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DSYS= 0 + + *** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 *** + DISTRIBUTED ANSYS Mechanical Enterprise + + 00208316 VERSION=WINDOWS x64 11:07:02 MAR 25, 2021 CP= 2.062 + + Unknown + + + + NODE X Y Z THXY THYZ THZX + 840914 0.0000 0.0000 0.28000E-001 0.00 0.00 0.00 + 840915 0.0000 0.0000 -0.28000E-001 0.00 0.00 0.00 + 840916 -0.34000E-001 0.0000 0.0000 0.00 0.00 0.00 + 840917 0.34000E-001 0.0000 0.0000 0.00 0.00 0.00 + + LIST MASTERS ON ALL SELECTED NODES. + CURRENT DOF SET= UX UY UZ ROTX ROTY ROTZ + + *** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 *** + DISTRIBUTED ANSYS Mechanical Enterprise + + 00208316 VERSION=WINDOWS x64 11:07:02 MAR 25, 2021 CP= 2.188 + + Unknown + + + NODE LABEL SUPPORT + 840914 UX + 840914 UY + 840914 UZ + 840914 ROTX + 840914 ROTY + 840914 ROTZ + 840915 UX + 840915 UY + 840915 UZ + 840915 ROTX + 840915 ROTY + 840915 ROTZ + 840916 UX + 840916 UY + 840916 UZ + 840916 ROTX + 840916 ROTY + 840916 ROTZ + 840917 UX + 840917 UY + 840917 UZ + 840917 ROTX + 840917 ROTY + 840917 ROTZ diff --git a/mat/APA300ML_full_mat_K.CSV b/mat/APA300ML_full_mat_K.CSV new file mode 100644 index 0000000..c760cd9 --- /dev/null +++ b/mat/APA300ML_full_mat_K.CSV @@ -0,0 +1,36 @@ 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b/mat/APA300ML_full_out_nodes_3D.txt @@ -0,0 +1,61 @@ + + LIST ALL SELECTED NODES. DSYS= 0 + + *** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 *** + DISTRIBUTED ANSYS Mechanical Enterprise + + 00208316 VERSION=WINDOWS x64 14:16:37 MAR 25, 2021 CP= 2.219 + + Unknown + + + + NODE X Y Z THXY THYZ THZX + 1 0.0000 0.0000 0.28000E-001 0.00 0.00 0.00 + 840915 0.0000 0.0000 -0.28000E-001 0.00 0.00 0.00 + 840916 -0.30000E-001 0.0000 0.0000 0.00 0.00 0.00 + 840917 0.10000E-001 0.0000 0.0000 0.00 0.00 0.00 + 840918 0.30000E-001 0.0000 0.0000 0.00 0.00 0.00 + + LIST MASTERS ON ALL SELECTED NODES. + CURRENT DOF SET= UX UY UZ ROTX ROTY ROTZ + + *** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 *** + DISTRIBUTED ANSYS Mechanical Enterprise + + 00208316 VERSION=WINDOWS x64 14:16:37 MAR 25, 2021 CP= 2.219 + + Unknown + + + NODE LABEL SUPPORT + 1 UX + 1 UY + 1 UZ + 1 ROTX + 1 ROTY + 1 ROTZ + 840915 UX + 840915 UY + 840915 UZ + 840915 ROTX + 840915 ROTY + 840915 ROTZ + 840916 UX + 840916 UY + 840916 UZ + 840916 ROTX + 840916 ROTY + 840916 ROTZ + 840917 UX + 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diff --git a/mat/APA300ML_out_nodes_3D.txt b/mat/APA300ML_out_nodes_3D.txt new file mode 100644 index 0000000..1afceab --- /dev/null +++ b/mat/APA300ML_out_nodes_3D.txt @@ -0,0 +1,75 @@ + + LIST ALL SELECTED NODES. DSYS= 0 + + *** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 *** + DISTRIBUTED ANSYS Academic Research + + 00208316 VERSION=WINDOWS x64 15:15:04 AUG 26, 2020 CP= 2.625 + + Piezo-APA300ML-param--Modal (B5) + + + + NODE X Y Z THXY THYZ THZX + 697783 0.0000 0.0000 -0.15000E-001 0.00 0.00 0.00 + 697784 0.0000 0.0000 0.15000E-001 0.00 0.00 0.00 + 697785 -0.32500E-001 0.0000 0.0000 0.00 0.00 0.00 + 697786 -0.12500E-001 0.0000 0.0000 0.00 0.00 0.00 + 697787 -0.75000E-002 0.0000 0.0000 0.00 0.00 0.00 + 697788 0.12500E-001 0.0000 0.0000 0.00 0.00 0.00 + 697789 0.32500E-001 0.0000 0.0000 0.00 0.00 0.00 + + LIST MASTERS ON ALL SELECTED NODES. + CURRENT DOF SET= UX UY UZ ROTX ROTY ROTZ + + *** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 *** + DISTRIBUTED ANSYS Academic Research + + 00208316 VERSION=WINDOWS x64 15:15:04 AUG 26, 2020 CP= 2.750 + + Piezo-APA300ML-param--Modal (B5) + + + NODE LABEL SUPPORT + 697783 UX + 697783 UY + 697783 UZ + 697783 ROTX + 697783 ROTY + 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DSYS= 0 + + *** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 *** + DISTRIBUTED ANSYS Mechanical Enterprise + + 00208316 VERSION=WINDOWS x64 15:36:08 MAR 18, 2021 CP= 4.797 + + Piezo-APA300ML-frame--Modal (C5) + + + + NODE X Y Z THXY THYZ THZX + 840914 0.0000 0.0000 0.28000E-001 0.00 0.00 0.00 + 840915 0.0000 0.0000 -0.28000E-001 0.00 0.00 0.00 + 840916 -0.34000E-001 0.0000 0.0000 0.00 0.00 0.00 + 840917 0.34000E-001 0.0000 0.0000 0.00 0.00 0.00 + + LIST MASTERS ON ALL SELECTED NODES. + CURRENT DOF SET= UX UY UZ ROTX ROTY ROTZ + + *** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 *** + DISTRIBUTED ANSYS Mechanical Enterprise + + 00208316 VERSION=WINDOWS x64 15:36:08 MAR 18, 2021 CP= 5.047 + + Piezo-APA300ML-frame--Modal (C5) + + + NODE LABEL SUPPORT + 840914 UX + 840914 UY + 840914 UZ + 840914 ROTX + 840914 ROTY + 840914 ROTZ + 840915 UX + 840915 UY + 840915 UZ + 840915 ROTX + 840915 ROTY + 840915 ROTZ + 840916 UX + 840916 UY + 840916 UZ + 840916 ROTX + 840916 ROTY + 840916 ROTZ + 840917 UX + 840917 UY + 840917 UZ + 840917 ROTX + 840917 ROTY + 840917 ROTZ diff --git a/mat/nano_hexapod_object.mat b/mat/nano_hexapod_object.mat new file mode 100644 index 0000000..f47bdad Binary files /dev/null and b/mat/nano_hexapod_object.mat differ diff --git a/matlab/nano_hexapod/apa300ml_2dof.slx b/matlab/nano_hexapod/apa300ml_2dof.slx new file mode 100644 index 0000000..faddecc Binary files /dev/null and b/matlab/nano_hexapod/apa300ml_2dof.slx differ diff --git a/matlab/nano_hexapod/apa300ml_flex_structure.slx b/matlab/nano_hexapod/apa300ml_flex_structure.slx new file mode 100644 index 0000000..dd1a454 Binary files /dev/null and b/matlab/nano_hexapod/apa300ml_flex_structure.slx differ diff --git a/matlab/nano_hexapod/apa300ml_flexible.slx b/matlab/nano_hexapod/apa300ml_flexible.slx new file mode 100644 index 0000000..a416e8a Binary files /dev/null and b/matlab/nano_hexapod/apa300ml_flexible.slx differ diff --git a/matlab/nano_hexapod/nano_hexapod.slx b/matlab/nano_hexapod/nano_hexapod.slx new file mode 100644 index 0000000..471311c Binary files /dev/null and b/matlab/nano_hexapod/nano_hexapod.slx differ diff --git a/matlab/nano_hexapod/nano_hexapod_left_strut.slx b/matlab/nano_hexapod/nano_hexapod_left_strut.slx new file mode 100644 index 0000000..a7df206 Binary files /dev/null and b/matlab/nano_hexapod/nano_hexapod_left_strut.slx differ diff --git a/matlab/nano_hexapod/nano_hexapod_right_strut.slx b/matlab/nano_hexapod/nano_hexapod_right_strut.slx new file mode 100644 index 0000000..9dceb46 Binary files /dev/null and b/matlab/nano_hexapod/nano_hexapod_right_strut.slx differ diff --git a/matlab/nano_hexapod/to-order/apa300ml.slx b/matlab/nano_hexapod/to-order/apa300ml.slx new file mode 100644 index 0000000..64be27f Binary files /dev/null and b/matlab/nano_hexapod/to-order/apa300ml.slx differ diff --git a/matlab/nano_hexapod/to-order/apa300ml_2dof.slx b/matlab/nano_hexapod/to-order/apa300ml_2dof.slx new file mode 100644 index 0000000..8287a95 Binary files /dev/null and b/matlab/nano_hexapod/to-order/apa300ml_2dof.slx differ diff --git a/matlab/nano_hexapod/to-order/apa300ml_structure.slx b/matlab/nano_hexapod/to-order/apa300ml_structure.slx new file mode 100644 index 0000000..40d9e72 Binary files /dev/null and b/matlab/nano_hexapod/to-order/apa300ml_structure.slx differ diff --git a/org/nano_hexapod.org b/org/nano_hexapod.org new file mode 100644 index 0000000..1df098b --- /dev/null +++ b/org/nano_hexapod.org @@ -0,0 +1,1801 @@ +#+TITLE: Nano-Hexapod +#+SETUPFILE: ./setup/org-setup-file.org + +* Nano-Hexapod +** Matlab Init :noexport:ignore: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) +<> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes +<> +#+end_src + +#+begin_src matlab :tangle no +simulinkproject('../'); +#+end_src + +#+begin_src matlab +addpath('matlab/nano_hexapod'); +open('matlab/nano_hexapod/nano_hexapod.slx') +#+end_src + +** Nano Hexapod object +The nano-hexapod can be initialized and configured using the =initializeNanoHexapodFinal= function. + +#+begin_src matlab +n_hexapod = initializeNanoHexapodFinal('flex_bot_type', '4dof', ... + 'flex_top_type', '3dof', ... + 'motion_sensor_type', 'struts', ... + 'actuator_type', '2dof'); +#+end_src + +** Jacobian from Solidworks Model + +Center of joints a_i with respect to {F}: +#+begin_src matlab +Fa = [[-86.05, -74.78, 22.49], + [86.05, -74.78, 22.49], + [107.79, -37.13, 22.49], + [21.74, 111.91, 22.49], + [-21.74, 111.91, 22.49], + [-107.79, -37.13, 22.49]]'*1e-3; +#+end_src + +Center of joints a_i with respect to {M}: +#+begin_src matlab +Mb = [[-28.47, -106.25, -22.50], + [28.47, -106.25, -22.50], + [106.25, 28.47, -22.50], + [77.78, 77.78, -22.50], + [-77.78, 77.78, -22.50], + [-106.25, 28.47, -22.50]]'*1e-3; +#+end_src + +#+begin_src matlab +Fb = Mb + [0; 0; 95e-3]; + +si = Fb - Fa; +si = si./vecnorm(si); +#+end_src + +#+begin_src matlab +ki = ones(1,6); +bi = Fb; +#+end_src + +#+begin_src matlab :results value replace :exports both +ki.