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Thomas Dehaeze 2021-01-11 09:09:48 +01:00
parent 2285284e91
commit e02f522e81
4 changed files with 1580 additions and 1605 deletions
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149
gravimeter/script.m
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@ -171,7 +171,7 @@ plot(freqs, abs(squeeze(freqresp(Gx(i_out, i_in), freqs, 'Hz'))), 'color', [0,0,
'DisplayName', '$G_x(i,j)\ i \neq j$'); 'DisplayName', '$G_x(i,j)\ i \neq j$');
set(gca,'ColorOrderIndex',1) set(gca,'ColorOrderIndex',1)
for i_in_out = 1:3 for i_in_out = 1:3
plot(freqs, abs(squeeze(freqresp(Gx(i_in_out, i_in_out), freqs, 'Hz'))), 'DisplayName', sprintf('$G_x(%d,%d)$', i_in_out, i_in_out)); plot(freqs, abs(squeeze(freqresp(Gx(i_in_out, i_in_out), freqs, 'Hz'))), 'DisplayName', sprintf('$G_x(%d,%d)$', i_in_out, i_in_out));
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
@ -256,7 +256,7 @@ plot(freqs, abs(squeeze(freqresp(Gsvd(i_out, i_in), freqs, 'Hz'))), 'color', [0,
'DisplayName', '$G_x(i,j)\ i \neq j$'); 'DisplayName', '$G_x(i,j)\ i \neq j$');
set(gca,'ColorOrderIndex',1) set(gca,'ColorOrderIndex',1)
for i_in_out = 1:3 for i_in_out = 1:3
plot(freqs, abs(squeeze(freqresp(Gsvd(i_in_out, i_in_out), freqs, 'Hz'))), 'DisplayName', sprintf('$G_x(%d,%d)$', i_in_out, i_in_out)); plot(freqs, abs(squeeze(freqresp(Gsvd(i_in_out, i_in_out), freqs, 'Hz'))), 'DisplayName', sprintf('$G_x(%d,%d)$', i_in_out, i_in_out));
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
@ -329,14 +329,14 @@ ylim([1e-4, 1e2]);
RGA_svd = zeros(length(freqs), size(Gsvd,1), size(Gsvd,2)); RGA_svd = zeros(length(freqs), size(Gsvd,1), size(Gsvd,2));
Gsvd_inv = inv(Gsvd); Gsvd_inv = inv(Gsvd);
for f_i = 1:length(freqs) for f_i = 1:length(freqs)
RGA_svd(f_i, :, :) = abs(evalfr(Gsvd, j*2*pi*freqs(f_i)).*evalfr(Gsvd_inv, j*2*pi*freqs(f_i))'); RGA_svd(f_i, :, :) = abs(evalfr(Gsvd, j*2*pi*freqs(f_i)).*evalfr(Gsvd_inv, j*2*pi*freqs(f_i))');
end end
% Relative Gain Array for the decoupled plant using the Jacobian: % Relative Gain Array for the decoupled plant using the Jacobian:
RGA_x = zeros(length(freqs), size(Gx,1), size(Gx,2)); RGA_x = zeros(length(freqs), size(Gx,1), size(Gx,2));
Gx_inv = inv(Gx); Gx_inv = inv(Gx);
for f_i = 1:length(freqs) for f_i = 1:length(freqs)
RGA_x(f_i, :, :) = abs(evalfr(Gx, j*2*pi*freqs(f_i)).*evalfr(Gx_inv, j*2*pi*freqs(f_i))'); RGA_x(f_i, :, :) = abs(evalfr(Gx, j*2*pi*freqs(f_i)).*evalfr(Gx_inv, j*2*pi*freqs(f_i))');
end end
figure; figure;
@ -356,8 +356,8 @@ plot(freqs, RGA_svd(:, 1, 2), '--', 'color', [0 0 0 0.2], ...
plot(freqs, RGA_svd(:, 1, 1), 'k-', ... plot(freqs, RGA_svd(:, 1, 1), 'k-', ...
'DisplayName', '$RGA_{SVD}(i,i)$'); 'DisplayName', '$RGA_{SVD}(i,i)$');
for ch_i = 1:3 for ch_i = 1:3
plot(freqs, RGA_svd(:, ch_i, ch_i), 'k-', ... plot(freqs, RGA_svd(:, ch_i, ch_i), 'k-', ...
