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[15, 7]: 4.929e-06 [15, 8]: 5.546e-02 [15, 9]: 2.951e-06 [15,10]: 1.953e-04 [15,11]:-1.424e-08 [15,12]: 4.034e-08 [15,13]: 0.000e+00 [15,14]: 0.000e+00 [15,15]: 1.000e+00 [15,16]: 0.000e+00 [15,17]: 0.000e+00 [15,18]: 0.000e+00 +[16, 1]: 2.900e-06 [16, 2]:-1.237e-02 [16, 3]: 4.241e-06 [16, 4]: 6.874e-05 [16, 5]: 2.704e-08 [16, 6]:-9.240e-10 [16, 7]:-4.308e-06 [16, 8]: 7.601e-02 [16, 9]:-1.252e-06 [16,10]: 6.785e-04 [16,11]: 5.036e-08 [16,12]:-2.487e-08 [16,13]: 0.000e+00 [16,14]: 0.000e+00 [16,15]: 0.000e+00 [16,16]: 1.000e+00 [16,17]: 0.000e+00 [16,18]: 0.000e+00 +[17, 1]: 8.272e-02 [17, 2]: 1.500e-07 [17, 3]:-9.604e-07 [17, 4]:-1.637e-08 [17, 5]: 8.113e-04 [17, 6]:-5.548e-09 [17, 7]:-9.224e-03 [17, 8]:-2.596e-06 [17, 9]: 5.979e-06 [17,10]:-2.458e-08 [17,11]: 4.737e-05 [17,12]: 4.305e-09 [17,13]: 0.000e+00 [17,14]: 0.000e+00 [17,15]: 0.000e+00 [17,16]: 0.000e+00 [17,17]: 1.000e+00 [17,18]: 0.000e+00 +[18, 1]:-2.468e-06 [18, 2]: 3.313e-02 [18, 3]:-2.639e-06 [18, 4]:-5.990e-04 [18, 5]:-2.302e-08 [18, 6]: 3.141e-08 [18, 7]: 1.941e-06 [18, 8]:-6.673e-03 [18, 9]:-2.257e-06 [18,10]:-7.855e-05 [18,11]:-1.820e-08 [18,12]: 7.568e-09 [18,13]: 0.000e+00 [18,14]: 0.000e+00 [18,15]: 0.000e+00 [18,16]: 0.000e+00 [18,17]: 0.000e+00 [18,18]: 1.000e+00 diff --git a/data/flexor_ID16/out_nodes_3D.txt b/data/flexor_ID16/out_nodes_3D.txt new file mode 100755 index 0000000..f6adc91 --- /dev/null +++ b/data/flexor_ID16/out_nodes_3D.txt @@ -0,0 +1,40 @@ + + LIST ALL SELECTED NODES. DSYS= 0 + + *** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 *** + DISTRIBUTED ANSYS Academic Research + + 00208316 VERSION=WINDOWS x64 16:37:53 JUL 30, 2020 CP= 3.062 + + Flex-FV--Modal (B5) + + + + NODE X Y Z THXY THYZ THZX + 181278 0.0000 0.0000 0.10000E-008 0.00 0.00 0.00 + 181279 0.0000 0.0000 -0.10000E-008 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 16:37:53 JUL 30, 2020 CP= 3.062 + + Flex-FV--Modal (B5) + + + NODE LABEL SUPPORT + 181278 UX + 181278 UY + 181278 UZ + 181278 ROTX + 181278 ROTY + 181278 ROTZ + 181279 UX + 181279 UY + 181279 UZ + 181279 ROTX + 181279 ROTY + 181279 ROTZ diff --git a/index.org b/index.org index 288a709..348a277 100644 --- a/index.org +++ b/index.org @@ -166,15 +166,15 @@ Parameters for the APA95ML: #+begin_src matlab d33 = 3e-10; % Strain constant [m/V] n = 80; % Number of layers per stack - eT = 1.6e-8; % Permittivity under constant stress [F/m] + eT = 1.6e-7; % Permittivity under constant stress [F/m] sD = 2e-11; % Elastic compliance under constant electric displacement [m2/N] ka = 235e6; % Stack stiffness [N/m] C = 5e-6; % Stack capactiance [F] #+end_src #+begin_src matlab - na = 3; % Number of stacks used as actuator - ns = 0; % Number of stacks used as force sensor + na = 2; % Number of stacks used as actuator + ns = 1; % Number of stacks used as force sensor #+end_src The ratio of the developed force to applied voltage is $d_{33} n k_a$ in [N/V]. @@ -185,7 +185,7 @@ We denote this constant by $g_a$ and: #+end_src #+RESULTS: -: 1.88 +: 3.76 From cite:fleming14_desig_model_contr_nanop_system (page 123), the relation between relative displacement and generated voltage is: \[ V_s = \frac{d_{33}}{\epsilon^T s^D n} \Delta h \] @@ -201,7 +201,7 @@ where: #+end_src #+RESULTS: -: 5.8594 +: 1.1719 ** Identification of the Dynamics The flexible element is imported using the =Reduced Order Flexible Solid= simscape block. @@ -622,6 +622,47 @@ The two identified dynamics are compared in Figure [[fig:dynamics_act_disp_comp_ save('../test-bench-apa/mat/fem_model_5kg.mat', 'G') #+end_src +** Dynamics from input