*si*si' +#+end_src + +#+RESULTS: +| 1.8977 | 2.4659e-17 | 1.3383e-18 | +| 2.4659e-17 | 1.8977 | -2.3143e-05 | +| 1.3383e-18 | -2.3143e-05 | 2.2046 | + +#+begin_src matlab +OkX = (ki.*cross(bi, si)*si')/(ki.*si*si'); +Ok = [OkX(3,2);OkX(1,3);OkX(2,1)] +#+end_src + +#+begin_src matlab :results value replace :exports results :tangle no +ans = Ok +#+end_src + +#+RESULTS: +| -1.7444e-18 | +| 2.1511e-06 | +| 0.052707 | + +The center of the cube is therefore 52.7mm above the bottom platform {F} frame. + +Let's compute the Jacobian at this location: +#+begin_src matlab +Jk = [si', cross(bi - Ok, si)']; +#+end_src + +And the stiffness matrix: +#+begin_src matlab :results value replace +Jk'*diag(ki)*Jk +#+end_src + +#+RESULTS: +| 1.8977 | 0 | 0 | 0 | -3.4694e-18 | 2.5509e-06 | +| 0 | 1.8977 | -2.3143e-05 | 4.1751e-06 | 1.3878e-17 | 0 | +| 0 | -2.3143e-05 | 2.2046 | -5.0916e-11 | -3.4694e-18 | 0 | +| 0 | 4.1751e-06 | -5.0916e-11 | 0.012594 | 2.1684e-19 | 8.6736e-19 | +| -3.2704e-18 | 0 | -4.206e-18 | 3.9451e-19 | 0.012594 | -9.3183e-08 | +| 2.5509e-06 | 0 | 0 | 8.6736e-19 | -9.3183e-08 | 0.043362 | + +** Jacobian for encoders on the plates + +*Goal*: Compute the 6-DoF motion of the top platform (relative to the bottom platform) from the 6 encoder measurements. + +The main differences with the case where the encoders are parallel with the strut are: +- the encoder and ruler may not be parallel anymore as the top platform is moving +- the derivation of the Jacobian (if possible) will not be the same + +** Compare encoders on the struts and encoders on the platforms +#+begin_src matlab +%% Options for Linearized +options = linearizeOptions; +options.SampleTime = 0; + +%% Name of the Simulink File +mdl = 'nano_hexapod'; + +%% Input/Output definition +clear io; io_i = 1; +io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs +io(io_i) = linio([mdl, '/D'], 1, 'openoutput'); io_i = io_i + 1; % Relative Motion Outputs +#+end_src + +#+begin_src matlab +n_hexapod.motion_sensor = struct(); +n_hexapod.motion_sensor.type = 1; % 1: Leg / 2: Plate +#+end_src + +#+begin_src matlab +Gs = linearize(mdl, io, 0.0, options); +Gs.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}; +Gs.OutputName = {'D1', 'D2', 'D3', 'D4', 'D5', 'D6'}; +#+end_src + +#+begin_src matlab +n_hexapod.motion_sensor = struct(); +n_hexapod.motion_sensor.type = 2; % 1: Leg / 2: Plate +#+end_src + +#+begin_src matlab +Gp = linearize(mdl, io, 0.0, options); +Gp.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}; +Gp.OutputName = {'D1', 'D2', 'D3', 'D4', 'D5', 'D6'}; +#+end_src + +#+begin_src matlab :exports none +freqs = logspace(0, 3, 1000); + +figure; +tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +for i = 1:6 + plot(freqs, abs(squeeze(freqresp(Gs(['D', num2str(i)], ['F', num2str(i)]), freqs, 'Hz')))); +end +for i = 1:5 + for j = i+1:6 + plot(freqs, abs(squeeze(freqresp(Gs(['D', num2str(i)], ['F', num2str(j)]), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2]); + end +end +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); +ylim([1e-10, 1e-6]); + +ax2 = nexttile; +hold on; +for i = 1:6 + plot(freqs, 180/pi*angle(squeeze(freqresp(Gs(['D', 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([0, 180]); +yticks([-180, -90, 0, 90, 180]); + +linkaxes([ax1,ax2],'x'); +xlim([freqs(1), freqs(end)]); +#+end_src + +#+begin_src matlab :exports none +freqs = logspace(0, 3, 1000); + +figure; +tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +for i = 1:6 + plot(freqs, abs(squeeze(freqresp(Gp(['D', num2str(i)], ['F', num2str(i)]), freqs, 'Hz')))); +end +for i = 1:5 + for j = i+1:6 + plot(freqs, abs(squeeze(freqresp(Gp(['D', num2str(i)], ['F', num2str(j)]), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2]); + end +end +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); +ylim([1e-10, 1e-6]); + +ax2 = nexttile; +hold on; +for i = 1:6 + plot(freqs, 180/pi*angle(squeeze(freqresp(Gp(['D', 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([0, 180]); +yticks([-180, -90, 0, 90, 180]); + +linkaxes([ax1,ax2],'x'); +xlim([freqs(1), freqs(end)]); +#+end_src + +** Nano Hexapod +#+begin_src matlab +%% Options for Linearized +options = linearizeOptions; +options.SampleTime = 0; + +%% Name of the Simulink File +mdl = 'nano_hexapod'; + +%% Input/Output definition +clear io; io_i = 1; +io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs +io(io_i) = linio([mdl, '/Fe'], 1, 'openinput'); io_i = io_i + 1; % External Force +io(io_i) = linio([mdl, '/D'], 1, 'openoutput'); io_i = io_i + 1; % Relative Motion Outputs +io(io_i) = linio([mdl, '/Fm'], 1, 'openoutput'); io_i = io_i + 1; % Force Sensors +io(io_i) = linio([mdl, '/X'], 1, 'openoutput'); io_i = io_i + 1; % Absolute Motion of top platform + +%% Run the linearization +G = linearize(mdl, io, 0.0, options); +G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6', ... + 'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'}; +G.OutputName = {'D1', 'D2', 'D3', 'D4', 'D5', 'D6', ... + 'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6' ... + 'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}; +#+end_src + +#+begin_src matlab :results output replace :exports results :tangle no +size(G) +#+end_src + +#+RESULTS: +: size(G) +: State-space model with 18 outputs, 12 inputs, and 60 states. + +Verify the number of DOF: +| Element | DoF | +|--------------------+-----| +| Bot Plate | 0 | +| Struts | 6*4 | +| Top Plate + Sample | 12 | +|--------------------+-----| +| Total: | 36 | +#+TBLFM: @>$2=vsum(@I..@II) + +*** DVF Plant + +The DC gain from actuator to relative motion sensor should be equal to (for the 2dof APA): +\[ \frac{1}{k + k_a + kk_a/k_e} \] + +#+begin_src matlab :results value replace :exports results :tangle no +1/(k + ka + k*ka/ke) +#+end_src + +#+RESULTS: +: 1.8732e-08 + +Which is almost the case: + +#+begin_src matlab :results value replace :exports results :tangle no +dcgain(G({'D1', 'D2', 'D3', 'D4', 'D5', 'D6'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'})) +#+end_src + +#+RESULTS: +| -1.8676e-08 | 5.2396e-11 | -8.8935e-11 | 2.6392e-11 | 9.7629e-11 | -1.5609e-10 | +| -1.4754e-11 | -1.8725e-08 | 1.4348e-11 | -5.7189e-11 | -3.3327e-11 | 7.0799e-11 | +| -3.4924e-11 | -7.7445e-11 | -1.8607e-08 | -4.6578e-11 | -1.9592e-11 | 4.0299e-11 | +| 6.1699e-11 | -7.1962e-11 | 1.3374e-11 | -1.8623e-08 | -1.7898e-10 | 5.4541e-11 | +| 9.735e-11 | -1.0698e-10 | -1.6424e-11 | 2.3718e-11 | -1.8826e-08 | 8.387e-11 | +| -3.94e-11 | 2.6436e-11 | -1.1338e-10 | 5.0793e-11 | 1.2358e-10 | -1.8792e-08 | + +Other (off-diagonal) elements should be close to zero (probably limited to joint's stiffness). +*However, when setting joint's axial stiffness to infinity, I obtain better diagonal*. + +#+begin_src matlab :exports none +Gdvf = minreal(G({'D1', 'D2', 'D3', 'D4', 'D5', 'D6'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'})); + +freqs = 2*logspace(0, 2, 1000); + +figure; +tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +for i = 1:6 + plot(freqs, abs(squeeze(freqresp(Gdvf(['D', num2str(i)], ['F', num2str(i)]), freqs, 'Hz')))); +end +for i = 1:5 + for j = i+1:6 + plot(freqs, abs(squeeze(freqresp(Gdvf(['D', num2str(i)], ['F', num2str(j)]), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2]); + end +end +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); +ylim([1e-10, 1e-6]); + +ax2 = nexttile; +hold on; +for i = 1:6 + plot(freqs, 180/pi*angle(squeeze(freqresp(Gdvf(['D', 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([0, 180]); +yticks([-180, -90, 0, 90, 180]); + +linkaxes([ax1,ax2],'x'); +xlim([freqs(1), freqs(end)]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/nano_hexapod_struts_2dof_dvf_plant.