From 12c2e4a5089a8a3fcfbdc32b1e504a0cab5081d5 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Tue, 25 Feb 2020 17:49:08 +0100 Subject: [PATCH] Huge Update - Modify the joints for Ty, Ry, Rz to have only one bushing joint. - Compensation of gravity --- active_damping/index.org | 151 +++++- disturbances/index.html | 241 +++++----- disturbances/index.org | 27 ++ disturbances/mat/dist_psd.mat | Bin 209689 -> 209339 bytes functions/index.org | 34 +- kinematics/index.org | 47 +- mat/Foffset.mat | Bin 0 -> 623 bytes mat/conf_log.mat | Bin 223 -> 225 bytes mat/conf_simscape.mat | Bin 13441 -> 208 bytes mat/controller.mat | Bin 1410 -> 1018 bytes mat/controllers.mat | Bin 233552 -> 317291 bytes mat/nass_disturbances.mat | Bin 50787 -> 50787 bytes mat/nass_references.mat | Bin 850751 -> 850961 bytes mat/pos_error.mat | Bin 0 -> 256 bytes mat/stages.mat | Bin 6629 -> 6728 bytes positioning_error/index.org | 118 ++--- .../matlab/sim_nano_station_metrology.slx | Bin 37193 -> 0 bytes simscape/nass_model.slx | Bin 185286 -> 193948 bytes simscape_subsystems/index.org | 432 +++++++++++------- simscape_subsystems/micro_hexapod_leg.slx | Bin 28562 -> 28218 bytes .../micro_hexapod_leg_rigid.slx | Bin 0 -> 30930 bytes .../nano_hexapod_leg_rigid.slx | Bin 0 -> 30687 bytes simscape_subsystems/nass_disturbances.slx | Bin 29901 -> 29904 bytes simscape_subsystems/nass_references.slx | Bin 31474 -> 31898 bytes src/computeReferencePose.m | 2 +- src/initializeGranite.m | 27 +- src/initializeLoggingConfiguration.m | 4 +- src/initializeMicroHexapod.m | 15 +- src/initializeMirror.m | 16 +- src/initializePosError.m | 28 ++ src/initializeReferences.m | 24 +- src/initializeRy.m | 53 +-- src/initializeRz.m | 32 +- src/initializeSample.m | 38 +- src/initializeTy.m | 34 +- src/inverseKinematicsHexapod.m | 20 - 36 files changed, 798 insertions(+), 545 deletions(-) create mode 100644 mat/Foffset.mat create mode 100644 mat/pos_error.mat delete mode 100644 positioning_error/matlab/sim_nano_station_metrology.slx create mode 100644 simscape_subsystems/micro_hexapod_leg_rigid.slx create mode 100644 simscape_subsystems/nano_hexapod_leg_rigid.slx create mode 100644 src/initializePosError.m delete mode 100644 src/inverseKinematicsHexapod.m diff --git a/active_damping/index.org b/active_damping/index.org index aafe399..101ac95 100644 --- a/active_damping/index.org +++ b/active_damping/index.org @@ -41,7 +41,7 @@ #+PROPERTY: header-args:latex+ :output-dir figs :END: -* Introduction :ignore: +* Introduction :ignore: The goal of this file is to study the use of active damping for the control of the NASS. In general, three sensors can be used for Active Damping: @@ -276,7 +276,7 @@ We identify the dynamics of the system using the =linearize= function. %% Input/Output definition clear io; io_i = 1; - io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs + io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs io(io_i) = linio([mdl, '/Tracking Error'], 1, 'openoutput', [], 'En'); io_i = io_i + 1; % Metrology Outputs #+end_src @@ -4105,3 +4105,150 @@ The obtained sensitivity to disturbances is shown in figure [[fig:ine_1dof_sensi #+name: fig:ine_1dof_sensitivitiy #+caption: Sensitivity to disturbance when INE is applied on the 1dof system ([[./figs/ine_1dof_sensitivitiy.png][png]], [[./figs/ine_1dof_sensitivitiy.pdf][pdf]]) [[file:figs/ine_1dof_sensitivitiy.png]] +* Test :noexport: +#+begin_src matlab + AP = [0; 0; 0]; +#+end_src + +#+begin_src matlab + load('mat/conf_simulink.mat'); + set_param(conf_simulink, 'StopTime', '0.5'); + + initializeSimscapeConfiguration('gravity', true); + + initializeLoggingConfiguration('log', 'forces'); + + initializeGround('type', 'none'); + initializeGranite('type', 'none'); + initializeTy('type', 'rigid'); + initializeRy('type', 'init'); + initializeRz('type', 'none'); + initializeMicroHexapod('type', 'rigid', 'AP', AP, 'Foffset', false); + initializeAxisc('type', 'none'); + initializeMirror('type', 'none'); + initializeNanoHexapod('type', 'none'); + initializeSample('type', 'init', 'Foffset', false); + + sim('nass_model'); +#+end_src + +#+begin_src matlab + save('./mat/Foffset.mat', 'Foffset'); +#+end_src + +#+begin_src matlab + initializeRz('type', 'flexible'); + initializeMicroHexapod('type', 'flexible', 'AP', AP); + initializeSample('type', 'flexible'); + + sim('nass_model'); +#+end_src +* Test bis :noexport: +#+begin_src matlab + AP = [0; 0; 0]; +#+end_src + +#+begin_src matlab + load('mat/conf_simulink.mat'); + set_param(conf_simulink, 'StopTime', '0.5'); + + initializeSimscapeConfiguration('gravity', true); + + initializeLoggingConfiguration('log', 'forces'); + + initializeGround('type', 'none'); + initializeGranite('type', 'none'); + initializeTy('type', 'rigid'); + initializeRy('type', 'flexible'); + initializeRz('type', 'none'); + initializeMicroHexapod('type', 'none'); + initializeAxisc('type', 'none'); + initializeMirror('type', 'none'); + initializeNanoHexapod('type', 'none'); + initializeSample('type', 'none'); + + sim('nass_model'); +#+end_src + +#+begin_src matlab + save('./mat/Foffset.mat', 'Foffset'); +#+end_src + +#+begin_src matlab + initializeRz('type', 'flexible'); + initializeMicroHexapod('type', 'flexible', 'AP', AP); + initializeSample('type', 'flexible'); + + sim('nass_model'); +#+end_src +* Use only one joint for the tilt stage +#+begin_src matlab + K = [2.8e4; 2.8e4; 2.8e4]; + %K = [1e8; 1e8; 1e8]; + + ty = 7*(2*pi)/180; + Ry = [ cos(ty) 0 sin(ty); + 0 1 0; + -sin(ty) 0 cos(ty)]; + + K11 = abs(Ry*K); + K12 = abs(Ry*K); + + ty = -7*(2*pi)/180; + Ry = [ cos(ty) 0 sin(ty); + 0 1 0; + -sin(ty) 0 cos(ty)]; + + K21 = abs(Ry*K); + K22 = abs(Ry*K); + + Ktot = zeros(6,1); + + Ktot(1) = K11(1) + K12(1) + K21(1) + K22(1); + Ktot(2) = K11(2) + K12(2) + K21(2) + K22(2); + Ktot(3) = K11(3) + K12(3) + K21(3) + K22(3); + + %% Stiffness in rotation + + % Position of the joint from the next wanted joint position (in the rotated frame) + P11 = [0; 0.334; 0]; + P12 = [0; 0.334; 0]; + P21 = [0; 0.334; 0]; + P22 = [0; 0.334; 0]; + + Ktot(4:6) = abs(cross(P11, K11)) + abs(cross(P12, K12)) + abs(cross(P21, K21)) + abs(cross(P22, K22)) +#+end_src + +#+begin_src matlab + Ry_init = 0; +#+end_src + +#+begin_src matlab + initializeSimscapeConfiguration('gravity', true); + initializeLoggingConfiguration('log', 'none'); + + initializeGround('type', 'none'); + initializeGranite('type', 'none'); + initializeTy('type', 'none'); + initializeRy('type', 'init', 'Ry_init', Ry_init); + initializeRz('type', 'init'); + initializeMicroHexapod('type', 'init'); + initializeAxisc('type', 'none'); + initializeMirror('type', 'none'); + initializeNanoHexapod('type', 'none'); + initializeSample('type', 'init'); + + sim('nass_model'); +#+end_src + +#+begin_src matlab + save('./mat/Foffset.mat', 'Fym'); +#+end_src + +#+begin_src matlab + initializeReferences('Ry_amplitude', 3*(2*pi)/180) + + initializeRy('type', 'flexible', 'Ry_init', 3*(2*pi)/180); + + sim('nass_model'); +#+end_src diff --git a/disturbances/index.html b/disturbances/index.html index 92786d3..e17037c 100644 --- a/disturbances/index.html +++ b/disturbances/index.html @@ -1,9 +1,10 @@ + - + Identification of the disturbances @@ -205,7 +206,7 @@ @licstart The following is the entire license notice for the JavaScript code in this tag. -Copyright (C) 2012-2019 Free Software Foundation, Inc. +Copyright (C) 2012-2020 Free Software Foundation, Inc. The JavaScript code in this tag is free software: you can redistribute it and/or modify it under the terms of the GNU @@ -246,31 +247,16 @@ for the JavaScript code in this tag. } /*]]>*///--> - - + +
@@ -283,13 +269,13 @@ for the JavaScript code in this tag.

