Change all the organization of the files
This commit is contained in:
241
to-order/active_damping_uniaxial/matlab/dvf.m
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241
to-order/active_damping_uniaxial/matlab/dvf.m
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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open 'simscape/sim_nano_station_id.slx'
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% Control Design
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% Let's load the undamped plant:
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load('./active_damping/mat/plants.mat', 'G');
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% Let's look at the transfer function from actuator forces in the nano-hexapod to the measured velocity of the nano-hexapod platform in the direction of the corresponding actuator for all 6 pairs of actuator/sensor (figure [[fig:dvf_plant]]).
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freqs = logspace(0, 3, 1000);
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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for i=1:6
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plot(freqs, abs(squeeze(freqresp(G.G_geoph(['Vm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
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ax2 = subplot(2, 1, 2);
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hold on;
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for i=1:6
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plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_geoph(['Vm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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linkaxes([ax1,ax2],'x');
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% #+NAME: fig:dvf_plant
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% #+CAPTION: Transfer function from forces applied in the legs to leg velocity sensor ([[./figs/dvf_plant.png][png]], [[./figs/dvf_plant.pdf][pdf]])
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% [[file:figs/dvf_plant.png]]
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% The controller is defined below and the obtained loop gain is shown in figure [[fig:dvf_open_loop_gain]].
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K_dvf = tf(3e4);
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freqs = logspace(0, 3, 1000);
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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for i=1:6
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plot(freqs, abs(squeeze(freqresp(K_dvf*G.G_geoph(['Vm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
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ax2 = subplot(2, 1, 2);
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hold on;
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for i=1:6
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plot(freqs, 180/pi*angle(squeeze(freqresp(K_dvf*G.G_geoph(['Vm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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linkaxes([ax1,ax2],'x');
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% Identification of the damped plant
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% Let's initialize the system prior to identification.
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initializeGround();
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initializeGranite();
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initializeTy();
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initializeRy();
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initializeRz();
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initializeMicroHexapod();
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initializeAxisc();
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initializeMirror();
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initializeNanoHexapod(struct('actuator', 'piezo'));
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initializeSample(struct('mass', 50));
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% And initialize the controllers.
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K = tf(zeros(6));
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save('./mat/controllers.mat', 'K', '-append');
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K_iff = tf(zeros(6));
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save('./mat/controllers.mat', 'K_iff', '-append');
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K_rmc = tf(zeros(6));
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save('./mat/controllers.mat', 'K_rmc', '-append');
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K_dvf = -K_dvf*eye(6);
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save('./mat/controllers.mat', 'K_dvf', '-append');
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% We identify the system dynamics now that the RMC controller is ON.
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G_dvf = identifyPlant();
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% And we save the damped plant for further analysis.
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save('./active_damping/mat/plants.mat', 'G_dvf', '-append');
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% Sensitivity to disturbances
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freqs = logspace(0, 3, 1000);
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figure;
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subplot(2, 1, 1);
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title('$D_g$ to $D$');
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hold on;
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plot(freqs, abs(squeeze(freqresp(G.G_gm('Dx', 'Dgx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / D_{g,x}\right|$');
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plot(freqs, abs(squeeze(freqresp(G.G_gm('Dy', 'Dgy'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / D_{g,y}\right|$');
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plot(freqs, abs(squeeze(freqresp(G.G_gm('Dz', 'Dgz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / D_{g,z}\right|$');
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set(gca,'ColorOrderIndex',1);
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plot(freqs, abs(squeeze(freqresp(G_dvf.G_gm('Dx', 'Dgx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G_dvf.G_gm('Dy', 'Dgy'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G_dvf.G_gm('Dz', 'Dgz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]');
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legend('location', 'northeast');
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subplot(2, 1, 2);
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title('$F_s$ to $D$');
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hold on;
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plot(freqs, abs(squeeze(freqresp(G.G_fs('Dx', 'Fsx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{s,x}\right|$');
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plot(freqs, abs(squeeze(freqresp(G.G_fs('Dy', 'Fsy'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / F_{s,y}\right|$');
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plot(freqs, abs(squeeze(freqresp(G.G_fs('Dz', 'Fsz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{s,z}\right|$');