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:nano_hexapod_struts_2dof_dvf_plant +#+caption: IFF Plant +#+RESULTS: +[[file:figs/nano_hexapod_struts_2dof_dvf_plant.png]] + +*** IFF Plant + +#+begin_src matlab :exports none +freqs = 2*logspace(0, 2, 1000); + +figure; +tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +for i = 1:6 + plot(freqs, abs(squeeze(freqresp(G(['Fm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz')))); +end +for i = 1:5 + for j = i+1:6 + plot(freqs, abs(squeeze(freqresp(G(['Fm', num2str(i)], ['F', num2str(j)]), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2]); + end +end +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); +ylim([1e-4, 1e1]); + +ax2 = nexttile; +hold on; +for i = 1:6 + plot(freqs, 180/pi*angle(squeeze(freqresp(G(['Fm', 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, 0]); +yticks([-180, -90, 0, 90, 180]); + +linkaxes([ax1,ax2],'x'); +xlim([freqs(1), freqs(end)]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/nano_hexapod_struts_2dof_iff_plant.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:nano_hexapod_struts_2dof_iff_plant +#+caption: DVF Plant +#+RESULTS: +[[file:figs/nano_hexapod_struts_2dof_iff_plant.png]] + +** Decoupling at the CoK + +#+begin_src matlab +Gx = inv(Jk)*G({'D1', 'D2', 'D3', 'D4', 'D5', 'D6'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'})*inv(Jk'); +Gx.inputname = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'}; +Gx.outputname = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}; +#+end_src + +#+begin_src matlab :results value replace :exports results :tangle no +dcgain(Gx) +#+end_src + +#+RESULTS: +| -9.8399e-09 | -8.0785e-11 | -1.5723e-11 | 2.6356e-10 | -4.9857e-10 | 5.2177e-11 | +| -8.7554e-11 | -9.8585e-09 | 2.6292e-11 | 2.0485e-10 | 2.0385e-10 | 8.2942e-11 | +| 4.3837e-11 | -5.5862e-14 | -8.4859e-09 | -9.0036e-12 | 2.9325e-10 | -3.104e-11 | +| 1.901e-09 | 5.3078e-10 | -7.5477e-10 | -1.4759e-06 | -7.7918e-09 | -7.491e-10 | +| -7.1795e-11 | -1.6333e-09 | -1.8359e-10 | 5.2707e-09 | -1.4794e-06 | 3.2304e-10 | +| 7.0322e-11 | 1.7713e-12 | -5.8019e-11 | 7.4838e-11 | -8.9677e-10 | -4.2938e-07 | + +#+begin_src matlab :exports none +freqs = 5*logspace(0, 2, 1000); + +figure; +tiledlayout(6, 6, 'TileSpacing', 'None', 'Padding', 'None'); + +for i = 1:6 + for j = 1:6 + nexttile; + plot(freqs, abs(squeeze(freqresp(Gx(i, j), freqs, 'Hz'))), 'k-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + end +end +axs = findobj(gcf,'Type','axes','Visible','on'); +linkaxes(axs, 'xy'); +xlim([freqs(1), freqs(end)]); ylim([1e-10, 1e-4]); +#+end_src + +#+begin_src matlab :exports none +freqs = logspace(0, 2, 1000); + +figure; +tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +for i = 1:6 + plot(freqs, abs(squeeze(freqresp(Gx(i,i), freqs, 'Hz'))), '-'); +end +for i = 1:5 + for j = i+1:6 + plot(freqs, abs(squeeze(freqresp(Gx(i, j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2]); + end +end +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + +ax2 = nexttile; +hold on; +for i = 1:6 + plot(freqs, 180/pi*angle(squeeze(freqresp(Gx(i,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'); +xlim([freqs(1), freqs(end)]); +#+end_src + +** Jacobian +*** Compute Jacobian +#+begin_src matlab +Ai = [out.b1.Data(1,:) + out.b2.Data(1,:) + out.b3.Data(1,:) + out.b4.Data(1,:) + out.b5.Data(1,:) + out.b6.Data(1,:)]'; + + +Bi = [out.a1.Data(1,:) + out.a2.Data(1,:) + out.a3.Data(1,:) + out.a4.Data(1,:) + out.a5.Data(1,:) + out.a6.Data(1,:)]'; +#+end_src + +#+begin_src matlab +stewart = initializeStewartPlatform(); +stewart = initializeFramesPositions(stewart, 'H', 95e-3, 'MO_B', 150e-3); +stewart = generateGeneralConfiguration(stewart); +stewart.platform_F.Fa = Ai; +stewart.platform_M.Mb = Bi - [0;0;1]*stewart.geometry.H; +stewart = computeJointsPose(stewart); +stewart = initializeStewartPose(stewart, 'AP', [0;0;0], 'ARB', eye(3)); +#+end_src + +#+begin_src matlab +stewart = initializeCylindricalPlatforms(stewart); +stewart = initializeCylindricalStruts(stewart); +#+end_src + +#+begin_src matlab +stewart = initializeStrutDynamics(stewart, 'K', 1e6*ones(6,1), 'C', 1e2*ones(6,1)); +stewart = initializeAmplifiedStrutDynamics(stewart); +stewart = initializeJointDynamics(stewart); +#+end_src + +#+begin_src matlab +displayArchitecture(stewart, 'views', 'all'); +#+end_src + +#+begin_src matlab :results output replace :exports results +describeStewartPlatform(stewart) +#+end_src + +#+RESULTS: +#+begin_example +describeStewartPlatform(stewart) +GEOMETRY: +- The height between the fixed based and the top platform is 95 [mm]. +- Frame {A} is located 150 [mm] above the top platform. +- The initial length of the struts are: + 82.8, 82.8, 82.8, 82.8, 82.8, 82.8 [mm] + +ACTUATORS: +- The actuators are mechanicaly amplified. +- The vertical stiffness and damping contribution of the piezoelectric stack is: + ka = 2e+07 [N/m] ca = 1e+01 [N/(m/s)] +- Vertical stiffness when the piezoelectric stack is removed is: + kr = 5e+06 [N/m] cr = 1e+01 [N/(m/s)] + +JOINTS: +- The joints on the fixed based are universal joints +- The joints on the mobile based are spherical joints +- The position of the joints on the fixed based with respect to {F} are (in [mm]): + -86.2 -74.7 22.3 + 86.3 -74.6 22.3 + 108 -37.3 22.3 + 21.5 112 22.3 + -21.5 112 22.3 + -108 -37.5 22.2 +- The position of the joints on the mobile based with respect to {M} are (in [mm]): + -28.4 -106 -22.4 + 28.5 -106 -22.5 + 106 28.5 -22.5 + 77.8 77.8 -22.5 + -77.8 77.8 -22.5 + -106 28.4 -22.5 +#+end_example + +#+begin_src matlab +stewart = computeJacobian(stewart); +#+end_src + +*** Verify Jacobian +#+begin_src matlab +load('./mat/nano_hexapod_object.mat', 'stewart'); +J = stewart.kinematics.J; +#+end_src + +Transformation of motion: +#+begin_src matlab +G1 = -inv(J)*G({'D1', 'D2', 'D3', 'D4', 'D5', 'D6'}, {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'}); +G2 = G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'}); +#+end_src + +#+begin_src matlab :exports none +freqs = logspace(1, 3, 1000); + +figure; +tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +for i = 1:6 + plot(freqs, abs(squeeze(freqresp(G1(i,i), freqs, 'Hz'))), '-'); +end +set(gca,'ColorOrderIndex',1); +for i = 1:6 + plot(freqs, abs(squeeze(freqresp(G2(i,i), freqs, 'Hz'))), '--'); +end +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + +ax2 = nexttile; +hold on; +for i = 1:6 + plot(freqs, 180/pi*angle(squeeze(freqresp(G1(i,i), freqs, 'Hz'))), '-'); +end +set(gca,'ColorOrderIndex',1); +for i = 1:6 + plot(freqs, 180/pi*angle(squeeze(freqresp(G2(i,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'); +#+end_src + +Transformation of Forces and Torques +#+begin_src matlab +G1 = G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'}); +G2 = G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'})*inv(J'); +#+end_src + +*Not working because the forces applied on the APA are not really forces applied on the top platform (reduced by a factor ~ka/ke)* + +#+begin_src matlab :exports none +freqs = logspace(1, 3, 1000); + +figure; +tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +for i = 1:6 + plot(freqs, abs(squeeze(freqresp(G1(i,i), freqs, 'Hz'))), '-'); +end +set(gca,'ColorOrderIndex',1); +for i = 1:6 + plot(freqs, abs(squeeze(freqresp(G2(i,i), freqs, 'Hz'))), '--'); +end +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + +ax2 = nexttile; +hold on; +for i = 1:6 + plot(freqs, 180/pi*angle(squeeze(freqresp(G1(i,i), freqs, 'Hz'))), '-'); +end +set(gca,'ColorOrderIndex',1); +for i = 1:6 + plot(freqs, 180/pi*angle(squeeze(freqresp(G2(i,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'); +#+end_src + +*** Plant from APA forces to sample's displacement +#+begin_src matlab +Gx = G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'})*inv(J'); +Gx.inputname = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'}; +#+end_src + +#+begin_src matlab :exports none +freqs = 5*logspace(0, 2, 1000); + +figure; +tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +for i = 1:6 + plot(freqs, abs(squeeze(freqresp(Gx(i,i), freqs, 'Hz'))), '-'); +end +for i = 1:5 + for j = i+1:6 + plot(freqs, abs(squeeze(freqresp(Gx(i, j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2]); + end +end +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + +ax2 = nexttile; +hold on; +for i = 1:6 + plot(freqs, 180/pi*angle(squeeze(freqresp(Gx(i,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'); +xlim([freqs(1), freqs(end)]); +#+end_src + +#+begin_src matlab :exports none +freqs = 5*logspace(0, 2, 1000); + +figure; +tiledlayout(6, 6, 'TileSpacing', 'None', 'Padding', 'None'); + +for i = 1:6 + for j = 1:6 + nexttile; + plot(freqs, abs(squeeze(freqresp(Gx(i, j), freqs, 'Hz'))), 'k-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + end +end +axs = findobj(gcf,'Type','axes','Visible','on'); +linkaxes(axs, 'xy'); +xlim([freqs(1), freqs(end)]); ylim([1e-10, 1e-4]); +#+end_src + +#+begin_src matlab :exports none +freqs = 5*logspace(0, 2, 1000); + +figure; +hold on; +for i = 1:3 + plot(freqs, abs(squeeze(freqresp(Gx(i, i), freqs, 'Hz'))), 'k-'); +end +for i = 1:3 + for j = i+1:3 + plot(freqs, abs(squeeze(freqresp(Gx(i, j), freqs, 'Hz'))), 'r-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + end +end +hold off; +xlim([freqs(1), freqs(end)]); +ylim([1e-10, 1e-4]); +#+end_src + +#+begin_src matlab :exports none +freqs = 5*logspace(0, 2, 1000); + +figure; +hold on; +for i = 4:6 + plot(freqs, abs(squeeze(freqresp(Gx(i, i), freqs, 'Hz'))), 'k-'); +end +for i = 4:6 + for j = i+1:6 + plot(freqs, abs(squeeze(freqresp(Gx(i, j), freqs, 'Hz'))), 'r-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + end +end +hold off; +xlim([freqs(1), freqs(end)]); +ylim([1e-10, 1e-4]); +#+end_src + +*** Plant in the Cartesian frame +Transfer function from forces/torque to displacement/rotation: +#+begin_src matlab +GJ = inv(J)*G({'D1', 'D2', 'D3', 'D4', 'D5', 'D6'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'})*inv(J'); +GJ.inputname = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'}; +GJ.outputname = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}; +#+end_src + +#+begin_src matlab :exports none +freqs = logspace(1, 3, 1000); + +figure; +tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +for i = 1:6 + plot(freqs, abs(squeeze(freqresp(GJ(i,i), freqs, 'Hz'))), '-'); +end +for i = 1:5 + for j = i+1:6 + plot(freqs, abs(squeeze(freqresp(GJ(i, j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2]); + end +end +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + +ax2 = nexttile; +hold on; +for i = 1:6 + plot(freqs, 180/pi*angle(squeeze(freqresp(GJ(i,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'); +#+end_src + +*** Plant in the frame of the legs => Verification of Jacobian for displacements +Transfer Function in the frame of the legs +#+begin_src matlab +G1 = -J*G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}); +G1.outputname = {'D1', 'D2', 'D3', 'D4', 'D5', 'D6'}; + +G2 = G({'D1', 'D2', 'D3', 'D4', 'D5', 'D6'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}); +#+end_src + +#+begin_important +It is working fine (until internal resonance of strut). +#+end_important + +#+begin_src matlab :exports none +freqs = logspace(1, 3, 1000); + +figure; +tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +for i = 1:6 + plot(freqs, abs(squeeze(freqresp(G1(i,i), freqs, 'Hz'))), '-'); +end +set(gca,'ColorOrderIndex',1); +for i = 1:6 + plot(freqs, abs(squeeze(freqresp(G2(i,i), freqs, 'Hz'))), '--'); +end +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + +ax2 = nexttile; +hold on; +for i = 1:6 + plot(freqs, 180/pi*angle(squeeze(freqresp(G1(i,i), freqs, 'Hz'))), '-'); +end +set(gca,'ColorOrderIndex',1); +for i = 1:6 + plot(freqs, 180/pi*angle(squeeze(freqresp(G2(i,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'); +#+end_src + +** Stiffness matrix +Neglecting stiffness of the joints, we have: +\[ K = J^t \mathcal{K} J \] +where $\mathcal{K}$ is a diagonal 6x6 matrix with axial stiffness of the struts on the diagonal. + +Let's note the axial stiffness of the APA: +\[ k_{\text{APA}} = k + \frac{k_e k_a}{k_e + k_a} \] + +Them axial stiffness of the struts $k_s$: +\[ k_s = \frac{k_z k_{\text{APA}}}{k_z + 2 k_{\text{APA}}} \] + +#+begin_src matlab +kAPA = k + ke*ka/(ke + ka); +ks = kz*kAPA/(kz + 2*kAPA); +#+end_src + +#+begin_src matlab +Ks = J'*(ks*eye(6))*J +#+end_src + +#+begin_src matlab :results value replace :exports results :tangle no +inv(Ks) +#+end_src + +#+RESULTS: +| 1.9937e-06 | 7.7027e-12 | -1.5885e-11 | -1.6811e-10 | 8.7902e-06 | 3.0476e-11 | +| 7.7027e-12 | 1.9937e-06 | 2.7221e-11 | -8.7901e-06 | 6.5081e-12 | 2.8619e-11 | +| -1.5885e-11 | 2.7221e-11 | 2.6114e-07 | -1.3209e-10 | -6.1725e-11 | 4.0402e-11 | +| -1.6811e-10 | -8.7901e-06 | -1.3209e-10 | 4.5712e-05 | -5.7781e-10 | -4.5817e-10 | +| 8.7902e-06 | 6.5081e-12 | -6.1725e-11 | -5.7781e-10 | 4.5712e-05 | 5.1628e-10 | +| 3.0476e-11 | 2.8619e-11 | 4.0402e-11 | -4.5817e-10 | 5.1628e-10 | 1.3277e-05 | + +#+begin_src matlab :results value replace :exports results :tangle no +dcgain(G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'})) +#+end_src + +#+RESULTS: +| 1.9869e-06 | 2.043e-08 | 1.6444e-09 | -4.094e-08 | 8.7579e-06 | -3.5002e-09 | +| 3.746e-09 | 1.9841e-06 | -5.5274e-09 | -8.7257e-06 | -5.5082e-08 | -7.6978e-09 | +| -3.2056e-09 | -6.4295e-11 | 2.6079e-07 | 3.4103e-10 | -9.3873e-09 | 9.6146e-10 | +| -1.1677e-08 | -8.736e-06 | 2.4322e-08 | 4.5343e-05 | 2.52e-07 | 2.5932e-08 | +| 8.7439e-06 | 8.441e-08 | 5.9144e-09 | -1.6879e-07 | 4.546e-05 | -9.8986e-09 | +| 3.3453e-09 | 4.508e-10 | 1.8718e-09 | -2.7294e-09 | 2.8776e-08 | 1.3193e-05 | + +We can see that we have almost the same stiffness: + +#+begin_src matlab :results value replace :exports results :tangle no +inv(Ks)./dcgain(G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'})) +#+end_src + +#+RESULTS: +| 1.0034 | 0.00037703 | -0.0096597 | 0.0041063 | 1.0037 | -0.0087071 | +| 0.0020562 | 1.0048 | -0.0049247 | 1.0074 | -0.00011815 | -0.0037178 | +| 0.0049552 | -0.42338 | 1.0013 | -0.38734 | 0.0065754 | 0.042021 | +| 0.014397 | 1.0062 | -0.005431 | 1.0081 | -0.0022929 | -0.017668 | +| 1.0053 | 7.7101e-05 | -0.010436 | 0.0034233 | 1.0055 | -0.052157 | +| 0.0091102 | 0.063485 | 0.021584 | 0.16786 | 0.017941 | 1.0063 | + +* To-order :noexport: +** APA300ML structure + +#+begin_src matlab +open('matlab/nano_hexapod/apa300ml.slx') +#+end_src + +#+begin_src matlab +%% Options for Linearized +options = linearizeOptions; +options.SampleTime = 0; + +%% Name of the Simulink File +mdl = 'apa300ml_structure'; + +%% Input/Output definition +clear io; io_i = 1; +io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs +io(io_i) = linio([mdl, '/Fa'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs +io(io_i) = linio([mdl, '/D'], 1, 'openoutput'); io_i = io_i + 1; % Relative Motion Outputs +io(io_i) = linio([mdl, '/x'], 1, 'openoutput'); io_i = io_i + 1; % Relative Motion Outputs + +%% Run the linearization +G = linearize(mdl, io, 0.0, options); +G.InputName = {'F', 'Fa'}; +G.OutputName = {'D', 'x'}; +#+end_src + +#+begin_src matlab +dcgain(G('D', 'Fa'))/dcgain(G('x', 'Fa')) +#+end_src + +#+begin_src matlab :exports none +freqs = logspace(1, 4, 1000); + +figure; +tiledlayout(1, 2, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile; +hold on; +plot(freqs, abs(squeeze(freqresp(G('D', 'Fa'), freqs, 'Hz')))); +plot(freqs, abs(squeeze(freqresp(G('x', 'Fa'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + +ax2 = nexttile; +hold on; +plot(freqs, 180/pi*angle(squeeze(freqresp(G('D', 'Fa'), freqs, 'Hz')))); +plot(freqs, 180/pi*angle(squeeze(freqresp(G('x', 'Fa'), freqs, 'Hz')))); +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'); +#+end_src + +#+begin_src matlab :exports none +freqs = logspace(1, 4, 1000); + +figure; + +ax1 = subplot(2, 1, 1); +hold on; +plot(freqs, abs(squeeze(freqresp(G('D', 'Fa'), freqs, 'Hz')))); +plot(freqs, abs(squeeze(freqresp(G('x', 'Fa'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + +ax2 = subplot(2, 1, 2); +hold on; +plot(freqs, 180/pi*angle(squeeze(freqresp(G('D', 'Fa'), freqs, 'Hz')))); +plot(freqs, 180/pi*angle(squeeze(freqresp(G('x', 'Fa'), freqs, 'Hz')))); +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'); +#+end_src + +** Full APA300ML +*** Matlab Init :noexport:ignore: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) +<> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes +<> +#+end_src + +#+begin_src matlab :tangle no +simulinkproject('../'); +#+end_src + +*** APA +#+begin_src matlab +K = readmatrix('APA300ML_full_mat_K.CSV'); +M = readmatrix('APA300ML_full_mat_M.CSV'); +[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('APA300ML_full_out_nodes_3D.txt'); +#+end_src + +#+begin_src matlab +open('matlab/nano_hexapod/apa300ml.slx') +#+end_src + +*** APA Stiffness +#+begin_src matlab +%% Options for Linearized +options = linearizeOptions; +options.SampleTime = 0; + +%% Name of the Simulink File +mdl = 'apa300ml'; + +%% Input/Output definition +clear io; io_i = 1; +io(io_i) = linio([mdl, '/Fext'], 1, 'openinput'); io_i = io_i + 1; +io(io_i) = linio([mdl, '/L'], 1, 'openoutput'); io_i = io_i + 1; + +%% Run the linearization +G = linearize(mdl, io, 0.0, options); +G.InputName = {'Fe'}; +G.OutputName = {'L'}; +#+end_src + +#+begin_src matlab :results value replace +1./dcgain(G) +#+end_src + +#+RESULTS: +: 1796000.0 + +Same as documentation + +*** Amplification Factor +#+begin_src matlab +%% Options for Linearized +options = linearizeOptions; +options.SampleTime = 0; + +%% Name of the Simulink File +mdl = 'apa300ml'; + +%% Input/Output definition +clear io; io_i = 1; +io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1; +io(io_i) = linio([mdl, '/L'], 1, 'openoutput'); io_i = io_i + 1; +io(io_i) = linio([mdl, '/Ls'], 1, 'openoutput'); io_i = io_i + 1; +% io(io_i) = linio([mdl, '/Sensor Stack'], 1, 'openoutput'); io_i = io_i + 1; +% io(io_i) = linio([mdl, '/Actuator Stack'], 1, 'openoutput'); io_i = io_i + 1; + +%% Run the linearization +G = linearize(mdl, io, 0.0, options); +G.InputName = {'F'}; +G.OutputName = {'L', 'Ls'}; +#+end_src + +#+begin_src matlab :results value replace +abs(dcgain(G('L', 'F'))./dcgain(G('Ls', 'F'))) +#+end_src + +#+RESULTS: +: 5.1155 + +Same as estimated. + +*** Plant +Identification +#+begin_src matlab +%% Options for Linearized +options = linearizeOptions; +options.SampleTime = 0; + +%% Name of the Simulink File +mdl = 'apa300ml'; + +%% Input/Output definition +clear io; io_i = 1; +io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs +io(io_i) = linio([mdl, '/L'], 1, 'openoutput'); io_i = io_i + 1; % Relative Motion Outputs +io(io_i) = linio([mdl, '/Sensor Stack'], 1, 'openoutput'); io_i = io_i + 1; % Force Sensor + +%% Run the linearization +G = linearize(mdl, io, 0.0, options); +G.InputName = {'F'}; +G.OutputName = {'L', 'dL'}; +#+end_src + +IFF Plant +#+begin_src matlab :exports none +freqs = logspace(1, 4, 1000); + +figure; + +ax1 = subplot(2, 1, 1); +hold on; +plot(freqs, abs(squeeze(freqresp(G('dL', 'F'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); + +ax2 = subplot(2, 1, 2); +hold on; +plot(freqs, 180/pi*angle(squeeze(freqresp(G('dL', 'F'), freqs, 'Hz')))); +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'); +#+end_src + +DVF Plant +#+begin_src matlab :exports none +freqs = logspace(1, 4, 1000); + +figure; + +ax1 = subplot(2, 1, 1); +hold on; +plot(freqs, abs(squeeze(freqresp(G('L', 'F'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + +ax2 = subplot(2, 1, 2); +hold on; +plot(freqs, 180/pi*angle(squeeze(freqresp(G('L', 'F'), freqs, 'Hz')))); +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'); +#+end_src + +*** Reduction from Full APA to 2DoF system + +#+begin_src matlab +m = 1; % [kg] +#+end_src + +Identification of the full APA model: +#+begin_src matlab +%% Options for Linearized +options = linearizeOptions; +options.SampleTime = 0; + +%% Name of the Simulink File +mdl = 'apa300ml'; + +%% Input/Output definition +clear io; io_i = 1; +io(io_i) = linio([mdl, '/Fa'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force +io(io_i) = linio([mdl, '/Fe'], 1, 'openinput'); io_i = io_i + 1; % External Force +io(io_i) = linio([mdl, '/Fm'], 1, 'openoutput'); io_i = io_i + 1; % Force Sensor +io(io_i) = linio([mdl, '/dL'], 1, 'openoutput'); io_i = io_i + 1; % Relative Motion Sensor + +%% Run the linearization +G = linearize(mdl, io, 0.0, options); +G.InputName = {'Fa', 'Fe'}; +G.OutputName = {'Fm', 'dL'}; +#+end_src + +#+begin_src matlab :results output replace :exports results :tangle no +size(G) +#+end_src + +#+RESULTS: +: size(G) +: State-space model with 2 outputs, 2 inputs, and 50 states. + +#+begin_src matlab +k = 0.35e6; +c = 3e1; +ka = 43e6; +ke = 1.5e6; + +Leq = 0.056; % [m] +#+end_src + +Identification of the 2-DoF APA model: +#+begin_src matlab +open('matlab/nano_hexapod/apa300ml_2dof.slx') + +%% Options for Linearized +options = linearizeOptions; +options.SampleTime = 0; + +%% Name of the Simulink File +mdl = 'apa300ml_2dof'; + +%% Input/Output definition +clear io; io_i = 1; +io(io_i) = linio([mdl, '/Fa'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force +io(io_i) = linio([mdl, '/Fe'], 1, 'openinput'); io_i = io_i + 1; % External Force +io(io_i) = linio([mdl, '/Fm'], 1, 'openoutput'); io_i = io_i + 1; % Force Sensor +io(io_i) = linio([mdl, '/dL'], 1, 'openoutput'); io_i = io_i + 1; % Relative Motion Sensor + +%% Run the linearization +Gb = linearize(mdl, io, 0.0, options); +Gb.InputName = {'Fa', 'Fe'}; +Gb.OutputName = {'Fm', 'dL'}; +#+end_src + +#+begin_src matlab :results output replace :exports results :tangle no +size(Gb) +#+end_src + +#+RESULTS: +: size(Gb) +: State-space model with 2 outputs, 2 inputs, and 4 states. + +From external force to displacement +#+begin_src matlab :exports none +freqs = logspace(1, 4, 1000); + +figure; + +ax1 = subplot(2, 1, 1); +hold on; +plot(freqs, abs(squeeze(freqresp(G( 'dL', 'Fe'), freqs, 'Hz')))); +plot(freqs, abs(squeeze(freqresp(Gb('dL', 'Fe'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); + +ax2 = subplot(2, 1, 2); +hold on; +plot(freqs, 180/pi*angle(squeeze(freqresp(G( 'dL', 