'HandleVisibility', 'off'); 'HandleVisibility', 'off');
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
@ -378,8 +378,8 @@ plot(freqs, RGA_x(:, 1, 2), '--', 'color', [0 0 0 0.2], ...
plot(freqs, RGA_x(:, 1, 1), 'k-', ... plot(freqs, RGA_x(:, 1, 1), 'k-', ...
'DisplayName', '$RGA_{X}(i,i)$'); 'DisplayName', '$RGA_{X}(i,i)$');
for ch_i = 1:3 for ch_i = 1:3
plot(freqs, RGA_x(:, ch_i, ch_i), 'k-', ... plot(freqs, RGA_x(:, ch_i, ch_i), 'k-', ...
'HandleVisibility', 'off'); 'HandleVisibility', 'off');
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
@ -406,14 +406,14 @@ ylim([1e-5, 1e1]);
RGA_svd = zeros(size(Gsvd,1), size(Gsvd,2), length(freqs)); RGA_svd = zeros(size(Gsvd,1), size(Gsvd,2), length(freqs));
Gsvd_inv = inv(Gsvd); Gsvd_inv = inv(Gsvd);
for f_i = 1:length(freqs) for f_i = 1:length(freqs)
RGA_svd(:, :, f_i) = abs(evalfr(Gsvd, j*2*pi*freqs(f_i)).*evalfr(Gsvd_inv, j*2*pi*freqs(f_i))'); RGA_svd(:, :, f_i) = abs(evalfr(Gsvd, j*2*pi*freqs(f_i)).*evalfr(Gsvd_inv, j*2*pi*freqs(f_i))');
end end
% Relative Gain Array for the decoupled plant using the Jacobian: % Relative Gain Array for the decoupled plant using the Jacobian:
RGA_x = zeros(size(Gx,1), size(Gx,2), length(freqs)); RGA_x = zeros(size(Gx,1), size(Gx,2), length(freqs));
Gx_inv = inv(Gx); Gx_inv = inv(Gx);
for f_i = 1:length(freqs) for f_i = 1:length(freqs)
RGA_x(:, :, f_i) = abs(evalfr(Gx, j*2*pi*freqs(f_i)).*evalfr(Gx_inv, j*2*pi*freqs(f_i))'); RGA_x(:, :, f_i) = abs(evalfr(Gx, j*2*pi*freqs(f_i)).*evalfr(Gx_inv, j*2*pi*freqs(f_i))');
end end
RGA_num_svd = squeeze(sum(sum(RGA_svd - eye(3)))); RGA_num_svd = squeeze(sum(sum(RGA_svd - eye(3))));
@ -448,8 +448,8 @@ plot(freqs, abs(squeeze(freqresp(Gsvd(1, 2), freqs, 'Hz'))), 'color', [0,0,0,0.5
'DisplayName', '$G_{SVD}(i,j),\ i \neq j$'); 'DisplayName', '$G_{SVD}(i,j),\ i \neq j$');
set(gca,'ColorOrderIndex',1) set(gca,'ColorOrderIndex',1)
for ch_i = 1:3 for ch_i = 1:3
plot(freqs, abs(squeeze(freqresp(Gsvd(ch_i, ch_i), freqs, 'Hz'))), ... plot(freqs, abs(squeeze(freqresp(Gsvd(ch_i, ch_i), freqs, 'Hz'))), ...