Table of Contents

@@ -299,7 +285,7 @@ The goal here is to extract the Power Spectral Density of the sources of perturb

-The sources of perturbations are (schematically shown in figure 1): +The sources of perturbations are (schematically shown in figure 1):

-Because we cannot measure directly the perturbation forces, we have the measure the effect of those perturbations on the system (in terms of velocity for instance using geophones, \(D\) on figure 1) and then, using a model, compute the forces that induced such velocity. +Because we cannot measure directly the perturbation forces, we have the measure the effect of those perturbations on the system (in terms of velocity for instance using geophones, \(D\) on figure 1) and then, using a model, compute the forces that induced such velocity.

-
+

uniaxial-model-micro-station.png

Figure 1: Schematic of the Micro Station and the sources of disturbance

@@ -324,19 +310,19 @@ Because we cannot measure directly the perturbation forces, we have the measure This file is divided in the following sections:

    -
  • Section 1: the simscape model used here is presented
  • -
  • Section 2: transfer functions from the disturbance forces to the relative velocity of the hexapod with respect to the granite are computed using the Simscape Model representing the experimental setup
  • -
  • Section 3: the bode plot of those transfer functions are shown
  • -
  • Section 4: the measured PSD of the effect of the disturbances are shown
  • -
  • Section 5: from the model and the measured PSD, the PSD of the disturbance forces are computed
  • -
  • Section 6: with the computed PSD, the noise budget of the system is done
  • +
  • Section 1: the simscape model used here is presented
  • +
  • Section 2: transfer functions from the disturbance forces to the relative velocity of the hexapod with respect to the granite are computed using the Simscape Model representing the experimental setup
  • +
  • Section 3: the bode plot of those transfer functions are shown
  • +
  • Section 4: the measured PSD of the effect of the disturbances are shown
  • +
  • Section 5: from the model and the measured PSD, the PSD of the disturbance forces are computed
  • +
  • Section 6: with the computed PSD, the noise budget of the system is done
-
-

1 Simscape Model

-
+
+

1 Simscape Model

+

- +

@@ -349,17 +335,12 @@ We add disturbances forces in the vertical direction for the Translation Stage a Also, we measure the absolute displacement of the granite and of the top platform of the Hexapod.

-
-
open('disturbances/matlab/sim_micro_station_disturbances.slx');
-
-
-

We load the configuration and we set a small StopTime.

-
load('mat/conf_simscape.mat');
-set_param(conf_simscape, 'StopTime', '0.5');
+
load('mat/conf_simulink.mat');
+set_param(conf_simulink, 'StopTime', '0.5');
 
@@ -367,72 +348,83 @@ We load the configuration and we set a small StopTime. We initialize all the stages.

-
initializeGround();
-initializeGranite();
-initializeTy();
-initializeRy();
-initializeRz();
-initializeMicroHexapod();
-initializeAxisc();
-initializeMirror();
-initializeNanoHexapod(struct('actuator', 'piezo'));
-initializeSample(struct('mass', 50));
+
initializeGround();
+initializeGranite('type', 'modal-analysis');
+initializeTy();
+initializeRy();
+initializeRz();
+initializeMicroHexapod('type', 'modal-analysis');
+initializeAxisc('type', 'none');
+initializeMirror('type', 'none');
+initializeNanoHexapod('type', 'none');
+initializeSample('type', 'none');
 
-
-

2 Identification

-
+
+

2 Identification

+

- + The transfer functions from the disturbance forces to the relative velocity of the hexapod with respect to the granite are computed using the Simscape Model representing the experimental setup with the code below.

%% Options for Linearized
 options = linearizeOptions;
-options.SampleTime = 0;
+options.SampleTime = 0;
 
 %% Name of the Simulink File
-mdl = 'sim_micro_station_disturbances';
+mdl = 'nass_model';
 
%% Micro-Hexapod
-% Input/Output definition
-io(1)  = linio([mdl, '/Dw'],   1, 'input');  % Ground Motion
-io(2)  = linio([mdl, '/Fty'], 1, 'input');  % Parasitic force Ty
-io(3)  = linio([mdl, '/Frz'], 1, 'input');  % Parasitic force Rz
-io(4)  = linio([mdl, '/Dgm'],  1, 'output'); % Absolute motion - Granite
-io(5)  = linio([mdl, '/Dhm'],  1, 'output'); % Absolute Motion - Hexapod
-io(6)  = linio([mdl, '/Vm'],   1, 'output'); % Relative Velocity hexapod/granite
+  clear io; io_i = 1;
+  io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Dwz'); io_i = io_i + 1; % Vertical Ground Motion
+  io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Fty_z'); io_i = io_i + 1; % Parasitic force Ty
+  io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Frz_z'); io_i = io_i + 1; % Parasitic force Rz
+  io(io_i) = linio([mdl, '/Micro-Station/Granite/Modal Analysis/accelerometer'], 1, 'openoutput'); io_i = io_i + 1; % Absolute motion - Granite
+  io(io_i) = linio([mdl, '/Micro-Station/Micro Hexapod/Modal Analysis/accelerometer'],  1, 'openoutput'); io_i = io_i + 1; % Absolute Motion - Hexapod
+  % io(io_i) = linio([mdl, '/Vm'],   1, 'openoutput'); io_i = io_i + 1; % Relative Velocity hexapod/granite
 