'Fe'), freqs, 'Hz')))); +plot(freqs, 180/pi*angle(squeeze(freqresp(Gb('dL', 'Fe'), freqs, 'Hz')))); +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'); +#+end_src + +From external force to force sensor +#+begin_src matlab :exports none +freqs = logspace(1, 4, 1000); + +figure; + +ax1 = subplot(2, 1, 1); +hold on; +plot(freqs, abs(squeeze(freqresp(G( 'Fm', 'Fe'), freqs, 'Hz')))); +plot(freqs, abs(squeeze(freqresp(Gb('Fm', 'Fe'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); + +ax2 = subplot(2, 1, 2); +hold on; +plot(freqs, 180/pi*angle(squeeze(freqresp(G( 'Fm', 'Fe'), freqs, 'Hz')))); +plot(freqs, 180/pi*angle(squeeze(freqresp(Gb('Fm', 'Fe'), freqs, 'Hz')))); +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'); +#+end_src + +From Actuator to displacement +#+begin_src matlab :exports none +freqs = logspace(1, 4, 1000); + +figure; + +ax1 = subplot(2, 1, 1); +hold on; +plot(freqs, abs(squeeze(freqresp(G( 'dL', 'Fa'), freqs, 'Hz')))); +plot(freqs, abs(squeeze(freqresp(Gb('dL', 'Fa'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); + +ax2 = subplot(2, 1, 2); +hold on; +plot(freqs, 180/pi*angle(squeeze(freqresp(G( 'dL', 'Fa'), freqs, 'Hz')))); +plot(freqs, 180/pi*angle(squeeze(freqresp(Gb('dL', 'Fa'), freqs, 'Hz')))); +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'); +#+end_src + +From Actuator to Force Sensor +#+begin_src matlab :exports none +freqs = logspace(1, 4, 1000); + +figure; + +ax1 = subplot(2, 1, 1); +hold on; +plot(freqs, abs(squeeze(freqresp(G( 'Fm', 'Fa'), freqs, 'Hz')))); +plot(freqs, abs(squeeze(freqresp(Gb('Fm', 'Fa'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); + +ax2 = subplot(2, 1, 2); +hold on; +plot(freqs, 180/pi*angle(squeeze(freqresp(G( 'Fm', 'Fa'), freqs, 'Hz')))); +plot(freqs, 180/pi*angle(squeeze(freqresp(Gb('Fm', 'Fa'), freqs, 'Hz')))); +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'); +#+end_src + +#+begin_src matlab +tiledlayout(2, 2, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile; +hold on; +plot(freqs, abs(squeeze(freqresp(G( 'dL', 'Fa'), freqs, 'Hz')))); +plot(freqs, abs(squeeze(freqresp(Gb('dL', 'Fa'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +set(gca, 'XTickLabel',[]); ylabel('To vertical motion [m]'); +title('From Actuator $F_a$ [N]'); + +ax2 = nexttile; +hold on; +plot(freqs, abs(squeeze(freqresp(G( 'dL', 'Fe'), freqs, 'Hz')))); +plot(freqs, abs(squeeze(freqresp(Gb('dL', 'Fe'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +set(gca, 'XTickLabel',[]); set(gca, 'YTickLabel',[]); +title('From External $F_e$ [N]'); + +ax3 = nexttile; +hold on; +plot(freqs, abs(squeeze(freqresp(G( 'Fm', 'Fa'), freqs, 'Hz')))); +plot(freqs, abs(squeeze(freqresp(Gb('Fm', 'Fa'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('To Force Sensor [N]'); + +ax4 = nexttile; +hold on; +plot(freqs, abs(squeeze(freqresp(G( 'Fm', 'Fe'), freqs, 'Hz')))); +plot(freqs, abs(squeeze(freqresp(Gb('Fm', 'Fe'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]); + +linkaxes([ax1,ax2,ax3,ax4],'x'); +linkaxes([ax1,ax2],'y'); +linkaxes([ax3,ax4],'y'); +#+end_src + +*** Reduction from Full APA to 2DoF system + +#+begin_src matlab +Ms = [0.1, 1, 5, 10]; % [kg] +#+end_src + +Identification of the full APA model: +#+begin_src matlab +%% Options for Linearized +options = linearizeOptions; +options.SampleTime = 0; + +%% Name of the Simulink File +mdl = 'apa300ml'; + +%% Input/Output definition +clear io; io_i = 1; +io(io_i) = linio([mdl, '/Fa'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force +io(io_i) = linio([mdl, '/Fe'], 1, 'openinput'); io_i = io_i + 1; % External Force +io(io_i) = linio([mdl, '/Fm'], 1, 'openoutput'); io_i = io_i + 1; % Force Sensor +io(io_i) = linio([mdl, '/dL'], 1, 'openoutput'); io_i = io_i + 1; % Relative Motion Sensor + +%% Run the linearization +G = linearize(mdl, io, 0.0, options); +G.InputName = {'Fa', 'Fe'}; +G.OutputName = {'Fm', 'dL'}; +#+end_src + +#+begin_src matlab :results output replace :exports results :tangle no +size(G) +#+end_src + +#+RESULTS: +: size(G) +: State-space model with 2 outputs, 2 inputs, and 50 states. + +#+begin_src matlab +k = 0.35e6; +c = 3e1; +ka = 43e6; +ke = 1.5e6; + +Leq = 0.056; % [m] +#+end_src + +Identification of the 2-DoF APA model: +#+begin_src matlab +open('matlab/nano_hexapod/apa300ml_2dof.slx') + +%% Options for Linearized +options = linearizeOptions; +options.SampleTime = 0; + +%% Name of the Simulink File +mdl = 'apa300ml_2dof'; + +%% Input/Output definition +clear io; io_i = 1; +io(io_i) = linio([mdl, '/Fa'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force +io(io_i) = linio([mdl, '/Fe'], 1, 'openinput'); io_i = io_i + 1; % External Force +io(io_i) = linio([mdl, '/Fm'], 1, 'openoutput'); io_i = io_i + 1; % Force Sensor +io(io_i) = linio([mdl, '/dL'], 1, 'openoutput'); io_i = io_i + 1; % Relative Motion Sensor + +%% Run the linearization +Gb = linearize(mdl, io, 0.0, options); +Gb.InputName = {'Fa', 'Fe'}; +Gb.OutputName = {'Fm', 'dL'}; +#+end_src + +#+begin_src matlab :results output replace :exports results :tangle no +size(Gb) +#+end_src + +#+RESULTS: +: size(Gb) +: State-space model with 2 outputs, 2 inputs, and 4 states. + +From external force to displacement +#+begin_src matlab :exports none +freqs = logspace(1, 4, 1000); + +figure; + +ax1 = subplot(2, 1, 1); +hold on; +plot(freqs, abs(squeeze(freqresp(G( 'dL', 'Fe'), freqs, 'Hz')))); +plot(freqs, abs(squeeze(freqresp(Gb('dL', 'Fe'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); + +ax2 = subplot(2, 1, 2); +hold on; +plot(freqs, 180/pi*angle(squeeze(freqresp(G( 'dL', 'Fe'), freqs, 'Hz')))); +plot(freqs, 180/pi*angle(squeeze(freqresp(Gb('dL', 'Fe'), freqs, 'Hz')))); +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'); +#+end_src + +From external force to force sensor +#+begin_src matlab :exports none +freqs = logspace(1, 4, 1000); + +figure; + +ax1 = subplot(2, 1, 1); +hold on; +plot(freqs, abs(squeeze(freqresp(G( 'Fm', 'Fe'), freqs, 'Hz')))); +plot(freqs, abs(squeeze(freqresp(Gb('Fm', 'Fe'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); + +ax2 = subplot(2, 1, 2); +hold on; +plot(freqs, 180/pi*angle(squeeze(freqresp(G( 'Fm', 'Fe'), freqs, 'Hz')))); +plot(freqs, 180/pi*angle(squeeze(freqresp(Gb('Fm', 'Fe'), freqs, 'Hz')))); +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'); +#+end_src + +From Actuator to displacement +#+begin_src matlab :exports none +freqs = logspace(1, 4, 1000); + +figure; + +ax1 = subplot(2, 1, 1); +hold on; +plot(freqs, abs(squeeze(freqresp(G( 'dL', 'Fa'), freqs, 'Hz')))); +plot(freqs, abs(squeeze(freqresp(Gb('dL', 'Fa'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); + +ax2 = subplot(2, 1, 2); +hold on; +plot(freqs, 180/pi*angle(squeeze(freqresp(G( 'dL', 'Fa'), freqs, 'Hz')))); +plot(freqs, 180/pi*angle(squeeze(freqresp(Gb('dL', 'Fa'), freqs, 'Hz')))); +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'); +#+end_src + +From Actuator to Force Sensor +#+begin_src matlab :exports none +freqs = logspace(1, 4, 1000); + +figure; + +ax1 = subplot(2, 1, 1); +hold on; +plot(freqs, abs(squeeze(freqresp(G( 'Fm', 'Fa'), freqs, 'Hz')))); +plot(freqs, abs(squeeze(freqresp(Gb('Fm', 'Fa'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); + +ax2 = subplot(2, 1, 2); +hold on; +plot(freqs, 180/pi*angle(squeeze(freqresp(G( 'Fm', 'Fa'), freqs, 'Hz')))); +plot(freqs, 180/pi*angle(squeeze(freqresp(Gb('Fm', 'Fa'), freqs, 'Hz')))); +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'); +#+end_src + +#+begin_src matlab +tiledlayout(2, 2, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile; +hold on; +plot(freqs, abs(squeeze(freqresp(G( 'dL', 'Fa'), freqs, 'Hz')))); +plot(freqs, abs(squeeze(freqresp(Gb('dL', 'Fa'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +set(gca, 