'DisplayName', sprintf('$G_{SVD}(%i,%i)$', ch_i, ch_i)); 'DisplayName', sprintf('$G_{SVD}(%i,%i)$', ch_i, ch_i));
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
@ -461,7 +461,7 @@ ylim([1e-8, 1e0])
ax2 = nexttile; ax2 = nexttile;
hold on; hold on;
for ch_i = 1:3 for ch_i = 1:3
plot(freqs, 180/pi*angle(squeeze(freqresp(Gsvd(ch_i, ch_i), freqs, 'Hz')))); plot(freqs, 180/pi*angle(squeeze(freqresp(Gsvd(ch_i, ch_i), freqs, 'Hz'))));
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
@ -558,16 +558,16 @@ ax1 = nexttile([2, 1]);
hold on; hold on;
plot(freqs, abs(squeeze(freqresp(L_svd(1, 1), freqs, 'Hz'))), 'DisplayName', '$L_{SVD}(i,i)$'); plot(freqs, abs(squeeze(freqresp(L_svd(1, 1), freqs, 'Hz'))), 'DisplayName', '$L_{SVD}(i,i)$');
for i_in_out = 2:3 for i_in_out = 2:3
set(gca,'ColorOrderIndex',1) set(gca,'ColorOrderIndex',1)
plot(freqs, abs(squeeze(freqresp(L_svd(i_in_out, i_in_out), freqs, 'Hz'))), 'HandleVisibility', 'off'); plot(freqs, abs(squeeze(freqresp(L_svd(i_in_out, i_in_out), freqs, 'Hz'))), 'HandleVisibility', 'off');
end end
set(gca,'ColorOrderIndex',2) set(gca,'ColorOrderIndex',2)
plot(freqs, abs(squeeze(freqresp(L_cen(1, 1), freqs, 'Hz'))), ... plot(freqs, abs(squeeze(freqresp(L_cen(1, 1), freqs, 'Hz'))), ...
'DisplayName', '$L_{J}(i,i)$'); 'DisplayName', '$L_{J}(i,i)$');
for i_in_out = 2:3 for i_in_out = 2:3
set(gca,'ColorOrderIndex',2) set(gca,'ColorOrderIndex',2)
plot(freqs, abs(squeeze(freqresp(L_cen(i_in_out, i_in_out), freqs, 'Hz'))), 'HandleVisibility', 'off'); plot(freqs, abs(squeeze(freqresp(L_cen(i_in_out, i_in_out), freqs, 'Hz'))), 'HandleVisibility', 'off');
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
@ -579,13 +579,13 @@ ylim([5e-2, 2e3])
ax2 = nexttile; ax2 = nexttile;
hold on; hold on;
for i_in_out = 1:3 for i_in_out = 1:3
set(gca,'ColorOrderIndex',1) set(gca,'ColorOrderIndex',1)
plot(freqs, 180/pi*angle(squeeze(freqresp(L_svd(i_in_out, i_in_out), freqs, 'Hz')))); plot(freqs, 180/pi*angle(squeeze(freqresp(L_svd(i_in_out, i_in_out), freqs, 'Hz'))));
end end
set(gca,'ColorOrderIndex',2) set(gca,'ColorOrderIndex',2)
for i_in_out = 1:3 for i_in_out = 1:3
set(gca,'ColorOrderIndex',2) set(gca,'ColorOrderIndex',2)
plot(freqs, 180/pi*angle(squeeze(freqresp(L_cen(i_in_out, i_in_out), freqs, 'Hz')))); plot(freqs, 180/pi*angle(squeeze(freqresp(L_cen(i_in_out, i_in_out), freqs, 'Hz'))));
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
@ -819,7 +819,7 @@ plot(freqs, abs(squeeze(freqresp(GM(i_out, i_in), freqs, 'Hz'))), 'color', [0,0,
'DisplayName', '$G_x(i,j)\ i \neq j$'); 'DisplayName', '$G_x(i,j)\ i \neq j$');
set(gca,'ColorOrderIndex',1) set(gca,'ColorOrderIndex',1)
for i_in_out = 1:3 for i_in_out = 1:3
plot(freqs, abs(squeeze(freqresp(GM(i_in_out, i_in_out), freqs, 'Hz'))), 'DisplayName', sprintf('$G_x(%d,%d)$', i_in_out, i_in_out)); plot(freqs, abs(squeeze(freqresp(GM(i_in_out, i_in_out), freqs, 'Hz'))), 'DisplayName', sprintf('$G_x(%d,%d)$', i_in_out, i_in_out));
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
@ -866,7 +866,7 @@ plot(freqs, abs(squeeze(freqresp(GK(i_out, i_in), freqs, 'Hz'))), 'color', [0,0,
'DisplayName', '$G_x(i,j)\ i \neq j$'); 'DisplayName', '$G_x(i,j)\ i \neq j$');
set(gca,'ColorOrderIndex',1) set(gca,'ColorOrderIndex',1)
for i_in_out = 1:3 for i_in_out = 1:3
plot(freqs, abs(squeeze(freqresp(GK(i_in_out, i_in_out), freqs, 'Hz'))), 'DisplayName', sprintf('$G_x(%d,%d)$', i_in_out, i_in_out)); plot(freqs, abs(squeeze(freqresp(GK(i_in_out, i_in_out), freqs, 'Hz'))), 'DisplayName', sprintf('$G_x(%d,%d)$', i_in_out, i_in_out));