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set(gca,'ColorOrderIndex',1);
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plot(freqs, abs(squeeze(freqresp(G_dvf.G_fs('Dx', 'Fsx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G_dvf.G_fs('Dy', 'Fsy'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G_dvf.G_fs('Dz', 'Fsz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
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legend('location', 'northeast');
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% #+NAME: fig:sensitivity_dist_dvf
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% #+CAPTION: Sensitivity to disturbance once the DVF controller is applied to the system ([[./figs/sensitivity_dist_dvf.png][png]], [[./figs/sensitivity_dist_dvf.pdf][pdf]])
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% [[file:figs/sensitivity_dist_dvf.png]]
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freqs = logspace(0, 3, 1000);
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(G.G_dist('Dz', 'Frzz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{rz, z}\right|$');
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plot(freqs, abs(squeeze(freqresp(G.G_dist('Dz', 'Ftyz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{ty, z}\right|$');
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plot(freqs, abs(squeeze(freqresp(G.G_dist('Dx', 'Ftyx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{ty, x}\right|$');
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set(gca,'ColorOrderIndex',1);
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plot(freqs, abs(squeeze(freqresp(G_dvf.G_dist('Dz', 'Frzz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G_dvf.G_dist('Dz', 'Ftyz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G_dvf.G_dist('Dx', 'Ftyx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
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legend('location', 'northeast');
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% Damped Plant
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freqs = logspace(0, 3, 1000);
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figure;
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ax1 = subplot(2, 2, 1);
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hold on;
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plot(freqs, abs(squeeze(freqresp(G.G_cart('Dx', 'Fnx'), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G.G_cart('Dy', 'Fny'), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G.G_cart('Dz', 'Fnz'), freqs, 'Hz'))));
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set(gca,'ColorOrderIndex',1);
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plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), '--');
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plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Dy', 'Fny'), freqs, 'Hz'))), '--');
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plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), '--');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
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ax2 = subplot(2, 2, 2);
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hold on;
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plot(freqs, abs(squeeze(freqresp(G.G_cart('Rx', 'Mnx'), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G.G_cart('Ry', 'Mny'), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G.G_cart('Rz', 'Mnz'), freqs, 'Hz'))));
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set(gca,'ColorOrderIndex',1);
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plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), '--');
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plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Ry', 'Mny'), freqs, 'Hz'))), '--');
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plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), '--');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [rad/(Nm)]'); xlabel('Frequency [Hz]');
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ax3 = subplot(2, 2, 3);
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hold on;
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plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{n,x}\right|$');
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plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dy', 'Fny'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / F_{n,y}\right|$');
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plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{n,z}\right|$');
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set(gca,'ColorOrderIndex',1);
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plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
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plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Dy', 'Fny'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
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plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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legend('location', 'northwest');
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ax4 = subplot(2, 2, 4);
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hold on;
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plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), 'DisplayName', '$\left|R_x / M_{n,x}\right|$');
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plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Ry', 'Mny'), freqs, 'Hz'))), 'DisplayName', '$\left|R_y / M_{n,y}\right|$');
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plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), 'DisplayName', '$\left|R_z / M_{n,z}\right|$');
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set(gca,'ColorOrderIndex',1);
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plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
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plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Ry', 'Mny'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
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plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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legend('location', 'northwest');
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linkaxes([ax1,ax2,ax3,ax4],'x');
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281
to-order/active_damping_uniaxial/matlab/iff.m
Normal file
281
to-order/active_damping_uniaxial/matlab/iff.m
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@@ -0,0 +1,281 @@
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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open 'simscape/sim_nano_station_id.slx'
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% Control Design
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% Let's load the undamped plant:
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load('./active_damping/mat/plants.mat', 'G');
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% Let's look at the transfer function from actuator forces in the nano-hexapod to the force sensor in the nano-hexapod legs for all 6 pairs of actuator/sensor (figure [[fig:iff_plant]]).
