), '--', 'DisplayName', '$|W_1|^{-1}$');
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set(gca,'ColorOrderIndex',2)
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plot(freqs, 1./abs(squeeze(freqresp(W2, freqs, 'Hz'))), '--', 'DisplayName', '$|W_2|^{-1}$');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Magnitude');
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hold off;
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xlim([freqs(1), freqs(end)]);
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ylim([1e-4, 20]);
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xticks([0.1, 1, 10, 100, 1000]);
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leg = legend('location', 'southeast', 'FontSize', 8);
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leg.ItemTokenSize(1) = 18;
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#+end_src
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#+begin_src matlab
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V = 1;
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#+end_src
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#+begin_src matlab
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P = [ V*W10 W10;
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0 W2;
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-V -1];
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#+end_src
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And we do the $\mathcal{H}_\infty$ synthesis using the =hinfsyn= command.
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#+begin_src matlab :results output replace :exports both
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[H2, ~, gamma, ~] = hinfsyn(P, 1, 1,'TOLGAM', 0.001, 'METHOD', 'lmi', 'DISPLAY', 'on');
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#+end_src
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#+begin_src matlab
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H1 = 1 - H2;
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#+end_src
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#+begin_src matlab :exports none
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figure;
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tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
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% Magnitude
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ax1 = nexttile([2, 1]);
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hold on;
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set(gca,'ColorOrderIndex',1)
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plot(freqs, 1./abs(squeeze(freqresp(W1, freqs, 'Hz'))), '--', 'DisplayName', '$w_1$');
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set(gca,'ColorOrderIndex',2)
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plot(freqs, 1./abs(squeeze(freqresp(W2, freqs, 'Hz'))), '--', 'DisplayName', '$w_2$');
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set(gca,'ColorOrderIndex',1)
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plot(freqs, abs(squeeze(freqresp(H1, freqs, 'Hz'))), '-', 'DisplayName', '$H_1$');
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set(gca,'ColorOrderIndex',2)
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plot(freqs, abs(squeeze(freqresp(H2, freqs, 'Hz'))), '-', 'DisplayName', '$H_2$');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Magnitude');
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set(gca, 'XTickLabel',[]);
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ylim([1e-4, 20]);
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yticks([1e-4, 1e-3, 1e-2, 1e-1, 1, 1e1]);
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leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
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leg.ItemTokenSize(1) = 18;
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% Phase
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ax2 = nexttile;
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hold on;
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set(gca,'ColorOrderIndex',1)
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plot(freqs, 180/pi*phase(squeeze(freqresp(H1, freqs, 'Hz'))), '-');
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set(gca,'ColorOrderIndex',2)
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plot(freqs, 180/pi*phase(squeeze(freqresp(H2, freqs, 'Hz'))), '-');
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hold off;
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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set(gca, 'XScale', 'log');
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yticks([-180:90:180]);
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linkaxes([ax1,ax2],'x');
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xlim([freqs(1), freqs(end)]);
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#+end_src
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*** Example 6.7.3
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#+begin_src matlab
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n = 2; w0 = 2*pi*10; G0 = 1000; G1 = 0.1; Gc = 0.45;
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W1 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
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n = 2; w0 = 2*pi*10; G0 = 1/10; G1 = 1000; Gc = 0.45;
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W2 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
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#+end_src
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#+begin_src matlab
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V = 1/(1 + s/2/pi/100);
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#+end_src
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#+begin_src matlab
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V = W2;
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W2 = tf(1);
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#+end_src
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#+begin_src matlab
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P = [W1 -W1;
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0 W2;
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V 0];
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#+end_src
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#+begin_src matlab :results output replace :exports both
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[H2, ~, gamma, ~] = hinfsyn(P, 1, 1,'TOLGAM', 0.001, 'METHOD', 'ric', 'DISPLAY', 'on');
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#+end_src
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#+begin_src matlab
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H2 = H2*V;
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#+end_src
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#+begin_src matlab
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H1 = 1 - H2;
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#+end_src
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#+begin_src matlab :exports none
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figure;
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tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
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% Magnitude
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ax1 = nexttile([2, 1]);
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hold on;
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set(gca,'ColorOrderIndex',1)
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plot(freqs, 1./abs(squeeze(freqresp(W1, freqs, 'Hz'))), '--', 'DisplayName', '$w_1$');
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set(gca,'ColorOrderIndex',2)
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plot(freqs, 1./abs(squeeze(freqresp(W2, freqs, 'Hz'))), '--', 'DisplayName', '$w_2$');
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set(gca,'ColorOrderIndex',1)
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plot(freqs, abs(squeeze(freqresp(H1, freqs, 'Hz'))), '-', 'DisplayName', '$H_1$');
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set(gca,'ColorOrderIndex',2)
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plot(freqs, abs(squeeze(freqresp(H2, freqs, 'Hz'))), '-', 'DisplayName', '$H_2$');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Magnitude');
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set(gca, 'XTickLabel',[]);
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ylim([1e-4, 20]);
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yticks([1e-4, 1e-3, 1e-2, 1e-1, 1, 1e1]);
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leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
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leg.ItemTokenSize(1) = 18;
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% Phase
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ax2 = nexttile;
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hold on;
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set(gca,'ColorOrderIndex',1)
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plot(freqs, 180/pi*phase(squeeze(freqresp(H1, freqs, 'Hz'))), '-');
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set(gca,'ColorOrderIndex',2)
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plot(freqs, 180/pi*phase(squeeze(freqresp(H2, freqs, 'Hz'))), '-');
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hold off;
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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set(gca, 'XScale', 'log');
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yticks([-180:90:180]);
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linkaxes([ax1,ax2],'x');
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xlim([freqs(1), freqs(end)]);
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#+end_src
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* Impose a positive slope at DC or a negative slope at infinite frequency
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** Introduction :ignore:
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