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
@ -930,7 +930,7 @@ plot(freqs, abs(squeeze(freqresp(GKM(i_out, i_in), freqs, 'Hz'))), 'color', [0,0
'DisplayName', '$G_x(i,j)\ i \neq j$'); 'DisplayName', '$G_x(i,j)\ i \neq j$');
set(gca,'ColorOrderIndex',1) set(gca,'ColorOrderIndex',1)
for i_in_out = 1:3 for i_in_out = 1:3
plot(freqs, abs(squeeze(freqresp(GKM(i_in_out, i_in_out), freqs, 'Hz'))), 'DisplayName', sprintf('$G_x(%d,%d)$', i_in_out, i_in_out)); plot(freqs, abs(squeeze(freqresp(GKM(i_in_out, i_in_out), freqs, 'Hz'))), 'DisplayName', sprintf('$G_x(%d,%d)$', i_in_out, i_in_out));
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
@ -938,11 +938,12 @@ xlabel('Frequency [Hz]'); ylabel('Magnitude');
legend('location', 'southeast'); legend('location', 'southeast');
ylim([1e-8, 1e0]); ylim([1e-8, 1e0]);
% SVD decoupling performances :noexport: % SVD decoupling performances
% As the SVD is applied on a *real approximation* of the plant dynamics at a frequency $\omega_0$, it is foreseen that the effectiveness of the decoupling depends on the validity of the real approximation.
% Let's do the SVD decoupling on a plant that is mostly real (low damping) and one with a large imaginary part (larger damping).
la = l/2; % Position of Act. [m] % Start with small damping, the obtained diagonal and off-diagonal terms are shown in Figure [[fig:gravimeter_svd_low_damping]].
ha = 0; % Position of Act. [m]
c = 2e1; % Actuator Damping [N/(m/s)] c = 2e1; % Actuator Damping [N/(m/s)]
@ -970,6 +971,37 @@ H1 = pinv(D*real(H1'*diag(exp(j*angle(diag(H1*D*H1.'))/2))));
[U,S,V] = svd(H1); [U,S,V] = svd(H1);
Gsvd = inv(U)*G*inv(V'); Gsvd = inv(U)*G*inv(V');
figure;
% Magnitude
hold on;
for i_in = 1:3
for i_out = [1:i_in-1, i_in+1:3]
plot(freqs, abs(squeeze(freqresp(Gsvd(i_out, i_in), freqs, 'Hz'))), 'color', [0,0,0,0.2], ...
'HandleVisibility', 'off');
end
end
plot(freqs, abs(squeeze(freqresp(Gsvd(i_out, i_in), freqs, 'Hz'))), 'color', [0,0,0,0.2], ...
'DisplayName', '$G_{svd}(i,j)\ i \neq j$');
set(gca,'ColorOrderIndex',1)
for i_in_out = 1:3
plot(freqs, abs(squeeze(freqresp(Gsvd(i_in_out, i_in_out), freqs, 'Hz'))), 'DisplayName', sprintf('$G_{svd}(%d,%d)$', i_in_out, i_in_out));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('Magnitude');
legend('location', 'northwest');
ylim([1e-8, 1e0]);
% #+name: fig:gravimeter_svd_low_damping
% #+caption: Diagonal and off-diagonal term when decoupling with SVD on the gravimeter with small damping
% #+RESULTS:
% [[file:figs/gravimeter_svd_low_damping.png]]
% Now take a larger damping, the obtained diagonal and off-diagonal terms are shown in Figure [[fig:gravimeter_svd_high_damping]].
c = 5e2; % Actuator Damping [N/(m/s)] c = 5e2; % Actuator Damping [N/(m/s)]
%% Name of the Simulink File %% Name of the Simulink File
@ -996,63 +1028,6 @@ H1 = pinv(D*real(H1'*diag(exp(j*angle(diag(H1*D*H1.'))/2))));
[U,S,V] = svd(H1); [U,S,V] = svd(H1);
Gsvdd = inv(U)*G*inv(V'); Gsvdd = inv(U)*G*inv(V');
JMa = [1 0 -h/2
0 1 l/2
1 0 h/2
0 1 0];
JMt = [1 0 -ha
0 1 la
0 1 -la];
GM = pinv(JMa)*G*pinv(JMt');
GM.InputName = {'Fx', 'Fy', 'Mz'};
GM.OutputName = {'Dx', 'Dy', 'Rz'};
figure;
% Magnitude
hold on;
for i_in = 1:3
for i_out = [1:i_in-1, i_in+1:3]
plot(freqs, abs(squeeze(freqresp(GM(i_out, i_in), freqs, 'Hz'))), 'color', [0,0,0,0.2], ...