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freqs = logspace(0, 3, 1000);
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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for i=1:6
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plot(freqs, abs(squeeze(freqresp(G.G_iff(['Fm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
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ax2 = subplot(2, 1, 2);
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hold on;
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for i=1:6
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plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_iff(['Fm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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linkaxes([ax1,ax2],'x');
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% #+NAME: fig:iff_plant
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% #+CAPTION: Transfer function from forces applied in the legs to force sensor ([[./figs/iff_plant.png][png]], [[./figs/iff_plant.pdf][pdf]])
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% [[file:figs/iff_plant.png]]
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% The controller for each pair of actuator/sensor is:
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K_iff = -1000/s;
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% The corresponding loop gains are shown in figure [[fig:iff_open_loop]].
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freqs = logspace(0, 3, 1000);
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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for i=1:6
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plot(freqs, abs(squeeze(freqresp(K_iff*G.G_iff(['Fm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
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ax2 = subplot(2, 1, 2);
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hold on;
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for i=1:6
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plot(freqs, 180/pi*angle(squeeze(freqresp(K_iff*G.G_iff(['Fm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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||||
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linkaxes([ax1,ax2],'x');
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% Identification of the damped plant
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% Let's initialize the system prior to identification.
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||||
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initializeGround();
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initializeGranite();
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initializeTy();
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initializeRy();
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initializeRz();
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initializeMicroHexapod();
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initializeAxisc();
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initializeMirror();
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initializeNanoHexapod(struct('actuator', 'piezo'));
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initializeSample(struct('mass', 50));
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% All the controllers are set to 0.
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K = tf(zeros(6));
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save('./mat/controllers.mat', 'K', '-append');
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K_iff = -K_iff*eye(6);
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save('./mat/controllers.mat', 'K_iff', '-append');
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K_rmc = tf(zeros(6));
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save('./mat/controllers.mat', 'K_rmc', '-append');
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K_dvf = tf(zeros(6));
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save('./mat/controllers.mat', 'K_dvf', '-append');
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% We identify the system dynamics now that the IFF controller is ON.
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G_iff = identifyPlant();
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% And we save the damped plant for further analysis
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save('./active_damping/mat/plants.mat', 'G_iff', '-append');
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||||
% Sensitivity to disturbances
|
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% As shown on figure [[fig:sensitivity_dist_iff]]:
|
||||
% - The top platform of the nano-hexapod how behaves as a "free-mass".
|
||||
% - The transfer function from direct forces $F_s$ to the relative displacement $D$ is equivalent to the one of an isolated mass.
|
||||
% - The transfer function from ground motion $D_g$ to the relative displacement $D$ tends to the transfer function from $D_g$ to the displacement of the granite (the sample is being isolated thanks to IFF).
|
||||
% However, as the goal is to make the relative displacement $D$ as small as possible (e.g. to make the sample motion follows the granite motion), this is not a good thing.
|
||||
|
||||
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
|
||||
subplot(2, 1, 1);
|
||||
title('$D_g$ to $D$');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_gm('Dx', 'Dgx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / D_{g,x}\right|$');
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_gm('Dy', 'Dgy'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / D_{g,y}\right|$');
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_gm('Dz', 'Dgz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / D_{g,z}\right|$');
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff.G_gm('Dx', 'Dgx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff.G_gm('Dy', 'Dgy'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff.G_gm('Dz', 'Dgz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
subplot(2, 1, 2);
|
||||
title('$F_s$ to $D$');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_fs('Dx', 'Fsx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{s,x}\right|$');
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_fs('Dy', 'Fsy'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / F_{s,y}\right|$');
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_fs('Dz', 'Fsz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{s,z}\right|$');
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff.G_fs('Dx', 'Fsx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff.G_fs('Dy', 'Fsy'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff.G_fs('Dz', 'Fsz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
|
||||
|
||||
% #+NAME: fig:sensitivity_dist_iff
|
||||
% #+CAPTION: Sensitivity to disturbance once the IFF controller is applied to the system ([[./figs/sensitivity_dist_iff.png][png]], [[./figs/sensitivity_dist_iff.pdf][pdf]])
|
||||
% [[file:figs/sensitivity_dist_iff.png]]
|
||||
|
||||
% #+begin_warning
|
||||
% The order of the models are very high and thus the plots may be wrong.