'XTickLabel',[]); ylabel('To vertical motion [m]'); +title('From Actuator $F_a$ [N]'); + +ax2 = nexttile; +hold on; +plot(freqs, abs(squeeze(freqresp(G( 'dL', 'Fe'), freqs, 'Hz')))); +plot(freqs, abs(squeeze(freqresp(Gb('dL', 'Fe'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +set(gca, 'XTickLabel',[]); set(gca, 'YTickLabel',[]); +title('From External $F_e$ [N]'); + +ax3 = nexttile; +hold on; +plot(freqs, abs(squeeze(freqresp(G( 'Fm', 'Fa'), freqs, 'Hz')))); +plot(freqs, abs(squeeze(freqresp(Gb('Fm', 'Fa'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('To Force Sensor [N]'); + +ax4 = nexttile; +hold on; +plot(freqs, abs(squeeze(freqresp(G( 'Fm', 'Fe'), freqs, 'Hz')))); +plot(freqs, abs(squeeze(freqresp(Gb('Fm', 'Fe'), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]); + +linkaxes([ax1,ax2,ax3,ax4],'x'); +linkaxes([ax1,ax2],'y'); +linkaxes([ax3,ax4],'y'); +#+end_src + +* Function - Initialize Nano Hexapod +:PROPERTIES: +:header-args:matlab+: :tangle ../src/initializeNanoHexapodFinal.m +:header-args:matlab+: :comments none :mkdirp yes :eval no +:END: +<> + +** Function description +:PROPERTIES: +:UNNUMBERED: t +:END: +#+begin_src matlab + function [nano_hexapod] = initializeNanoHexapodFinal(args) +#+end_src + +** Optional Parameters +:PROPERTIES: +:UNNUMBERED: t +:END: +#+begin_src matlab + arguments + %% Bottom Flexible Joints + args.flex_bot_type char {mustBeMember(args.flex_bot_type,{'2dof', '3dof', '4dof', 'flexible'})} = '4dof' + args.flex_bot_kRx (6,1) double {mustBeNumeric} = ones(6,1)*5 % X bending stiffness [Nm/rad] + args.flex_bot_kRy (6,1) double {mustBeNumeric} = ones(6,1)*5 % Y bending stiffness [Nm/rad] + args.flex_bot_kRz (6,1) double {mustBeNumeric} = ones(6,1)*260 % Torsionnal stiffness [Nm/rad] + args.flex_bot_kz (6,1) double {mustBeNumeric} = ones(6,1)*1e8 % Axial Stiffness [N/m] + args.flex_bot_cRx (6,1) double {mustBeNumeric} = ones(6,1)*0.1 % X bending Damping [Nm/(rad/s)] + args.flex_bot_cRy (6,1) double {mustBeNumeric} = ones(6,1)*0.1 % Y bending Damping [Nm/(rad/s)] + args.flex_bot_cRz (6,1) double {mustBeNumeric} = ones(6,1)*0.1 % Torsionnal Damping [Nm/(rad/s)] + args.flex_bot_cz (6,1) double {mustBeNumeric} = ones(6,1)*1e2 % Axial Damping [N/(m/s)] + %% Top Flexible Joints + args.flex_top_type char {mustBeMember(args.flex_top_type,{'2dof', '3dof', '4dof', 'flexible'})} = '4dof' + args.flex_top_kRx (6,1) double {mustBeNumeric} = ones(6,1)*5 % X bending stiffness [Nm/rad] + args.flex_top_kRy (6,1) double {mustBeNumeric} = ones(6,1)*5 % Y bending stiffness [Nm/rad] + args.flex_top_kRz (6,1) double {mustBeNumeric} = ones(6,1)*260 % Torsionnal stiffness [Nm/rad] + args.flex_top_kz (6,1) double {mustBeNumeric} = ones(6,1)*1e8 % Axial Stiffness [N/m] + args.flex_top_cRx (6,1) double {mustBeNumeric} = ones(6,1)*0.1 % X bending Damping [Nm/(rad/s)] + args.flex_top_cRy (6,1) double {mustBeNumeric} = ones(6,1)*0.1 % Y bending Damping [Nm/(rad/s)] + args.flex_top_cRz (6,1) double {mustBeNumeric} = ones(6,1)*0.1 % Torsionnal Damping [Nm/(rad/s)] + args.flex_top_cz (6,1) double {mustBeNumeric} = ones(6,1)*1e2 % Axial Damping [N/(m/s)] + %% Relative Motion Sensor + args.motion_sensor_type char {mustBeMember(args.motion_sensor_type,{'struts', 'plates'})} = 'struts' + %% Actuators + args.actuator_type char {mustBeMember(args.actuator_type,{'2dof', 'flexible frame', 'flexible'})} = 'flexible' + args.actuator_Ga (6,1) double {mustBeNumeric} = ones(6,1)*1 % Actuator gain [N/V] + args.actuator_Gs (6,1) double {mustBeNumeric} = ones(6,1)*1 % Sensor gain [V/m] + % For 2DoF + args.actuator_k (6,1) double {mustBeNumeric} = ones(6,1)*0.35e6 % [N/m] + args.actuator_ke (6,1) double {mustBeNumeric} = ones(6,1)*1.5e6 % [N/m] + args.actuator_ka (6,1) double {mustBeNumeric} = ones(6,1)*43e6 % [N/m] + args.actuator_c (6,1) double {mustBeNumeric} = ones(6,1)*3e1 % [N/(m/s)] + args.actuator_ce (6,1) double {mustBeNumeric} = ones(6,1)*1e1 % [N/(m/s)] + args.actuator_ca (6,1) double {mustBeNumeric} = ones(6,1)*1e1 % [N/(m/s)] + args.actuator_Leq (6,1) double {mustBeNumeric} = ones(6,1)*0.056 % [m] + % For Flexible Frame + args.actuator_ks (6,1) double {mustBeNumeric} = ones(6,1)*235e6 % Stiffness of one stack [N/m] + args.actuator_cs (6,1) double {mustBeNumeric} = ones(6,1)*1e1 % Stiffness of one stack [N/m] + % For Flexible + args.actuator_xi (1,1) double {mustBeNumeric} = 0.01 % Sensor gain [V/m] + end +#+end_src + +** Nano Hexapod Object +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +nano_hexapod = struct(); +#+end_src + +** Flexible Joints - Bot +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +nano_hexapod.flex_bot = struct(); + +switch args.flex_bot_type + case '2dof' + nano_hexapod.flex_bot.type = 1; + case '3dof' + nano_hexapod.flex_bot.type = 2; + case '4dof' + nano_hexapod.flex_bot.type = 3; + case 'flexible' + nano_hexapod.flex_bot.type = 4; +end + +nano_hexapod.flex_bot.kRx = args.flex_bot_kRx; % X bending stiffness [Nm/rad] +nano_hexapod.flex_bot.kRy = args.flex_bot_kRy; % Y bending stiffness [Nm/rad] +nano_hexapod.flex_bot.kRz = args.flex_bot_kRz; % Torsionnal stiffness [Nm/rad] +nano_hexapod.flex_bot.kz = args.flex_bot_kz; % Axial stiffness [N/m] + +nano_hexapod.flex_bot.cRx = args.flex_bot_cRx; % [Nm/(rad/s)] +nano_hexapod.flex_bot.cRy = args.flex_bot_cRy; % [Nm/(rad/s)] +nano_hexapod.flex_bot.cRz = args.flex_bot_cRz; % [Nm/(rad/s)] +nano_hexapod.flex_bot.cz = args.flex_bot_cz; %[N/(m/s)] +#+end_src + +** Flexible Joints - Top +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +nano_hexapod.flex_top = struct(); + +switch args.flex_top_type + case '2dof' + nano_hexapod.flex_top.type = 1; + case '3dof' + nano_hexapod.flex_top.type = 2; + case '4dof' + nano_hexapod.flex_top.type = 3; + case 'flexible' + nano_hexapod.flex_top.type = 4; +end + +nano_hexapod.flex_top.kRx = args.flex_top_kRx; % X bending stiffness [Nm/rad] +nano_hexapod.flex_top.kRy = args.flex_top_kRy; % Y bending stiffness [Nm/rad] +nano_hexapod.flex_top.kRz = args.flex_top_kRz; % Torsionnal stiffness [Nm/rad] +nano_hexapod.flex_top.kz = args.flex_top_kz; % Axial stiffness [N/m] + +nano_hexapod.flex_top.cRx = args.flex_top_cRx; % [Nm/(rad/s)] +nano_hexapod.flex_top.cRy = args.flex_top_cRy; % [Nm/(rad/s)] +nano_hexapod.flex_top.cRz = args.flex_top_cRz; % [Nm/(rad/s)] +nano_hexapod.flex_top.cz = args.flex_top_cz; %[N/(m/s)] +#+end_src + +** Relative Motion Sensor +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +nano_hexapod.motion_sensor = struct(); + +switch args.motion_sensor_type + case 'struts' + nano_hexapod.motion_sensor.type = 1; + case 'plates' + nano_hexapod.motion_sensor.type = 2; +end +#+end_src + +** Amplified Piezoelectric Actuator +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +nano_hexapod.actuator = struct(); + +switch args.actuator_type + case '2dof' + nano_hexapod.actuator.type = 1; + case 'flexible frame' + nano_hexapod.actuator.type = 2; + case 'flexible' + nano_hexapod.actuator.type = 3; +end +#+end_src + +#+begin_src matlab +nano_hexapod.actuator.Ga = args.actuator_Ga; % Actuator gain [N/V] +nano_hexapod.actuator.Gs = args.actuator_Gs; % Sensor gain [V/m] +#+end_src + +2dof +#+begin_src matlab +nano_hexapod.actuator.k = args.actuator_k; % [N/m] +nano_hexapod.actuator.ke = args.actuator_ke; % [N/m] +nano_hexapod.actuator.ka = args.actuator_ka; % [N/m] + +nano_hexapod.actuator.c = args.actuator_c; % [N/(m/s)] +nano_hexapod.actuator.ce = args.actuator_ce; % [N/(m/s)] +nano_hexapod.actuator.ca = args.actuator_ca; % [N/(m/s)] + +nano_hexapod.actuator.Leq = args.actuator_Leq; % [m] +#+end_src + +Flexible frame and fully flexible +#+begin_src matlab +switch args.actuator_type + case 'flexible frame' + nano_hexapod.actuator.K = readmatrix('APA300ML_b_mat_K.CSV'); % Stiffness Matrix + nano_hexapod.actuator.M = readmatrix('APA300ML_b_mat_M.CSV'); % Mass Matrix + nano_hexapod.actuator.P = extractNodes('APA300ML_b_out_nodes_3D.txt'); % Node coordinates [m] + case 'flexible' + nano_hexapod.actuator.K = readmatrix('APA300ML_full_mat_K.CSV'); % Stiffness Matrix + nano_hexapod.actuator.M = readmatrix('APA300ML_full_mat_M.CSV'); % Mass Matrix + nano_hexapod.actuator.P = extractNodes('APA300ML_full_out_nodes_3D.txt'); % Node coordiantes [m] +end + +nano_hexapod.actuator.xi = args.actuator_xi; % Damping ratio + +nano_hexapod.actuator.ks = args.actuator_ks; % Stiffness of one stack [N/m] +nano_hexapod.actuator.cs = args.actuator_cs; % Damping of one stack [N/m] +#+end_src + +** Save the Structure +:PROPERTIES: +:UNNUMBERED: t +:END: +#+begin_src matlab +save('./mat/stages.mat', 'nano_hexapod', '-append'); +#+end_src diff --git a/src/initializeNanoHexapodFinal.m b/src/initializeNanoHexapodFinal.m new file mode 100644 index 0000000..2ca89dd --- /dev/null +++ b/src/initializeNanoHexapodFinal.m @@ -0,0 +1,142 @@ + function [nano_hexapod] = initializeNanoHexapodFinal(args) + + arguments + %% Bottom Flexible Joints + args.flex_bot_type char {mustBeMember(args.flex_bot_type,{'2dof', '3dof', '4dof', 'flexible'})} = '4dof' + args.flex_bot_kRx (6,1) double {mustBeNumeric} = ones(6,1)*5 % X bending stiffness [Nm/rad] + args.flex_bot_kRy (6,1) double {mustBeNumeric} = ones(6,1)*5 % Y bending stiffness [Nm/rad] + args.flex_bot_kRz (6,1) double {mustBeNumeric} = ones(6,1)*260 % Torsionnal stiffness [Nm/rad] + args.flex_bot_kz (6,1) double {mustBeNumeric} = ones(6,1)*1e8 % Axial Stiffness [N/m] + args.flex_bot_cRx (6,1) double {mustBeNumeric} = ones(6,1)*0.1 % X bending Damping [Nm/(rad/s)] + args.flex_bot_cRy (6,1) double {mustBeNumeric} = ones(6,1)*0.1 % Y bending Damping [Nm/(rad/s)] + args.flex_bot_cRz (6,1) double {mustBeNumeric} = ones(6,1)*0.1 % Torsionnal Damping [Nm/(rad/s)] + args.flex_bot_cz (6,1) double {mustBeNumeric} = ones(6,1)*1e2 % Axial Damping [N/(m/s)] + %% Top Flexible Joints + args.flex_top_type char {mustBeMember(args.flex_top_type,{'2dof', '3dof', '4dof', 'flexible'})} = '4dof' + args.flex_top_kRx (6,1) double {mustBeNumeric} = ones(6,1)*5 % X bending stiffness [Nm/rad] + args.flex_top_kRy (6,1) double {mustBeNumeric} = ones(6,1)*5 % Y bending stiffness [Nm/rad] + args.flex_top_kRz (6,1) double {mustBeNumeric} = ones(6,1)*260 % Torsionnal stiffness [Nm/rad] + args.flex_top_kz (6,1) double {mustBeNumeric} = ones(6,1)*1e8 % Axial Stiffness [N/m] + args.flex_top_cRx (6,1) double {mustBeNumeric} = ones(6,1)*0.1 % X bending Damping [Nm/(rad/s)] + args.flex_top_cRy (6,1) double {mustBeNumeric} = ones(6,1)*0.1 % Y bending Damping [Nm/(rad/s)] + args.flex_top_cRz (6,1) double {mustBeNumeric} = ones(6,1)*0.1 % Torsionnal Damping [Nm/(rad/s)] + args.flex_top_cz (6,1) double {mustBeNumeric} = ones(6,1)*1e2 % Axial Damping [N/(m/s)] + %% Relative Motion Sensor + args.motion_sensor_type char {mustBeMember(args.motion_sensor_type,{'struts', 'plates'})} = 'struts' + %% Actuators + args.actuator_type char {mustBeMember(args.actuator_type,{'2dof', 'flexible frame', 'flexible'})} = 'flexible' + args.actuator_Ga (6,1) double {mustBeNumeric} = ones(6,1)*1 % Actuator gain [N/V] + args.actuator_Gs (6,1) double {mustBeNumeric} = ones(6,1)*1 % Sensor gain [V/m] + % For 2DoF + args.actuator_k (6,1) double {mustBeNumeric} = ones(6,1)*0.35e6 % [N/m] + args.actuator_ke (6,1) double {mustBeNumeric} = ones(6,1)*1.5e6 % [N/m] + args.actuator_ka (6,1) double {mustBeNumeric} = ones(6,1)*43e6 % [N/m] + args.actuator_c (6,1) double {mustBeNumeric} = ones(6,1)*3e1 % [N/(m/s)] + args.actuator_ce (6,1) double {mustBeNumeric} = ones(6,1)*1e1 % [N/(m/s)] + args.actuator_ca (6,1) double {mustBeNumeric} = ones(6,1)*1e1 % [N/(m/s)] + args.actuator_Leq (6,1) double {mustBeNumeric} = ones(6,1)*0.056 % [m] + % For Flexible Frame + args.actuator_ks (6,1) double {mustBeNumeric} = ones(6,1)*235e6 % Stiffness of one stack [N/m] + args.actuator_cs (6,1) double {mustBeNumeric} = ones(6,1)*1e1 % Stiffness of one stack [N/m] + % For Flexible + args.actuator_xi (1,1) double {mustBeNumeric} = 0.01 % Sensor gain [V/m] + end + +nano_hexapod = struct(); + +nano_hexapod.flex_bot = struct(); + +switch args.flex_bot_type + case '2dof' + nano_hexapod.flex_bot.type = 1; + case '3dof' + nano_hexapod.flex_bot.type = 2; + case '4dof' + nano_hexapod.flex_bot.type = 3; + case 'flexible' + nano_hexapod.flex_bot.type = 4; +end + +nano_hexapod.flex_bot.kRx = args.flex_bot_kRx; % X bending stiffness [Nm/rad] +nano_hexapod.flex_bot.kRy = args.flex_bot_kRy; % Y bending stiffness [Nm/rad] +nano_hexapod.flex_bot.kRz = args.flex_bot_kRz; % Torsionnal stiffness [Nm/rad] +nano_hexapod.flex_bot.kz = args.flex_bot_kz; % Axial stiffness [N/m] + +nano_hexapod.flex_bot.cRx = args.flex_bot_cRx; % [Nm/(rad/s)] +nano_hexapod.flex_bot.cRy = args.flex_bot_cRy; % [Nm/(rad/s)] +nano_hexapod.flex_bot.cRz = args.flex_bot_cRz; % [Nm/(rad/s)] +nano_hexapod.flex_bot.cz = args.flex_bot_cz; %[N/(m/s)] + +nano_hexapod.flex_top = struct(); + +switch args.flex_top_type + case '2dof' + nano_hexapod.flex_top.type = 1; + case '3dof' + nano_hexapod.flex_top.type = 2; + case '4dof' + nano_hexapod.flex_top.type = 3; + case 'flexible' + nano_hexapod.flex_top.type = 4; +end + +nano_hexapod.flex_top.kRx = args.flex_top_kRx; % X bending stiffness [Nm/rad] +nano_hexapod.flex_top.kRy = args.flex_top_kRy; % Y bending stiffness [Nm/rad] +nano_hexapod.flex_top.kRz = args.flex_top_kRz; % Torsionnal stiffness [Nm/rad] +nano_hexapod.flex_top.kz = args.flex_top_kz; % Axial stiffness [N/m] + +nano_hexapod.flex_top.cRx = args.flex_top_cRx; % [Nm/(rad/s)] +nano_hexapod.flex_top.cRy = args.flex_top_cRy; % [Nm/(rad/s)] +nano_hexapod.flex_top.cRz = args.flex_top_cRz; % [Nm/(rad/s)] +nano_hexapod.flex_top.cz = args.flex_top_cz; %[N/(m/s)] + +nano_hexapod.motion_sensor = struct(); + +switch args.motion_sensor_type + case 'struts' + nano_hexapod.motion_sensor.type = 1; + case 'plates' + nano_hexapod.motion_sensor.type = 2; +end + +nano_hexapod.actuator = struct(); + +switch args.actuator_type + case '2dof' + nano_hexapod.actuator.type = 1; + case 'flexible frame' + nano_hexapod.actuator.type = 2; + case 'flexible' + nano_hexapod.actuator.type = 3; +end + +nano_hexapod.actuator.Ga = args.actuator_Ga; % Actuator gain [N/V] +nano_hexapod.actuator.Gs = args.actuator_Gs; % Sensor gain [V/m] + +nano_hexapod.actuator.k = args.actuator_k; % [N/m] +nano_hexapod.actuator.ke = args.actuator_ke; % [N/m] +nano_hexapod.actuator.ka = args.actuator_ka; % [N/m] + +nano_hexapod.actuator.c = args.actuator_c; % [N/(m/s)] +nano_hexapod.actuator.ce = args.actuator_ce; % [N/(m/s)] +nano_hexapod.actuator.ca = args.actuator_ca; % [N/(m/s)] + +nano_hexapod.actuator.Leq = args.actuator_Leq; % [m] + +switch args.actuator_type + case 'flexible frame' + nano_hexapod.actuator.K = readmatrix('APA300ML_b_mat_K.CSV'); % Stiffness Matrix + nano_hexapod.actuator.M = readmatrix('APA300ML_b_mat_M.CSV'); % Mass Matrix + nano_hexapod.actuator.P = extractNodes('APA300ML_b_out_nodes_3D.txt'); % Node coordinates [m] + case 'flexible' + nano_hexapod.actuator.K = readmatrix('APA300ML_full_mat_K.CSV'); % Stiffness Matrix + nano_hexapod.actuator.M = readmatrix('APA300ML_full_mat_M.CSV'); % Mass Matrix + nano_hexapod.actuator.P = extractNodes('APA300ML_full_out_nodes_3D.txt'); % Node coordiantes [m] +end + +nano_hexapod.actuator.xi = args.actuator_xi; % Damping ratio + +nano_hexapod.actuator.ks = args.actuator_ks; % Stiffness of one stack [N/m] +nano_hexapod.actuator.cs = args.actuator_cs; % Damping of one stack [N/m] + +save('./mat/stages.mat', 'nano_hexapod', '-append');