'HandleVisibility', 'off');
end
end
plot(freqs, abs(squeeze(freqresp(GM(i_out, i_in), freqs, 'Hz'))), 'color', [0,0,0,0.2], ...
'DisplayName', '$G_x(i,j)\ i \neq j$');
set(gca,'ColorOrderIndex',1)
for i_in_out = 1:3
plot(freqs, abs(squeeze(freqresp(GM(i_in_out, i_in_out), freqs, 'Hz'))), 'DisplayName', sprintf('$G_x(%d,%d)$', i_in_out, i_in_out));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('Magnitude');
legend('location', 'southeast');
ylim([1e-8, 1e0]);
figure;
% Magnitude
hold on;
for i_in = 1:3
for i_out = [1:i_in-1, i_in+1:3]
plot(freqs, abs(squeeze(freqresp(Gsvd(i_out, i_in), freqs, 'Hz'))), 'color', [0,0,0,0.2], ...
'HandleVisibility', 'off');
end
end
plot(freqs, abs(squeeze(freqresp(Gsvd(i_out, i_in), freqs, 'Hz'))), 'color', [0,0,0,0.2], ...
'DisplayName', '$G_x(i,j)\ i \neq j$');
set(gca,'ColorOrderIndex',1)
for i_in_out = 1:3
plot(freqs, abs(squeeze(freqresp(Gsvd(i_in_out, i_in_out), freqs, 'Hz'))), 'DisplayName', sprintf('$G_x(%d,%d)$', i_in_out, i_in_out));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('Magnitude');
legend('location', 'southeast');
ylim([1e-8, 1e0]);
figure; figure;
% Magnitude % Magnitude
@ -1064,13 +1039,13 @@ for i_in = 1:3
end end
end end
plot(freqs, abs(squeeze(freqresp(Gsvdd(i_out, i_in), freqs, 'Hz'))), 'color', [0,0,0,0.2], ... plot(freqs, abs(squeeze(freqresp(Gsvdd(i_out, i_in), freqs, 'Hz'))), 'color', [0,0,0,0.2], ...
'DisplayName', '$G_x(i,j)\ i \neq j$'); 'DisplayName', '$G_{svd}(i,j)\ i \neq j$');
set(gca,'ColorOrderIndex',1) set(gca,'ColorOrderIndex',1)
for i_in_out = 1:3 for i_in_out = 1:3
plot(freqs, abs(squeeze(freqresp(Gsvdd(i_in_out, i_in_out), freqs, 'Hz'))), 'DisplayName', sprintf('$G_x(%d,%d)$', i_in_out, i_in_out)); plot(freqs, abs(squeeze(freqresp(Gsvdd(i_in_out, i_in_out), freqs, 'Hz'))), 'DisplayName', sprintf('$G_{svd}(%d,%d)$', i_in_out, i_in_out));
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('Magnitude'); xlabel('Frequency [Hz]'); ylabel('Magnitude');
legend('location', 'southeast'); legend('location', 'northwest');
ylim([1e-8, 1e0]); ylim([1e-8, 1e0]);

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index.html
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stewart_platform/script.m
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@ -108,7 +108,7 @@ plot(freqs, abs(squeeze(freqresp(Gu(i_out, i_in), freqs, 'Hz'))), 'color', [0,0,
'DisplayName', '$G_u(i,j)\ i \neq j$'); 'DisplayName', '$G_u(i,j)\ i \neq j$');
set(gca,'ColorOrderIndex',1) set(gca,'ColorOrderIndex',1)
for i_in_out = 1:6 for i_in_out = 1:6