% Run the linearization
-G = linearize(mdl, io, 0);
+G = linearize(mdl, io, 0);
+
+% We Take only the outputs corresponding to the vertical acceleration
+G = G([3,9], :);
 
 % Input/Output names
-G.InputName  = {'Dw', 'Fty', 'Frz'};
-G.OutputName = {'Dgm', 'Dhm', 'Vm'};
+G.InputName  = {'Dw', 'Fty', 'Frz'};
+G.OutputName = {'Agm', 'Ahm'};
+
+% We integrate 1 time the output to have the velocity and we
+% substract the absolute velocities to have the relative velocity
+G = (1/s)*tf([-1, 1])*G;
+
+% Input/Output names
+G.InputName  = {'Dw', 'Fty', 'Frz'};
+G.OutputName = {'Vm'};
 
-
-

3 Sensitivity to Disturbances

-
+
+

3 Sensitivity to Disturbances

+

- +

-
+

sensitivity_dist_gm.png

Figure 2: Sensitivity to Ground Motion (png, pdf)

@@ -440,7 +432,7 @@ G.OutputName = { +

sensitivity_dist_fty.png

Figure 3: Sensitivity to vertical forces applied by the Ty stage (png, pdf)

@@ -448,7 +440,7 @@ G.OutputName = { +

sensitivity_dist_frz.png

Figure 4: Sensitivity to vertical forces applied by the Rz stage (png, pdf)

@@ -456,11 +448,11 @@ G.OutputName = {
-
-

4 Power Spectral Density of the effect of the disturbances

-
+
+

4 Power Spectral Density of the effect of the disturbances

+

- + The PSD of the relative velocity between the hexapod and the marble in \([(m/s)^2/Hz]\) are loaded for the following sources of disturbance:

    @@ -473,10 +465,10 @@ Also, the Ground Motion is measured.

    -
    gm  = load('./disturbances/mat/psd_gm.mat', 'f', 'psd_gm', 'psd_gv');
    -rz  = load('./disturbances/mat/pxsp_r.mat', 'f', 'pxsp_r');
    -tyz = load('./disturbances/mat/pxz_ty_r.mat', 'f', 'pxz_ty_r');
    -tyx = load('./disturbances/mat/pxe_ty_r.mat', 'f', 'pxe_ty_r');
    +
    gm  = load('./disturbances/mat/psd_gm.mat', 'f', 'psd_gm', 'psd_gv');
    +rz  = load('./disturbances/mat/pxsp_r.mat', 'f', 'pxsp_r');
    +tyz = load('./disturbances/mat/pxz_ty_r.mat', 'f', 'pxz_ty_r');
    +tyx = load('./disturbances/mat/pxe_ty_r.mat', 'f', 'pxe_ty_r');
     
    @@ -484,20 +476,20 @@ tyx = load( -
    gm.psd_rv = gm.psd_gm.*abs(squeeze(freqresp(G('Vm', 'Dw'), gm.f, 'Hz'))).^2;
    +
    gm.psd_rv = gm.psd_gm.*abs(squeeze(freqresp(G('Vm', 'Dw'), gm.f, 'Hz'))).^2;
     

-The Power Spectral Density of the relative motion/velocity of the hexapod with respect to the granite are shown in figures 5 and 6. +The Power Spectral Density of the relative motion/velocity of the hexapod with respect to the granite are shown in figures 5 and 6.

-The Cumulative Amplitude Spectrum of the relative motion is shown in figure 7. +The Cumulative Amplitude Spectrum of the relative motion is shown in figure 7.

-
+

dist_effect_relative_velocity.png

Figure 5: Amplitude Spectral Density of the relative velocity of the hexapod with respect to the granite due to different sources of perturbation (png, pdf)

@@ -505,14 +497,14 @@ The Cumulative Amplitude Spectrum of the relative motion is shown in figure + -
+

dist_effect_relative_motion_cas.png

Figure 7: Cumulative Amplitude Spectrum of the relative motion due to different sources of perturbation (png, pdf)

@@ -520,25 +512,25 @@ The Cumulative Amplitude Spectrum of the relative motion is shown in figure
-
-

5 Compute the Power Spectral Density of the disturbance force

-
+
+

5 Compute the Power Spectral Density of the disturbance force

+

- +

-Now, from the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section 3) and from the measured PSD of the relative motion (section 4), we can compute the PSD of the disturbance force. +Now, from the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section 3) and from the measured PSD of the relative motion (section 4), we can compute the PSD of the disturbance force.

-
rz.psd_f  = rz.pxsp_r./abs(squeeze(freqresp(G('Vm', 'Frz'), rz.f, 'Hz'))).^2;
-tyz.psd_f = tyz.pxz_ty_r./abs(squeeze(freqresp(G('Vm', 'Fty'), tyz.f, 'Hz'))).^2;
+
rz.psd_f  = rz.pxsp_r./abs(squeeze(freqresp(G('Vm', 'Frz'), rz.f, 'Hz'))).^2;
+tyz.psd_f = tyz.pxz_ty_r./abs(squeeze(freqresp(G('Vm', 'Fty'), tyz.f, 'Hz'))).^2;
 
-
+

dist_force_psd.png

Figure 8: Amplitude Spectral Density of the disturbance force (png, pdf)

@@ -546,11 +538,11 @@ tyz.psd_f = tyz.pxz_ty_r./abs -

6 Noise Budget

-
+
+

6 Noise Budget

+

- +

@@ -559,7 +551,7 @@ We should verify that this is coherent with the measurements.

-
+

psd_effect_dist_verif.png

Figure 9: Computed Effect of the disturbances on the relative displacement hexapod/granite (png, pdf)

@@ -567,7 +559,7 @@ We should verify that this is coherent with the measurements. -
+

cas_computed_relative_displacement.png

Figure 10: CAS of the total Relative Displacement due to all considered sources of perturbation (png, pdf)

@@ -575,23 +567,23 @@ We should verify that this is coherent with the measurements.
-
-

7 Save

-
+
+

7 Save

+

The PSD of the disturbance force are now saved for further analysis (the mat file is accessible here).

-
dist_f = struct();
+
dist_f = struct();
 
 dist_f.f = gm.f; % Frequency Vector [Hz]
 
-dist_f.psd_gm = gm.psd_gm; % Power Spectral Density of the Ground Motion [m^2/Hz]
-dist_f.psd_ty = tyz.psd_f; % Power Spectral Density of the force induced by the Ty stage in the Z direction [N^2/Hz]
-dist_f.psd_rz = rz.psd_f; % Power Spectral Density of the force induced by the Rz stage in the Z direction [N^2/Hz]
+dist_f.psd_gm = gm.psd_gm; % Power Spectral Density of the Ground Motion [m^2/Hz]
+dist_f.psd_ty = tyz.psd_f; % Power Spectral Density of the force induced by the Ty stage in the Z direction [N^2/Hz]
+dist_f.psd_rz = rz.psd_f; % Power Spectral Density of the force induced by the Rz stage in the Z direction [N^2/Hz]
 
-save('./disturbances/mat/dist_psd.mat', 'dist_f');
+save('./disturbances/mat/dist_psd.mat', 'dist_f');
 