voltage to output voltage +#+begin_src matlab + m = 5; +#+end_src + +#+begin_src matlab + %% Name of the Simulink File + mdl = 'piezo_amplified_3d'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/Va'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; + + G = -linearize(mdl, io); +#+end_src + +#+begin_src matlab :exports none + freqs = logspace(1, 4, 5000); + + figure; + + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(squeeze(freqresp(G, freqs, 'Hz')))); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude'); set(gca, 'XTickLabel',[]); + hold off; + + ax2 = subplot(2,1,2); + hold on; + plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G, freqs, 'Hz'))))); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + yticks(-360:90:360); + xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); + hold off; + linkaxes([ax1,ax2],'x'); + xlim([10, 5e3]); +#+end_src + * 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) @@ -643,6 +684,11 @@ The two identified dynamics are compared in Figure [[fig:dynamics_act_disp_comp_ ** Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates We first extract the stiffness and mass matrices. +#+begin_src matlab + K = extractMatrix('mat_K-48modes-7MDoF.matrix'); + M = extractMatrix('mat_M-48modes-7MDoF.matrix'); +#+end_src + #+begin_src matlab K = extractMatrix('mat_K-80modes-7MDoF.matrix'); M = extractMatrix('mat_M-80modes-7MDoF.matrix'); @@ -768,9 +814,6 @@ where: #+RESULTS: : 5.8594 - - - ** Identification of the Dynamics The flexible element is imported using the =Reduced Order Flexible Solid= simscape block. @@ -976,6 +1019,386 @@ The two identified dynamics are compared in Figure [[fig:dynamics_act_disp_comp_ xlabel('Real Part'); ylabel('Imaginary Part'); #+end_src +** Sensor Fusion +- [ ] What is the goal of that? Special control properties, lower the sensor noise? + +Use the relative motion sensor at low frequency and the force sensor at high frequency. +#+begin_src matlab + m = 10; +#+end_src + +#+begin_src matlab + %% Name of the Simulink File + mdl = 'APA300ML_test_bench'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/Va'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/y'], 1, 'openoutput'); io_i = io_i + 1; + + G = linearize(mdl, io); +#+end_src + +#+begin_src matlab :exports none + freqs = logspace(1, 5, 1000); + + Gresp = squeeze(freqresp(G, freqs, 'Hz')); + + figure; + + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(Gresp(1, :)), '-'); + plot(freqs, abs(Gresp(2, :)), '-'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude'); set(gca, 'XTickLabel',[]); + hold off; + + ax2 = subplot(2,1,2); + hold on; + plot(freqs, 180/pi*unwrap(angle(Gresp(1, :))), '-', ... + 'DisplayName', 'Force'); + plot(freqs, 180/pi*unwrap(angle(Gresp(2, :))), '-', ... + 'DisplayName', 'Displacement'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + yticks(-360:90:360); + ylim([-390 30]); + xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); + hold off; + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); + legend('location', 'southwest'); +#+end_src + +Merge around 1kHz +#+begin_src matlab :exports none + freqs = logspace(1, 5, 1000); + + figure; + + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(Gresp(1, :).*squeeze(freqresp(0.0065/s^2, freqs, 'Hz'))'), '-'); + plot(freqs, abs(Gresp(2, :)), '-'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude'); set(gca, 'XTickLabel',[]); + hold off; + + ax2 = subplot(2,1,2); + hold on; + plot(freqs, 180/pi*unwrap(angle(Gresp(1, :).