plot(freqs, abs(squeeze(freqresp(Gu(i_in_out, i_in_out), freqs, 'Hz'))), 'DisplayName', sprintf('$G_u(%d,%d)$', i_in_out, i_in_out)); plot(freqs, abs(squeeze(freqresp(Gu(i_in_out, i_in_out), freqs, 'Hz'))), 'DisplayName', sprintf('$G_u(%d,%d)$', i_in_out, i_in_out));
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
@ -246,21 +246,21 @@ ylim([1e-3, 1e3]);
RGA_coupled = zeros(length(freqs), size(Gu,1), size(Gu,2)); RGA_coupled = zeros(length(freqs), size(Gu,1), size(Gu,2));
Gu_inv = inv(Gu); Gu_inv = inv(Gu);
for f_i = 1:length(freqs) for f_i = 1:length(freqs)
RGA_coupled(f_i, :, :) = abs(evalfr(Gu, j*2*pi*freqs(f_i)).*evalfr(Gu_inv, j*2*pi*freqs(f_i))'); RGA_coupled(f_i, :, :) = abs(evalfr(Gu, j*2*pi*freqs(f_i)).*evalfr(Gu_inv, j*2*pi*freqs(f_i))');
end end
% Relative Gain Array for the decoupled plant using SVD: % Relative Gain Array for the decoupled plant using SVD:
RGA_svd = zeros(length(freqs), size(Gsvd,1), size(Gsvd,2)); RGA_svd = zeros(length(freqs), size(Gsvd,1), size(Gsvd,2));
Gsvd_inv = inv(Gsvd); Gsvd_inv = inv(Gsvd);
for f_i = 1:length(freqs) for f_i = 1:length(freqs)
RGA_svd(f_i, :, :) = abs(evalfr(Gsvd, j*2*pi*freqs(f_i)).*evalfr(Gsvd_inv, j*2*pi*freqs(f_i))'); RGA_svd(f_i, :, :) = abs(evalfr(Gsvd, j*2*pi*freqs(f_i)).*evalfr(Gsvd_inv, j*2*pi*freqs(f_i))');
end end
% Relative Gain Array for the decoupled plant using the Jacobian: % Relative Gain Array for the decoupled plant using the Jacobian:
RGA_x = zeros(length(freqs), size(Gx,1), size(Gx,2)); RGA_x = zeros(length(freqs), size(Gx,1), size(Gx,2));
Gx_inv = inv(Gx); Gx_inv = inv(Gx);
for f_i = 1:length(freqs) for f_i = 1:length(freqs)
RGA_x(f_i, :, :) = abs(evalfr(Gx, j*2*pi*freqs(f_i)).*evalfr(Gx_inv, j*2*pi*freqs(f_i))'); RGA_x(f_i, :, :) = abs(evalfr(Gx, j*2*pi*freqs(f_i)).*evalfr(Gx_inv, j*2*pi*freqs(f_i))');
end end
figure; figure;
@ -280,8 +280,8 @@ plot(freqs, RGA_svd(:, 1, 2), '--', 'color', [0 0 0 0.2], ...
plot(freqs, RGA_svd(:, 1, 1), 'k-', ... plot(freqs, RGA_svd(:, 1, 1), 'k-', ...
'DisplayName', '$RGA_{SVD}(i,i)$'); 'DisplayName', '$RGA_{SVD}(i,i)$');
for ch_i = 1:6 for ch_i = 1:6
plot(freqs, RGA_svd(:, ch_i, ch_i), 'k-', ... plot(freqs, RGA_svd(:, ch_i, ch_i), 'k-', ...
'HandleVisibility', 'off'); 'HandleVisibility', 'off');
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
@ -302,8 +302,8 @@ plot(freqs, RGA_x(:, 1, 2), '--', 'color', [0 0 0 0.2], ...
plot(freqs, RGA_x(:, 1, 1), 'k-', ... plot(freqs, RGA_x(:, 1, 1), 'k-', ...
'DisplayName', '$RGA_{X}(i,i)$'); 'DisplayName', '$RGA_{X}(i,i)$');
for ch_i = 1:6 for ch_i = 1:6
plot(freqs, RGA_x(:, ch_i, ch_i), 'k-', ... plot(freqs, RGA_x(:, ch_i, ch_i), 'k-', ...