@@ -599,8 +591,7 @@ save(

Author: Dehaeze Thomas

-

Created: 2019-12-13 ven. 16:39

-

Validate

+

Created: 2020-02-18 mar. 17:44

diff --git a/disturbances/index.org b/disturbances/index.org index 1c04d3c..51ff49d 100644 --- a/disturbances/index.org +++ b/disturbances/index.org @@ -42,6 +42,9 @@ :END: * Introduction :ignore: +:PROPERTIES: +:CUSTOM_ID: Introduction +:END: The goal here is to extract the Power Spectral Density of the sources of perturbation. The sources of perturbations are (schematically shown in figure [[fig:uniaxial-model-micro-station]]): @@ -172,6 +175,9 @@ This file is divided in the following sections: - Section [[sec:noise_budget]]: with the computed PSD, the noise budget of the system is done * Matlab Init :noexport:ignore: +:PROPERTIES: +:CUSTOM_ID: Matlab-Init +:END: #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) <> #+end_src @@ -189,6 +195,9 @@ This file is divided in the following sections: #+end_src * Simscape Model +:PROPERTIES: +:CUSTOM_ID: Simscape-Model +:END: <> The following Simscape model of the micro-station is the same model used for the dynamical analysis. @@ -218,6 +227,9 @@ We initialize all the stages. #+end_src * Identification +:PROPERTIES: +:CUSTOM_ID: Identification +:END: <> The transfer functions from the disturbance forces to the relative velocity of the hexapod with respect to the granite are computed using the Simscape Model representing the experimental setup with the code below. @@ -262,6 +274,9 @@ The transfer functions from the disturbance forces to the relative velocity of t #+end_src * Sensitivity to Disturbances +:PROPERTIES: +:CUSTOM_ID: Sensitivity-to-Disturbances +:END: <> #+begin_src matlab :exports none @@ -330,6 +345,9 @@ The transfer functions from the disturbance forces to the relative velocity of t [[file:figs/sensitivity_dist_frz.png]] * Power Spectral Density of the effect of the disturbances +:PROPERTIES: +:CUSTOM_ID: Power-Spectral-Density-of-the-effect-of-the-disturbances +:END: <> The PSD of the relative velocity between the hexapod and the marble in $[(m/s)^2/Hz]$ are loaded for the following sources of disturbance: - Slip Ring Rotation @@ -434,6 +452,9 @@ The Cumulative Amplitude Spectrum of the relative motion is shown in figure [[fi [[file:figs/dist_effect_relative_motion_cas.png]] * Compute the Power Spectral Density of the disturbance force +:PROPERTIES: +:CUSTOM_ID: Compute-the-Power-Spectral-Density-of-the-disturbance-force +:END: <> Now, from the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section [[sec:sensitivity_disturbances]]) and from the measured PSD of the relative motion (section [[sec:psd_dist]]), we can compute the PSD of the disturbance force. @@ -466,6 +487,9 @@ Now, from the extracted transfer functions from the disturbance force to the rel [[file:figs/dist_force_psd.png]] * Noise Budget +:PROPERTIES: +:CUSTOM_ID: Noise-Budget +:END: <> Now, from the compute spectral density of the disturbance sources, we can compute the resulting relative motion of the Hexapod with respect to the granite using the model. @@ -526,6 +550,9 @@ We should verify that this is coherent with the measurements. [[file:figs/cas_computed_relative_displacement.png]] * Save +:PROPERTIES: +:CUSTOM_ID: Save +:END: The PSD of the disturbance force are now saved for further analysis (the mat file is accessible [[file:mat/dist_psd.mat][here]]). #+begin_src matlab diff --git a/disturbances/mat/dist_psd.mat b/disturbances/mat/dist_psd.mat index 56b78fa508ec408a0788fa757bc5cb367d77a24e..4ab206ec6d77e9a4b155dcf043e6e26c7953d82d 100644 GIT binary patch delta 126032 zcmV(wKz43IP!RCQ$_MrC3kF*qPGH##ynIyE;SGB7eQkx?U&UAnl(RX@BN(Vn^@Tm#~Q&bx&7tbX&%5}oW;n4d4@2%w{P>ZuMA)q zZ|9b9;q+os;$0Ra8T&E!pW>!XISyj*FNy9s(hXsMxJ9v(Ecym9DUb8-620lexCD&J zT4fGkSdV2C?mwBp2>JUqRwho_XI>}C9ur$lJ_}j)Y7rT8=ZOtYylJDP=&fT5B z%#Tc!4^NL^qEq;4C^Gvo)%wEif?7kE3PJA2H!4RlGwp(O%#@Ru5J!?;lkxl(gu~ZHh8~ z#RdyD4$RS^eVdKWFH6L?&!=Q8;E2>~?AkB`uIRNZBMUw9L?8GxuPd`$cwh)YN2YaqPpmRmXj<}pemq$CEph{c6}q-&GSaNC51+$KirXvh0jBRPFFY%>}-28nS^Mk)SoftG@$08rOYa&Pbi(d=*N6dE0Vj*;woXBiMH4l6tJC~ 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diff --git a/functions/index.org b/functions/index.org index 82e3e21..024e30a 100644 --- a/functions/index.org +++ b/functions/index.org @@ -284,38 +284,6 @@ This Matlab function is accessible [[file:../src/converErrorBasis.m][here]]. end #+end_src -* Inverse Kinematics of the Hexapod -:PROPERTIES: -:header-args:matlab+: :tangle ../src/inverseKinematicsHexapod.m -:header-args:matlab+: :comments none :mkdirp yes :eval no -:END: -<> - -This Matlab function is accessible [[file:src/inverseKinematicsHexapod.m][here]]. - -#+begin_src matlab - function [L] = inverseKinematicsHexapod(hexapod, AP, ARB) - % inverseKinematicsHexapod - Compute the initial position of each leg to have the wanted Hexapod's position - % - % Syntax: inverseKinematicsHexapod(hexapod, AP, ARB) - % - % Inputs: - % - hexapod - Hexapod object containing the geometry of the hexapod - % - AP - Position vector of point OB expressed in frame {A} in [m] - % - ARB - Rotation Matrix expressed in frame {A} - - % Wanted Length of the hexapod's legs [m] - L = zeros(6, 1); - - for i = 1:length(L) - Bbi = hexapod.pos_top_tranform(i, :)' - 1e-3*[0 ; 0 ; hexapod.TP.thickness+hexapod.Leg.sphere.top+hexapod.SP.thickness.top+hexapod.jacobian]; % [m] - Aai = hexapod.pos_base(i, :)' + 1e-3*[0 ; 0 ; hexapod.BP.thickness+hexapod.Leg.sphere.bottom+hexapod.SP.thickness.bottom-hexapod.h-hexapod.jacobian]; % [m] - - L(i) = sqrt(AP'*AP + Bbi'*Bbi + Aai'*Aai - 2*AP'*Aai + 2*AP'*(ARB*Bbi) - 2*(ARB*Bbi)'*Aai); - end - end -#+end_src - * computeReferencePose :PROPERTIES: :header-args:matlab+: :tangle ../src/computeReferencePose.m @@ -398,7 +366,7 @@ This Matlab function is accessible [[file:src/computeReferencePose.m][here]]. 