|
||||
% For instance, the plots are not the same when using =minreal=.
|
||||
% #+end_warning
|
||||
|
||||
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_dist('Dz', 'Frzz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{rz, z}\right|$');
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_dist('Dz', 'Ftyz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{ty, z}\right|$');
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_dist('Dx', 'Ftyx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{ty, x}\right|$');
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, abs(squeeze(freqresp(minreal(prescale(G_iff.G_dist('Dz', 'Frzz'), {2*pi, 2*pi*1e3})), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, abs(squeeze(freqresp(minreal(G_iff.G_dist('Dz', 'Ftyz')), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, abs(squeeze(freqresp(minreal(G_iff.G_dist('Dx', 'Ftyx')), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
% Damped Plant
|
||||
% Now, look at the new damped plant to control.
|
||||
|
||||
% It damps the plant (resonance of the nano hexapod as well as other resonances) as shown in figure [[fig:plant_iff_damped]].
|
||||
|
||||
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
|
||||
ax1 = subplot(2, 2, 1);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_cart('Dx', 'Fnx'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_cart('Dy', 'Fny'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_cart('Dz', 'Fnz'), freqs, 'Hz'))));
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), '--');
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff.G_cart('Dy', 'Fny'), freqs, 'Hz'))), '--');
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), '--');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||
|
||||
ax2 = subplot(2, 2, 2);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_cart('Rx', 'Mnx'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_cart('Ry', 'Mny'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_cart('Rz', 'Mnz'), freqs, 'Hz'))));
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), '--');
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff.G_cart('Ry', 'Mny'), freqs, 'Hz'))), '--');
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), '--');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [rad/(Nm)]'); xlabel('Frequency [Hz]');
|
||||
|
||||
ax3 = subplot(2, 2, 3);
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{n,x}\right|$');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dy', 'Fny'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / F_{n,y}\right|$');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{n,z}\right|$');
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff.G_cart('Dy', 'Fny'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
legend('location', 'northwest');
|
||||
|
||||
ax4 = subplot(2, 2, 4);
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), 'DisplayName', '$\left|R_x / M_{n,x}\right|$');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Ry', 'Mny'), freqs, 'Hz'))), 'DisplayName', '$\left|R_y / M_{n,y}\right|$');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), 'DisplayName', '$\left|R_z / M_{n,z}\right|$');
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff.G_cart('Ry', 'Mny'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
legend('location', 'northwest');
|
||||
|
||||
linkaxes([ax1,ax2,ax3,ax4],'x');
|
||||
|
||||
|
||||
|
||||
% #+NAME: fig:plant_iff_damped
|
||||
% #+CAPTION: Damped Plant after IFF is applied ([[./figs/plant_iff_damped.png][png]], [[./figs/plant_iff_damped.pdf][pdf]])
|
||||
% [[file:figs/plant_iff_damped.png]]
|
||||
|
||||
% However, it increases coupling at low frequency (figure [[fig:plant_iff_coupling]]).
|
||||
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
|
||||
for ix = 1:6
|
||||
for iy = 1:6
|
||||
subplot(6, 6, (ix-1)*6 + iy);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_cart(ix, iy), freqs, 'Hz'))), 'k-');
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff.G_cart(ix, iy), freqs, 'Hz'))), 'k--');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylim([1e-12, 1e-5]);
|
||||
end
|
||||
end
|
||||
246
to-order/active_damping_uniaxial/matlab/rmc.m
Normal file
246
to-order/active_damping_uniaxial/matlab/rmc.m
Normal file
@@ -0,0 +1,246 @@
|
||||
%% Clear Workspace and Close figures
|
||||
clear; close all; clc;
|
||||
|
||||
%% Intialize Laplace variable
|
||||
s = zpk('s');
|
||||
|
||||
open 'simscape/sim_nano_station_id.slx'
|
||||
|
||||
% Control Design
|
||||
% Let's load the undamped plant:
|
||||
|
||||
load('./active_damping/mat/plants.mat', 'G');
|
||||
|
||||
|
||||
|
||||
% Let's look at the transfer function from actuator forces in the nano-hexapod to the measured displacement of the actuator for all 6 pairs of actuator/sensor (figure [[fig:rmc_plant]]).