'HandleVisibility', 'off'); 'HandleVisibility', 'off');
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
@ -335,8 +335,8 @@ plot(freqs, abs(squeeze(freqresp(Gsvd(1, 2), freqs, 'Hz'))), 'color', [0,0,0,0.5
'DisplayName', '$G_{SVD}(i,j),\ i \neq j$'); 'DisplayName', '$G_{SVD}(i,j),\ i \neq j$');
set(gca,'ColorOrderIndex',1) set(gca,'ColorOrderIndex',1)
for ch_i = 1:6 for ch_i = 1:6
plot(freqs, abs(squeeze(freqresp(Gsvd(ch_i, ch_i), freqs, 'Hz'))), ... plot(freqs, abs(squeeze(freqresp(Gsvd(ch_i, ch_i), freqs, 'Hz'))), ...
'DisplayName', sprintf('$G_{SVD}(%i,%i)$', ch_i, ch_i)); 'DisplayName', sprintf('$G_{SVD}(%i,%i)$', ch_i, ch_i));
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
@ -348,7 +348,7 @@ ylim([1e-1, 1e5])
ax2 = nexttile; ax2 = nexttile;
hold on; hold on;
for ch_i = 1:6 for ch_i = 1:6
plot(freqs, 180/pi*angle(squeeze(freqresp(Gsvd(ch_i, ch_i), freqs, 'Hz')))); plot(freqs, 180/pi*angle(squeeze(freqresp(Gsvd(ch_i, ch_i), freqs, 'Hz'))));
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
@ -450,16 +450,16 @@ ax1 = nexttile([2, 1]);
hold on; hold on;
plot(freqs, abs(squeeze(freqresp(L_svd(1, 1), freqs, 'Hz'))), 'DisplayName', '$L_{SVD}(i,i)$'); plot(freqs, abs(squeeze(freqresp(L_svd(1, 1), freqs, 'Hz'))), 'DisplayName', '$L_{SVD}(i,i)$');
for i_in_out = 2:6 for i_in_out = 2:6
set(gca,'ColorOrderIndex',1) set(gca,'ColorOrderIndex',1)
plot(freqs, abs(squeeze(freqresp(L_svd(i_in_out, i_in_out), freqs, 'Hz'))), 'HandleVisibility', 'off'); plot(freqs, abs(squeeze(freqresp(L_svd(i_in_out, i_in_out), freqs, 'Hz'))), 'HandleVisibility', 'off');
end end
set(gca,'ColorOrderIndex',2) set(gca,'ColorOrderIndex',2)
plot(freqs, abs(squeeze(freqresp(L_cen(1, 1), freqs, 'Hz'))), ... plot(freqs, abs(squeeze(freqresp(L_cen(1, 1), freqs, 'Hz'))), ...
'DisplayName', '$L_{J}(i,i)$'); 'DisplayName', '$L_{J}(i,i)$');
for i_in_out = 2:6 for i_in_out = 2:6
set(gca,'ColorOrderIndex',2) set(gca,'ColorOrderIndex',2)
plot(freqs, abs(squeeze(freqresp(L_cen(i_in_out, i_in_out), freqs, 'Hz'))), 'HandleVisibility', 'off'); plot(freqs, abs(squeeze(freqresp(L_cen(i_in_out, i_in_out), freqs, 'Hz'))), 'HandleVisibility', 'off');
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
@ -471,13 +471,13 @@ ylim([5e-2, 2e3])
ax2 = nexttile; ax2 = nexttile;
hold on; hold on;
for i_in_out = 1:6 for i_in_out = 1:6
set(gca,'ColorOrderIndex',1) set(gca,'ColorOrderIndex',1)
plot(freqs, 180/pi*angle(squeeze(freqresp(L_svd(i_in_out, i_in_out), freqs, 'Hz')))); plot(freqs, 180/pi*angle(squeeze(freqresp(L_svd(i_in_out, i_in_out), freqs, 'Hz'))));
end end
set(gca,'ColorOrderIndex',2) set(gca,'ColorOrderIndex',2)
for i_in_out = 1:6 for i_in_out = 1:6
set(gca,'ColorOrderIndex',2) set(gca,'ColorOrderIndex',2)
plot(freqs, 180/pi*angle(squeeze(freqresp(L_cen(i_in_out, i_in_out), freqs, 'Hz')))); plot(freqs, 180/pi*angle(squeeze(freqresp(L_cen(i_in_out, i_in_out), freqs, 'Hz'))));
end end
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');