0 0 1 Dn(3) ; 0 0 0 1 ]; - Rn(1:3, 1:3) = Rnx*Rny*Rnz; + Rn(1:3, 1:3) = Rnz*Rny*Rnx; %% Total Homogeneous transformation WTr = Rty*Rry*Rrz*Rh*Rn; diff --git a/kinematics/index.org b/kinematics/index.org index 760f62f..86775a5 100644 --- a/kinematics/index.org +++ b/kinematics/index.org @@ -97,7 +97,7 @@ The three rotations that we define thus corresponds to the Euler U-V-W angles. We should have the *same behavior* for the Micro-Hexapod on Simscape (same inputs at least). However, the Bushing Joint makes rotations around mobiles axes (X, Y' and then Z'') and not fixed axes (X, Y and Z). -*** TODO Using Inverse Kinematics and Leg Actuators +*** Using Inverse Kinematics and Leg Actuators Here, we can use the Inverse Kinematic of the Hexapod to determine the length of each leg in order to obtain some defined translation and rotation of the mobile platform. The advantages are: @@ -147,20 +147,20 @@ Otherwise, when the limbs' lengths derived yield complex numbers, then the posit **** Matlab Implementation We open the Simulink file. #+begin_src matlab - + open('nass_model.slx') #+end_src We load the configuration and set a small =StopTime=. #+begin_src matlab load('mat/conf_simulink.mat'); - set_param(conf_simulink, 'StopTime', '0.5'); + set_param(conf_simulink, 'StopTime', '0.1'); #+end_src We define the wanted position/orientation of the Hexapod under study. #+begin_src matlab - tx = 0.1; % [rad] - ty = 0.2; % [rad] - tz = 0.05; % [rad] + tx = 0.05; % [rad] + ty = 0.1; % [rad] + tz = 0.02; % [rad] Rx = [1 0 0; 0 cos(tx) -sin(tx); @@ -175,34 +175,47 @@ We define the wanted position/orientation of the Hexapod under study. 0 0 1]; ARB = Rz*Ry*Rx; - AP = [0.01; 0.02; 0.03]; % [m] + AP = [0.1; 0.005; 0.01]; % [m] +#+end_src - hexapod = initializeMicroHexapod('AP', AP, 'ARB', ARB); +#+begin_src matlab + initializeSimscapeConfiguration('gravity', false); + initializeGround('type', 'none'); + initializeGranite('type', 'none'); + initializeTy('type', 'none'); + initializeRy('type', 'none'); + initializeRz('type', 'none'); + initializeMicroHexapod('type', 'rigid', 'AP', AP, 'ARB', ARB); + initializeAxisc('type', 'none'); + initializeMirror('type', 'none'); + initializeNanoHexapod('type', 'none'); + initializeSample('type', 'none'); + initializeLoggingConfiguration('log', 'all'); #+end_src We run the simulation. #+begin_src matlab - sim() + sim('nass_model'); #+end_src And we verify that we indeed succeed to go to the wanted position. #+begin_src matlab :results table replace - [simout.x.Data(end) ; simout.y.Data(end) ; simout.z.Data(end)] - AP + [simout.Dhm.x.Data(end) ; simout.Dhm.y.Data(end) ; simout.Dhm.z.Data(end)] - AP #+end_src #+RESULTS: -| 1.611e-10 | -| -1.3748e-10 | -| 8.4879e-11 | +| 8.4655e-16 | +| 1.5586e-15 | +| -2.1337e-16 | #+begin_src matlab :results table replace - simout.R.Data(:, :, end)-ARB + simout.Dhm.R.Data(:, :, end)-ARB #+end_src #+RESULTS: -| -1.2659e-10 | 6.5603e-11 | 6.2183e-10 | -| 1.0354e-10 | -5.2439e-11 | -5.2425e-10 | -| -5.9816e-10 | 5.532e-10 | -1.7737e-10 | +| -1.1102e-16 | -1.36e-15 | 4.2744e-15 | +| 1.0651e-15 | 6.6613e-16 | 5.1278e-15 | +| -4.2882e-15 | -4.9336e-15 | 1.1102e-16 | * TODO Tests on the transformation from reference to wanted position :noexport: :PROPERTIES: diff --git a/mat/Foffset.mat b/mat/Foffset.mat new file mode 100644 index 0000000000000000000000000000000000000000..9712f2b8277c4f334f31df59131b2217f8faac11 GIT binary patch literal 623 zcmeZu4DoSvQZUssQ1EpO(M`+DN!3vZ$Vn_o%P-2cQgHY2i*PhE(NS}aZCnS7eNHSA+ z)^JJT0M}DvCPU*HX=w%C=TjfBY*Jm2CBgOSyOYG(ZRfYYh^xHu?EwQrS32h|kOARv z13Zuoa5^d>IYaV}QIVuYV-B;zy)QQu|G3q?YII9I*{!O&lHJSe?OQdbm-6d=F5)`6 zlD%)O$nBqNHNGBbn^_~dyzv#ox!+PEgx#lo4(h&j`8>C{mniwI6uJG6z42!$JHvKv zULBAD0l3{4A#uk`tJo6gz7GLxpN@qmX)o3^jmCdGy9%Rap_Z+SzA=- 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functions are defined below. :END: #+begin_src matlab arguments - args.log char {mustBeMember(args.log,{'none', 'all'})} = 'none' + args.log char {mustBeMember(args.log,{'none', 'all', 'forces'})} = 'none' args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-3 end #+end_src @@ -152,6 +152,8 @@ These functions are defined below. conf_log.type = 0; case 'all' conf_log.type = 1; + case 'forces' + conf_log.type = 2; end #+end_src @@ -298,7 +300,8 @@ The output =sample_pos= corresponds to the impact point of the X-ray. :END: #+begin_src matlab arguments - args.type char {mustBeMember(args.type,{'rigid', 'flexible', 'none', 'modal-analysis'})} = 'flexible' + args.type char {mustBeMember(args.type,{'rigid', 'flexible', 'none', 'modal-analysis', 'init'})} = 'flexible' + args.Foffset logical {mustBeNumericOrLogical} = true args.density (1,1) double {mustBeNumeric, mustBeNonnegative} = 2800 % Density [kg/m3] args.x0 (1,1) double {mustBeNumeric} = 0 % Rest position of the Joint in the X direction [m] args.y0 (1,1) double {mustBeNumeric} = 0 % Rest position of the Joint in the Y direction [m] @@ -330,45 +333,51 @@ First, we initialize the =granite= structure. granite.type = 2; case 'modal-analysis' granite.type = 3; + case 'init' + granite.type = 4; end #+end_src -** Function content +** Material and Geometry :PROPERTIES: :UNNUMBERED: t :END: + Properties of the Material and link to the geometry of the granite. #+begin_src matlab granite.density = args.density; % [kg/m3] granite.STEP = './STEPS/granite/granite.STEP'; #+end_src -Stiffness of the connection with Ground. -#+begin_src matlab - granite.k.x = 4e9; % [N/m] - granite.k.y = 3e8; % [N/m] - granite.k.z = 8e8; % [N/m] -#+end_src - -Damping of the connection with Ground. -#+begin_src matlab - granite.c.x = 4.0e5; % [N/(m/s)] - granite.c.y = 1.1e5; % [N/(m/s)] - granite.c.z = 9.0e5; % [N/(m/s)] -#+end_src - -Equilibrium position of the Cartesian joint. -#+begin_src matlab - granite.x0 = args.x0; - granite.y0 = args.y0; - granite.z0 = args.z0; -#+end_src - Z-offset for the initial position of the