|
||||
|
||||
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
|
||||
ax1 = subplot(2, 1, 1);
|
||||
hold on;
|
||||
for i=1:6
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_dleg(['Dm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
|
||||
ax2 = subplot(2, 1, 2);
|
||||
hold on;
|
||||
for i=1:6
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_dleg(['Dm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
|
||||
|
||||
|
||||
% #+NAME: fig:rmc_plant
|
||||
% #+CAPTION: Transfer function from forces applied in the legs to leg displacement sensor ([[./figs/rmc_plant.png][png]], [[./figs/rmc_plant.pdf][pdf]])
|
||||
% [[file:figs/rmc_plant.png]]
|
||||
|
||||
% The Relative Motion Controller is defined below.
|
||||
% A Low pass Filter is added to make the controller transfer function proper.
|
||||
|
||||
K_rmc = s*50000/(1 + s/2/pi/10000);
|
||||
|
||||
|
||||
|
||||
% The obtained loop gains are shown in figure [[fig:rmc_open_loop]].
|
||||
|
||||
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
|
||||
ax1 = subplot(2, 1, 1);
|
||||
hold on;
|
||||
for i=1:6
|
||||
plot(freqs, abs(squeeze(freqresp(K_rmc*G.G_dleg(['Dm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
|
||||
ax2 = subplot(2, 1, 2);
|
||||
hold on;
|
||||
for i=1:6
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(K_rmc*G.G_dleg(['Dm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
|
||||
% Identification of the damped plant
|
||||
% Let's initialize the system prior to identification.
|
||||
|
||||
initializeGround();
|
||||
initializeGranite();
|
||||
initializeTy();
|
||||
initializeRy();
|
||||
initializeRz();
|
||||
initializeMicroHexapod();
|
||||
initializeAxisc();
|
||||
initializeMirror();
|
||||
initializeNanoHexapod(struct('actuator', 'piezo'));
|
||||
initializeSample(struct('mass', 50));
|
||||
|
||||
|
||||
|
||||
% And initialize the controllers.
|
||||
|
||||
K = tf(zeros(6));
|
||||
save('./mat/controllers.mat', 'K', '-append');
|
||||
K_iff = tf(zeros(6));
|
||||
save('./mat/controllers.mat', 'K_iff', '-append');
|
||||
K_rmc = -K_rmc*eye(6);
|
||||
save('./mat/controllers.mat', 'K_rmc', '-append');
|
||||
K_dvf = tf(zeros(6));
|
||||
save('./mat/controllers.mat', 'K_dvf', '-append');
|
||||
|
||||
|
||||
|
||||
% We identify the system dynamics now that the RMC controller is ON.
|
||||
|
||||
G_rmc = identifyPlant();
|
||||
|
||||
|
||||
|
||||
% And we save the damped plant for further analysis.
|
||||
|
||||
save('./active_damping/mat/plants.mat', 'G_rmc', '-append');
|
||||
|
||||
% Sensitivity to disturbances
|
||||
% As shown in figure [[fig:sensitivity_dist_rmc]], RMC control succeed in lowering the sensitivity to disturbances near resonance of the system.