*squeeze(freqresp(1/s^2, freqs, 'Hz'))')), '-', ... + 'DisplayName', 'Force'); + plot(freqs, 180/pi*unwrap(angle(Gresp(2, :))), '-', ... + 'DisplayName', 'Displacement'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + yticks(-360:90:360); + xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); + hold off; + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); + legend('location', 'southwest'); +#+end_src + +LPF and HPF +#+begin_src matlab + n = 3; w0 = 2*pi*1e3; G0 = 1/10; G1 = 1e5; Gc = 1/2; + W1 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n; + + n = 3; w0 = 2*pi*1e3; G0 = 1e5; G1 = 0.1; Gc = 1/2; + W2 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n; +#+end_src + +#+begin_src matlab + P = [W1 -W1; + 0 W2; + 1 0]; + + [H2, ~, gamma, ~] = hinfsyn(P, 1, 1,'TOLGAM', 0.001, 'METHOD', 'ric', 'DISPLAY', 'on'); + H1 = 1 - H2; +#+end_src + +#+begin_src matlab :exports none + freqs = logspace(1, 5, 1000); + + Gresp = squeeze(freqresp(G, freqs, 'Hz')); + + figure; + + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(Gresp(1, :).*squeeze(freqresp(0.0065/s^2*H2, freqs, 'Hz'))'), '-'); + plot(freqs, abs(Gresp(2, :).*squeeze(freqresp(H1, freqs, 'Hz'))'), '-'); + plot(freqs, abs(Gresp(2, :).*squeeze(freqresp(H1, freqs, 'Hz'))' + Gresp(1, :).*squeeze(freqresp(0.0065/s^2*H2, freqs, 'Hz'))'), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude'); set(gca, 'XTickLabel',[]); + hold off; + + ax2 = subplot(2,1,2); + hold on; + plot(freqs, 180/pi*unwrap(angle(Gresp(1, :).*squeeze(freqresp(0.0065/s^2*H2, freqs, 'Hz'))')), '-', ... + 'DisplayName', 'Force'); + plot(freqs, 180/pi*unwrap(angle(Gresp(2, :).*squeeze(freqresp(H1, freqs, 'Hz'))')), '-', ... + 'DisplayName', 'Displacement'); + plot(freqs, 180/pi*unwrap(angle(Gresp(2, :).*squeeze(freqresp(H1, freqs, 'Hz'))' + Gresp(1, :).*squeeze(freqresp(0.0065/s^2*H2, freqs, 'Hz'))')), 'k--', ... + 'DisplayName', 'Super Sensor'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + yticks(-360:90:360); + xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); + hold off; + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); + legend('location', 'southwest'); +#+end_src + +#+begin_src matlab :exports none + Gss = -zpk(G(1)*0.0065/s^2*H2 + G(2)*H1); + + freqs = logspace(1, 5, 1000); + + figure; + + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(squeeze(freqresp(Gss, freqs, 'Hz'))'), '-'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude'); set(gca, 'XTickLabel',[]); + hold off; + + ax2 = subplot(2,1,2); + hold on; + plot(freqs, 180/pi*(angle(squeeze(freqresp(Gss, freqs, 'Hz'))')), '-', ... + 'DisplayName', 'Force'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + yticks(-360:90:360); + xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); + hold off; + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); + legend('location', 'southwest'); +#+end_src + +Root locus +#+begin_src matlab + figure; + + gains = logspace(4, 7, 100); + + hold on; + plot(real(pole(Gss)), imag(pole(Gss)), 'kx'); + plot(real(tzero(Gss)), imag(tzero(Gss)), 'ko'); + for k = 1:length(gains) + cl_poles = pole(feedback(Gss, gains(k)*s)); + plot(real(cl_poles), imag(cl_poles), 'k.'); + end + hold off; + axis square; + xlim([-500, 10]); ylim([0, 510]); + + xlabel('Real Part'); ylabel('Imaginary Part'); +#+end_src + +* Flexible Joint +** 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 + addpath('./src/'); + addpath('./data/flexor_ID16/'); +#+end_src + +#+begin_src matlab :exports none + open('flexor_ID16.slx'); +#+end_src + +** Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates +We first extract the stiffness and mass matrices. +#+begin_src matlab + K = extractMatrix('mat_K_6modes_2MDoF.matrix'); + M = extractMatrix('mat_M_6modes_2MDoF.matrix'); +#+end_src + +Then, we extract the coordinates of the interface nodes. +#+begin_src matlab + [int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('out_nodes_3D.txt'); +#+end_src + +#+begin_src matlab + save('./mat/flexor_ID16.