sample with respect to the granite top surface. #+begin_src matlab granite.sample_pos = 0.8; % [m] #+end_src +** Stiffness and Damping properties +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab + granite.K = [4e9; 3e8; 8e8]; % [N/m] + granite.C = [4.0e5; 1.1e5; 9.0e5]; % [N/(m/s)] +#+end_src + +** Equilibrium position of the each joint. +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab + if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init') + load('mat/Foffset.mat', 'Fgm'); + granite.Deq = -Fgm'./granite.K; + else + granite.Deq = zeros(6,1); + end +#+end_src + ** Save the Structure :PROPERTIES: :UNNUMBERED: t @@ -423,15 +432,8 @@ The Simscape model of the Translation stage consist of: :END: #+begin_src matlab arguments - args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis'})} = 'flexible' - args.x11 (1,1) double {mustBeNumeric} = 0 % [m] - args.z11 (1,1) double {mustBeNumeric} = 0 % [m] - args.x21 (1,1) double {mustBeNumeric} = 0 % [m] - args.z21 (1,1) double {mustBeNumeric} = 0 % [m] - args.x12 (1,1) double {mustBeNumeric} = 0 % [m] - args.z12 (1,1) double {mustBeNumeric} = 0 % [m] - args.x22 (1,1) double {mustBeNumeric} = 0 % [m] - args.z22 (1,1) double {mustBeNumeric} = 0 % [m] + args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible' + args.Foffset logical {mustBeNumericOrLogical} = true end #+end_src @@ -444,7 +446,6 @@ First, we initialize the =ty= structure. ty = struct(); #+end_src - ** Add Translation Stage Type :PROPERTIES: :UNNUMBERED: t @@ -459,11 +460,12 @@ First, we initialize the =ty= structure. ty.type = 2; case 'modal-analysis' ty.type = 3; + case 'init' + ty.type = 4; end #+end_src - -** Function content +** Material and Geometry :PROPERTIES: :UNNUMBERED: t :END: @@ -506,28 +508,28 @@ Define the density of the materials as well as the geometry (STEP files). ty.rotor.STEP = './STEPS/ty/Ty_Motor_Rotor.STEP'; #+end_src -Stiffness of the stage. +** Stiffness and Damping properties +:PROPERTIES: +:UNNUMBERED: t +:END: + #+begin_src matlab - ty.k.ax = 5e8; % Axial Stiffness for each of the 4 guidance (y) [N/m] - ty.k.rad = 5e7; % Radial Stiffness for each of the 4 guidance (x-z) [N/m] + ty.K = [2e8; 1e8; 2e8; 6e7; 9e7; 6e7]; % [N/m, N*m/rad] + ty.C = [8e4; 5e4; 8e4; 2e4; 3e4; 2e4]; % [N/(m/s), N*m/(rad/s)] #+end_src -Damping of the stage. -#+begin_src matlab - ty.c.ax = 70710; % [N/(m/s)] - ty.c.rad = 22360; % [N/(m/s)] -#+end_src +** Equilibrium position of the each joint. +:PROPERTIES: +:UNNUMBERED: t +:END: -Equilibrium position of the joints. #+begin_src matlab - ty.x0_11 = args.x11; - ty.z0_11 = args.z11; - ty.x0_12 = args.x12; - ty.z0_12 = args.z12; - ty.x0_21 = args.x21; - ty.z0_21 = args.z21; - ty.x0_22 = args.x22; - ty.z0_22 = args.z22; + if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init') + load('mat/Foffset.mat', 'Ftym'); + ty.Deq = -Ftym'./ty.K; + else + ty.Deq = zeros(6,1); + end #+end_src ** Save the Structure @@ -584,19 +586,9 @@ The Simscape model of the Tilt stage is composed of: :END: #+begin_src matlab arguments - args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis'})} = 'flexible' - args.x11 (1,1) double {mustBeNumeric} = 0 % [m] - args.y11 (1,1) double {mustBeNumeric} = 0 % [m] - args.z11 (1,1) double {mustBeNumeric} = 0 % [m] - args.x12 (1,1) double {mustBeNumeric} = 0 % [m] - args.y12 (1,1) double {mustBeNumeric} = 0 % [m] - args.z12 (1,1) double {mustBeNumeric} = 0 % [m] - args.x21 (1,1) double {mustBeNumeric} = 0 % [m] - args.y21 (1,1) double {mustBeNumeric} = 0 % [m] - args.z21 (1,1) double {mustBeNumeric} = 0 % [m] - args.x22 (1,1) double {mustBeNumeric} = 0 % [m] - args.y22 (1,1) double {mustBeNumeric} = 0 % [m] - args.z22 (1,1) double {mustBeNumeric} = 0 % [m] + args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible' + args.Foffset logical {mustBeNumericOrLogical} = true + args.Ry_init (1,1) double {mustBeNumeric} = 0 end #+end_src @@ -624,12 +616,12 @@ First, we initialize the =ry= structure. ry.type = 2; case 'modal-analysis' ry.type = 3; + case 'init' + ry.type = 4; end #+end_src - - -** Function content +** Material and Geometry :PROPERTIES: :UNNUMBERED: t :END: @@ -652,48 +644,44 @@ Properties of the Material and link to the geometry of the Tilt stage. ry.stage.STEP = './STEPS/ry/Tilt_Stage.STEP'; #+end_src -Stiffness of the stage. -#+begin_src matlab - ry.k.tilt = 1e4; % Rotation stiffness around y [N*m/deg] - ry.k.h = 1e8; % Stiffness in the direction of the guidance [N/m] - ry.k.rad = 1e8; % Stiffness in the top direction [N/m] - ry.k.rrad = 1e8; % Stiffness in the side direction [N/m] -#+end_src - -Damping of the stage. -#+begin_src matlab - ry.c.tilt = 2.8e2; - ry.c.h = 2.8e4; - ry.c.rad = 2.8e4; - ry.c.rrad = 2.8e4; -#+end_src - -Equilibrium position of the joints. -#+begin_src matlab - ry.x0_11 = args.x11; - ry.y0_11 = args.y11; - ry.z0_11 = args.z11; - ry.x0_12 = args.x12; - ry.y0_12 = args.y12; - ry.z0_12 = args.z12; - ry.x0_21 = args.x21; - ry.y0_21 = args.y21; - ry.z0_21 = args.z21; - ry.x0_22 = args.x22; - ry.y0_22 = args.y22; - ry.z0_22 = args.z22; -#+end_src - Z-Offset so that the center of rotation matches the sample center; #+begin_src matlab ry.z_offset = 0.58178; % [m] #+end_src +#+begin_src matlab + ry.Ry_init = args.Ry_init; % [rad] +#+end_src + +** Stiffness and Damping properties +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab + ry.K = [3.8e8; 4e8; 3.8e8; 1.2e8; 6e4; 1.2e8]; + ry.C = [1e5; 1e5; 1e5; 3e4; 1e3; 3e4]; +#+end_src + +** Equilibrium position of the each joint. +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab + if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init') + load('mat/Foffset.mat', 'Fym'); + ry.Deq = -Fym'./ry.K; + else + ry.Deq = zeros(6,1); + end +#+end_src + ** Save the Structure :PROPERTIES: :UNNUMBERED: t :END: -The =ty= structure is saved. +The =ry= structure is saved. #+begin_src