|
||||
|
||||
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
|
||||
subplot(2, 1, 1);
|
||||
title('$D_g$ to $D$');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_gm('Dx', 'Dgx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / D_{g,x}\right|$');
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_gm('Dy', 'Dgy'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / D_{g,y}\right|$');
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_gm('Dz', 'Dgz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / D_{g,z}\right|$');
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, abs(squeeze(freqresp(G_rmc.G_gm('Dx', 'Dgx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, abs(squeeze(freqresp(G_rmc.G_gm('Dy', 'Dgy'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, abs(squeeze(freqresp(G_rmc.G_gm('Dz', 'Dgz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
subplot(2, 1, 2);
|
||||
title('$F_s$ to $D$');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_fs('Dx', 'Fsx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{s,x}\right|$');
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_fs('Dy', 'Fsy'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / F_{s,y}\right|$');
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_fs('Dz', 'Fsz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{s,z}\right|$');
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, abs(squeeze(freqresp(G_rmc.G_fs('Dx', 'Fsx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, abs(squeeze(freqresp(G_rmc.G_fs('Dy', 'Fsy'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, abs(squeeze(freqresp(G_rmc.G_fs('Dz', 'Fsz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
|
||||
|
||||
% #+NAME: fig:sensitivity_dist_rmc
|
||||
% #+CAPTION: Sensitivity to disturbance once the RMC controller is applied to the system ([[./figs/sensitivity_dist_rmc.png][png]], [[./figs/sensitivity_dist_rmc.pdf][pdf]])
|
||||
% [[file:figs/sensitivity_dist_rmc.png]]
|
||||
|
||||
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_dist('Dz', 'Frzz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{rz, z}\right|$');
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_dist('Dz', 'Ftyz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{ty, z}\right|$');
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_dist('Dx', 'Ftyx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{ty, x}\right|$');
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, abs(squeeze(freqresp(G_rmc.G_dist('Dz', 'Frzz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, abs(squeeze(freqresp(G_rmc.G_dist('Dz', 'Ftyz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, abs(squeeze(freqresp(G_rmc.G_dist('Dx', 'Ftyx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
% Damped Plant
|
||||
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
|
||||
ax1 = subplot(2, 2, 1);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_cart('Dx', 'Fnx'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_cart('Dy', 'Fny'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_cart('Dz', 'Fnz'), freqs, 'Hz'))));
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, abs(squeeze(freqresp(G_rmc.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), '--');
|
||||
plot(freqs, abs(squeeze(freqresp(G_rmc.G_cart('Dy', 'Fny'), freqs, 'Hz'))), '--');
|
||||
plot(freqs, abs(squeeze(freqresp(G_rmc.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), '--');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||
|
||||
ax2 = subplot(2, 2, 2);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_cart('Rx', 'Mnx'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_cart('Ry', 'Mny'), freqs, 'Hz'))));
|
||||
plot(freqs, abs(squeeze(freqresp(G.G_cart('Rz', 'Mnz'), freqs, 'Hz'))));
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, abs(squeeze(freqresp(G_rmc.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), '--');
|
||||
plot(freqs, abs(squeeze(freqresp(G_rmc.G_cart('Ry', 'Mny'), freqs, 'Hz'))), '--');
|
||||
plot(freqs, abs(squeeze(freqresp(G_rmc.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), '--');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [rad/(Nm)]'); xlabel('Frequency [Hz]');
|
||||
|
||||
ax3 = subplot(2, 2, 3);
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{n,x}\right|$');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dy', 'Fny'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / F_{n,y}\right|$');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{n,z}\right|$');
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_rmc.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_rmc.G_cart('Dy', 'Fny'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_rmc.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
legend('location', 'northwest');
|
||||
|
||||
ax4 = subplot(2, 2, 4);
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), 'DisplayName', '$\left|R_x / M_{n,x}\right|$');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Ry', 'Mny'), freqs, 'Hz'))), 'DisplayName', '$\left|R_y / M_{n,y}\right|$');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), 'DisplayName', '$\left|R_z / M_{n,z}\right|$');
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_rmc.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_rmc.G_cart('Ry', 'Mny'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_rmc.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
legend('location', 'northwest');
|
||||
|
||||
linkaxes([ax1,ax2,ax3,ax4],'x');
|
||||
BIN
to-order/active_damping_uniaxial/matlab/sim_nano_station_id.slx
Normal file
BIN
to-order/active_damping_uniaxial/matlab/sim_nano_station_id.slx
Normal file
Binary file not shown.
Reference in New Issue
Block a user