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K'); +#+end_src + +** Output parameters +#+begin_src matlab + load('./mat/flexor_ID16.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K'); +#+end_src + +#+begin_src matlab :exports results :results value table replace :tangle no + data2orgtable([length(n_i); length(int_i); size(M,1) - 6*length(int_i); size(M,1)], {'Total number of Nodes', 'Number of interface Nodes', 'Number of Modes', 'Size of M and K matrices'}, {}, ' %.0f '); +#+end_src + +#+RESULTS: +| Total number of Nodes | 2 | +| Number of interface Nodes | 2 | +| Number of Modes | 6 | +| Size of M and K matrices | 18 | + +#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*) + data2orgtable([[1:length(int_i)]', int_i, int_xyz], {}, {'Node i', 'Node Number', 'x [m]', 'y [m]', 'z [m]'}, ' %f '); +#+end_src + +#+caption: Coordinates of the interface nodes +#+RESULTS: +| Node i | Node Number | x [m] | y [m] | z [m] | +|--------+-------------+-------+-------+-------| +| 1.0 | 181278.0 | 0.0 | 0.0 | 0.0 | +| 2.0 | 181279.0 | 0.0 | 0.0 | -0.0 | + +#+begin_src matlab :exports results :results value table replace :tangle no + data2orgtable(K(1:10, 1:10), {}, {}, ' %.2e '); +#+end_src + +#+caption: First 10x10 elements of the Stiffness matrix +#+RESULTS: +| 11200000.0 | 195.0 | 2220.0 | -0.719 | -265.0 | 1.59 | -11200000.0 | -213.0 | -2220.0 | 0.147 | +| 195.0 | 11400000.0 | 1290.0 | -148.0 | -0.188 | 2.41 | -212.0 | -11400000.0 | -1290.0 | 148.0 | +| 2220.0 | 1290.0 | 119000000.0 | 1.31 | 1.49 | 1.79 | -2220.0 | -1290.0 | -119000000.0 | -1.31 | +| -0.719 | -148.0 | 1.31 | 33.0 | 0.000488 | -0.000977 | 0.141 | 148.0 | -1.31 | -33.0 | +| -265.0 | -0.188 | 1.49 | 0.000488 | 33.0 | 0.00293 | 266.0 | 0.154 | -1.49 | 0.00026 | +| 1.59 | 2.41 | 1.79 | -0.000977 | 0.00293 | 236.0 | -1.32 | -2.55 | -1.79 | 0.000379 | +| -11200000.0 | -212.0 | -2220.0 | 0.141 | 266.0 | -1.32 | 11400000.0 | 24600.0 | 1640.0 | 120.0 | +| -213.0 | -11400000.0 | -1290.0 | 148.0 | 0.154 | -2.55 | 24600.0 | 11400000.0 | 1290.0 | -72.0 | +| -2220.0 | -1290.0 | -119000000.0 | -1.31 | -1.49 | -1.79 | 1640.0 | 1290.0 | 119000000.0 | 1.32 | +| 0.147 | 148.0 | -1.31 | -33.0 | 0.00026 | 0.000379 | 120.0 | -72.0 | 1.32 | 34.7 | + + +#+begin_src matlab :exports results :results value table replace :tangle no + data2orgtable(M(1:10, 1:10), {}, {}, ' %.1g '); +#+end_src + +#+caption: First 10x10 elements of the Mass matrix +#+RESULTS: +| 0.02 | 1e-09 | -4e-08 | -1e-10 | 0.0002 | -3e-11 | 0.004 | 5e-08 | 7e-08 | 1e-10 | +| 1e-09 | 0.02 | -3e-07 | -0.0002 | -1e-10 | -2e-09 | 2e-08 | 0.004 | 3e-07 | 1e-05 | +| -4e-08 | -3e-07 | 0.02 | 7e-10 | -2e-09 | 1e-09 | 3e-07 | 7e-08 | 0.003 | 1e-09 | +| -1e-10 | -0.0002 | 7e-10 | 4e-06 | -1e-12 | -6e-13 | 2e-10 | -7e-06 | -8e-10 | -1e-09 | +| 0.0002 | -1e-10 | -2e-09 | -1e-12 | 3e-06 | 2e-13 | 9e-06 | 4e-11 | 2e-09 | -3e-13 | +| -3e-11 | -2e-09 | 1e-09 | -6e-13 | 2e-13 | 4e-07 | 8e-11 | 9e-10 | -1e-09 | 2e-12 | +| 0.004 | 2e-08 | 3e-07 | 2e-10 | 9e-06 | 8e-11 | 0.02 | -7e-08 | -3e-07 | -2e-10 | +| 5e-08 | 0.004 | 7e-08 | -7e-06 | 4e-11 | 9e-10 | -7e-08 | 0.01 | -4e-08 | 0.0002 | +| 7e-08 | 3e-07 | 0.003 | -8e-10 | 2e-09 | -1e-09 | -3e-07 | -4e-08 | 0.02 | -1e-09 | +| 1e-10 | 1e-05 | 1e-09 | -1e-09 | -3e-13 | 2e-12 | -2e-10 | 0.0002 | -1e-09 | 2e-06 | + +Using =K=, =M= and =int_xyz=, we can use the =Reduced Order Flexible Solid= simscape block. + +** Flexible Joint Characteristics +#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*) + data2orgtable([1e-6*K(3,3), K(4,4), K(5,5), K(6,6)]', {'Axial Stiffness [N/um]', 'Bending Stiffness [Nm/rad]', 'Bending Stiffness [Nm/rad]', 'Torsion Stiffness [Nm/rad]'}, {'*Caracteristic*', '*Value*'}, ' %0.f '); +#+end_src + +#+RESULTS: +| *Caracteristic* | *Value* | +|----------------------------+---------| +| Axial Stiffness [N/um] | 119 | +| Bending Stiffness [Nm/rad] | 33 | +| Bending Stiffness [Nm/rad] | 33 | +| Torsion Stiffness [Nm/rad] | 236 | + +** Identification +#+begin_src matlab + m = 10; +#+end_src + +The dynamics is identified from the applied force to the measured relative displacement. +#+begin_src matlab + %% Name of the Simulink File + mdl = 'flexor_ID16'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/T'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/D'], 1, 'openoutput'); io_i = io_i + 1; + + G = linearize(mdl, io); +#+end_src + +#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*) + data2orgtable([1e-6*K(3,3), K(4,4), K(5,5), K(6,6) ; 1e-6./dcgain(G(3,3)), 1./dcgain(G(4,4)), 1./dcgain(G(5,5)), 1./dcgain(G(6,6))]', {'Axial Stiffness Dz [N/um]', 'Bending Stiffness Rx [Nm/rad]', 'Bending Stiffness Ry [Nm/rad]', 'Torsion Stiffness Rz [Nm/rad]'}, {'*Caracteristic*', '*Value*', '*Identification*'}, ' %0.f '); +#+end_src + +#+RESULTS: +| *Caracteristic* | *Value* | *Identification* | +|-------------------------------+---------+------------------| +| Axial Stiffness Dz [N/um] | 119 | 119 | +| Bending Stiffness Rx [Nm/rad] | 33 | 34 | +| Bending Stiffness Ry [Nm/rad] | 33 | 126 | +| Torsion Stiffness Rz [Nm/rad] | 236 | 238 | + +#+begin_src matlab :exports none + freqs = logspace(0, 5, 1000); + + figure; + + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(squeeze(freqresp(G(1,1), freqs, 'Hz'))), '-'); + plot(freqs, abs(squeeze(freqresp(G(2,2), freqs, 'Hz'))), '-'); + plot(freqs, abs(squeeze(freqresp(G(3,3), freqs, 'Hz'))), '-'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude'); set(gca, 'XTickLabel',[]); + hold off; + + ax2 = subplot(2,1,2); + hold on + plot(freqs, 180/pi*(angle(squeeze(freqresp(G(1,1), freqs, 'Hz')))), '-'); + plot(freqs, 180/pi*(angle(squeeze(freqresp(G(2,2), freqs, 'Hz')))), '-'); + plot(freqs, 180/pi*(angle(squeeze(freqresp(G(3,3), freqs, 'Hz')))), '-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + yticks(-360:90:360); + xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); + hold off; + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); +#+end_src + +#+begin_src matlab :exports none + freqs = logspace(0, 5, 1000); + + figure; + + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(squeeze(freqresp(G(4,4), freqs, 'Hz'))), '-'); + plot(freqs, abs(squeeze(freqresp(G(5,5), freqs, 'Hz'))), '-'); + plot(freqs, abs(squeeze(freqresp(G(6,6), freqs, 'Hz'))), '-'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude'); set(gca, 'XTickLabel',[]); + hold off; + + ax2 = subplot(2,1,2); + hold on + plot(freqs, 180/pi*(angle(squeeze(freqresp(G(4,4), freqs, 'Hz')))), '-'); + plot(freqs, 180/pi*(angle(squeeze(freqresp(G(5,5), freqs, 'Hz')))), '-'); + plot(freqs, 180/pi*(angle(squeeze(freqresp(G(6,6), freqs, 'Hz')))), '-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + yticks(-360:90:360); + xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); + hold off; + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); +#+end_src + * Integral Force Feedback with Amplified Piezo ** Matlab Init :noexport:ignore: #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)