matlab save('./mat/stages.mat', 'ry', '-append'); #+end_src @@ -739,12 +727,8 @@ The Simscape model of the Spindle is composed of: :END: #+begin_src matlab arguments - args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis'})} = 'flexible' - args.x0 (1,1) double {mustBeNumeric} = 0 % Equilibrium position of the Joint [m] - args.y0 (1,1) double {mustBeNumeric} = 0 % Equilibrium position of the Joint [m] - args.z0 (1,1) double {mustBeNumeric} = 0 % Equilibrium position of the Joint [m] - args.rx0 (1,1) double {mustBeNumeric} = 0 % Equilibrium position of the Joint [rad] - args.ry0 (1,1) double {mustBeNumeric} = 0 % Equilibrium position of the Joint [rad] + args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible' + args.Foffset logical {mustBeNumericOrLogical} = true end #+end_src @@ -757,7 +741,6 @@ First, we initialize the =rz= structure. rz = struct(); #+end_src - ** Add Spindle Type :PROPERTIES: :UNNUMBERED: t @@ -772,13 +755,16 @@ First, we initialize the =rz= structure. rz.type = 2; case 'modal-analysis' rz.type = 3; + case 'init' + rz.type = 4; end #+end_src -** Function content +** Material and Geometry :PROPERTIES: :UNNUMBERED: t :END: + Properties of the Material and link to the geometry of the spindle. #+begin_src matlab % Spindle - Slip Ring @@ -794,29 +780,28 @@ Properties of the Material and link to the geometry of the spindle. rz.stator.STEP = './STEPS/rz/Spindle_Stator.STEP'; #+end_src -Stiffness of the stage. +** Stiffness and Damping properties +:PROPERTIES: +:UNNUMBERED: t +:END: + #+begin_src matlab - rz.k.rot = 1e6; % TODO - Rotational Stiffness (Rz) [N*m/deg] - rz.k.tilt = 1e6; % Rotational Stiffness (Rx, Ry) [N*m/deg] - rz.k.ax = 2e9; % Axial Stiffness (Z) [N/m] - rz.k.rad = 7e8; % Radial Stiffness (X, Y) [N/m] + rz.K = [7e8; 7e8; 2e9; 1e7; 1e7; 1e7]; + rz.C = [4e4; 4e4; 7e4; 1e4; 1e4; 1e4]; #+end_src -Damping of the stage. -#+begin_src matlab - rz.c.rot = 1.6e3; - rz.c.tilt = 1.6e3; - rz.c.ax = 7.1e4; - rz.c.rad = 4.2e4; -#+end_src +** Equilibrium position of the each joint. +:PROPERTIES: +:UNNUMBERED: t +:END: -Equilibrium position of the joints. #+begin_src matlab - rz.x0 = args.x0; - rz.y0 = args.y0; - rz.z0 = args.z0; - rz.rx0 = args.rx0; - rz.ry0 = args.ry0; + if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init') + load('mat/Foffset.mat', 'Fzm'); + rz.Deq = -Fzm'./rz.K; + else + rz.Deq = zeros(6,1); + end #+end_src ** Save the Structure @@ -864,7 +849,7 @@ The =rz= structure is saved. :END: #+begin_src matlab arguments - args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis'})} = 'flexible' + args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible' % initializeFramesPositions args.H (1,1) double {mustBeNumeric, mustBePositive} = 350e-3 args.MO_B (1,1) double {mustBeNumeric} = 270e-3 @@ -895,8 +880,8 @@ The =rz= structure is saved. % inverseKinematics args.AP (3,1) double {mustBeNumeric} = zeros(3,1) args.ARB (3,3) double {mustBeNumeric} = eye(3) - % Equilibrium position of each leg - args.dLeq (6,1) double {mustBeNumeric} = zeros(6,1) + % Force that stiffness of each joint should apply at t=0 + args.Foffset logical {mustBeNumericOrLogical} = true end #+end_src @@ -919,10 +904,14 @@ The =rz= structure is saved. Equilibrium position of the each joint. #+begin_src matlab - micro_hexapod.dLeq = args.dLeq; + if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init') + load('mat/Foffset.mat', 'Fhm'); + micro_hexapod.dLeq = -Fhm'./args.Ki; + else + micro_hexapod.dLeq = zeros(6,1); + end #+end_src - ** Add Type :PROPERTIES: :UNNUMBERED: t @@ -937,6 +926,8 @@ Equilibrium position of the each joint. micro_hexapod.type = 2; case 'modal-analysis' micro_hexapod.type = 3; + case 'init' + micro_hexapod.type = 4; end #+end_src @@ -1017,10 +1008,11 @@ First, we initialize the =axisc= structure. end #+end_src -** Function content +** Material and Geometry :PROPERTIES: :UNNUMBERED: t :END: + Properties of the Material and link to the geometry files. #+begin_src matlab % Structure @@ -1116,29 +1108,30 @@ First, we initialize the =mirror= structure. end #+end_src -** Function content +** Material and Geometry :PROPERTIES: :UNNUMBERED: t :END: + We define the geometrical values. #+begin_src matlab - mirror.h = 50; % Height of the mirror [mm] + mirror.h = 0.05; % Height of the mirror [m] - mirror.thickness = 25; % Thickness of the plate supporting the sample [mm] + mirror.thickness = 0.025; % Thickness of the plate supporting the sample [m] - mirror.hole_rad = 120; % radius of the hole in the mirror [mm] + mirror.hole_rad = 0.120; % radius of the hole in the mirror [m] - mirror.support_rad = 100; % radius of the support plate [mm] + mirror.support_rad = 0.1; % radius of the support plate [m] - % point of interest offset in z (above the top surfave) [mm] + % point of interest offset in z (above the top surfave) [m] switch args.type case 'none' - mirror.jacobian = 200; + mirror.jacobian = 0.20; case 'rigid' - mirror.jacobian = 200 - mirror.h; + mirror.jacobian = 0.20 - mirror.h; end - mirror.rad = 180; % radius of the mirror (at the bottom surface) [mm] + mirror.rad = 0.180; % radius of the mirror (at the bottom surface) [m] #+end_src #+begin_src matlab @@ -1352,15 +1345,13 @@ The Simscape model of the sample environment is composed of: :END: #+begin_src matlab arguments - args.type char {mustBeMember(args.type,{'rigid', 'flexible', 'none'})} = 'flexible' - args.radius (1,1) double {mustBeNumeric, mustBePositive} = 0.1 % [m] - args.height (1,1) double {mustBeNumeric, mustBePositive} = 0.3 % [m] - args.mass (1,1) double {mustBeNumeric, mustBePositive} = 50 % [kg] - args.freq (1,1) double {mustBeNumeric, mustBePositive} = 100 % [Hz] - args.offset (1,1) double {mustBeNumeric} = 0 % [m] - args.x0 (1,1) double {mustBeNumeric} = 0 % [m] - args.y0 (1,1) double {mustBeNumeric} = 0 % [m] - args.z0 (1,1) double {mustBeNumeric} = 0 % [m] + args.type char {mustBeMember(args.type,{'rigid', 'flexible', 'none', 'init'})} = 'flexible' + args.radius (1,1) double {mustBeNumeric, mustBePositive} = 0.1 % [m] + args.height (1,1) double {mustBeNumeric, mustBePositive} = 0.3 % [m] + args.mass (1,1) double {mustBeNumeric, mustBePositive} = 50 % [kg] + args.freq (1,1) double {mustBeNumeric, mustBePositive} = 100 % [Hz] + args.offset (1,1) double {mustBeNumeric} = 0 % [m] + args.Foffset logical {mustBeNumericOrLogical} = true end #+end_src @@ -1385,40 +1376,46 @@ First, we initialize the =sample= structure. sample.type = 1; case 'flexible' sample.type = 2; + case 'init' + sample.type = 3; end #+end_src -** Function content +** Material and Geometry :PROPERTIES: :UNNUMBERED: t :END: + We define the geometrical parameters of the sample as well as its mass and position. #+begin_src matlab sample.radius = args.radius; % [m] sample.height = args.height; % [m] - sample.mass = args.mass; % [kg] + sample.mass = args.mass; % [kg] sample.offset = args.offset; % [m] #+end_src -Stiffness of the sample fixation. +** Stiffness and Damping properties +:PROPERTIES: +:UNNUMBERED: t +:END: + #+begin_src matlab - sample.k.x = sample.mass * (2*pi * args.freq)^2; % [N/m] - sample.k.y = sample.mass * (2*pi * args.freq)^2; % [N/m] - sample.k.z = sample.mass * (2*pi * args.freq)^2; % [N/m] + sample.K = ones(3,1) * sample.mass * (2*pi * args.freq)^2; % [N/m] + sample.C = 0.1 * sqrt(sample.K*sample.mass); % [N/(m/s)] #+end_src -Damping of the sample fixation. -#+begin_src matlab - sample.c.x = 0.1*sqrt(sample.k.x*sample.mass); % [N/(m/s)] - sample.c.y = 0.1*sqrt(sample.k.y*sample.mass); % [N/(m/s)] - sample.c.z = 0.1*sqrt(sample.k.z*sample.mass); % [N/(m/s)] -#+end_src +** Equilibrium position of the each joint. +:PROPERTIES: +:UNNUMBERED: t +:END: -Equilibrium position of the Cartesian joint corresponding to the sample fixation. #+begin_src matlab - sample.x0 = args.x0; % [m] - sample.y0 = args.y0; % [m] - sample.z0 = args.z0; % [m] + if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init') + load('mat/Foffset.mat', 'Fsm'); + sample.Deq = -Fsm'./sample.K; + else + sample.Deq = zeros(3,1); + end #+end_src ** Save the Structure @@ -1746,11 +1743,33 @@ The =controller= structure is saved. switch args.Dn_type case 'constant' Dn = [args.Dn_pos, args.Dn_pos]; + + load('mat/stages.mat', 'nano_hexapod'); + + AP = [args.Dn_pos(1) ; args.Dn_pos(2) ; args.Dn_pos(3)]; + + tx = args.Dn_pos(4); + ty = args.Dn_pos(5); + tz = args.Dn_pos(6); + + ARB = [cos(tz) -sin(tz) 0; + sin(tz) cos(tz) 0; + 0 0 1]*... + [ cos(ty) 0 sin(ty); + 0 1 0; + -sin(ty) 0 cos(ty)]*... + [1 0 0; + 0 cos(tx) -sin(tx); + 0 sin(tx) cos(tx)]; + + [~, Dnl] = inverseKinematics(nano_hexapod, 'AP', AP, 'ARB', ARB); + Dnl = [Dnl, Dnl]; otherwise warning('Dn_type is not set correctly'); end Dn = struct('time', t, 'signals', struct('values', Dn)); + Dnl = struct('time', t, 'signals', struct('values', Dnl)); #+end_src ** Save @@ -1759,7 +1778,7 @@ The =controller= structure is saved. :END: #+begin_src matlab %% Save - save('mat/nass_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'Rm', 'Dn', 'Ts'); + save('mat/nass_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'Rm', 'Dn', 'Dnl', 'Ts'); end #+end_src @@ -1985,6 +2004,81 @@ We define some parameters that will be used in the algorithm. save('mat/nass_disturbances.mat', 'Dwx', 'Dwy', 'Dwz', 'Fty_x', 'Fty_z', 'Frz_z', 'Fd', 'Ts', 't'); #+end_src +* Initialize Position Errors +:PROPERTIES: +:header-args:matlab+: :tangle ../src/initializePosError.m +:header-args:matlab+: :comments none :mkdirp yes +:header-args:matlab+: :eval no :results none +:END: +<> + +** Function Declaration and Documentation +:PROPERTIES: +:UNNUMBERED: t +:END: +#+begin_src matlab + function [] = initializePosError(args) + % initializePosError - Initialize the position errors + % + % Syntax: [] = initializePosError(args) + % + % Inputs: + % - args - + +#+end_src + +** Optional Parameters +:PROPERTIES: +:UNNUMBERED: t +:END: +#+begin_src matlab + arguments + args.error logical {mustBeNumericOrLogical} = false + args.Dy (1,1) double {mustBeNumeric} = 0 % [m] + args.Ry (1,1) double {mustBeNumeric} = 0 % [m] + args.Rz (1,1) double {mustBeNumeric} = 0 % [m] + end +#+end_src + +** Structure initialization +:PROPERTIES: +:UNNUMBERED: t +:END: +First, we initialize the =pos_error= structure. +#+begin_src matlab + pos_error = struct(); +#+end_src + +** Type +:PROPERTIES: +:UNNUMBERED: t +:END: +#+begin_src matlab + if args.error + pos_error.type = 1; + else + pos_error.type = 0; + end +#+end_src + +** Position Errors +:PROPERTIES: +:UNNUMBERED: t +:END: +#+begin_src matlab + pos_error.Dy = args.Dy; + pos_error.Ry = args.Ry; + pos_error.Rz = args.Rz; +#+end_src + +** Save +:PROPERTIES: +:UNNUMBERED: t +:END: +#+begin_src matlab + save('mat/pos_error.mat', 'pos_error'); +#+end_src + * Z-Axis Geophone :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeZAxisGeophone.m diff --git a/simscape_subsystems/micro_hexapod_leg.slx b/simscape_subsystems/micro_hexapod_leg.slx index 4d88953e6a5554230249eac083f513116b30e81f..2cd6419107e27611310ebdae6c0496583d524663 100644 GIT binary patch delta 10926 zcmZX419W6d)NX9swl%SB+cqcG^u%VzoH&_G>||n0Y}>Y-mpk`gZ~gbZv-0Re#l;Z@VFK|}`w|CDv)U~!i6c zpqB*WEjjcdrH7MUW`)xBeiyCa3*H7!`w1RAN7ww_MbVmO2~$TmPnhdO`>MH1yn8jY z8GVJScs>r~k6X7YQ;I^t-+Nfxs3H8IWHxL*`^Au zPxO0P8cpF7R|e^msJWJ<&tK<~nzy!rfYk3c1RKV%vDm9FtN5W~hvAATAvlbg*=5i{ zqQ<2nfnTwJ;hRnszw{Tn=CG}j?0ltJ0Oshs8aPl~&5dV)Z@8H$;BLpJ4zhLB9Vp3_xY5 zx4*-o3=IbQx1a%Ii}rV1K( zvn1jHRJb4h9DSP%+Li^0&y9+nYpr8DV~9h{X{qaRjKivtXgCdAZ(g=jCnH??d4JCH zbV6C$vn_eDKODxD*<}0^sJ*gZiX;wDikX8Mo)Hv_6+>^Fgp5+ueWkLB%!|0Cz5!S= z=8n(4O=m?gSYfy$%hbloWJeKON_Rf9b}>?H`3GVV%FwhJ`p%Hix{A1>5pyuKZ(N^35E6YXyJ1YQH7ni~PH*SU9Wd3BvRa`Q;#)lF8AX4ZG$89Te zc5*Km;?jm*FAbralJTB945E%vCdXKN?#t!6Ny=5CmUnk~=;>UAL(9+3ZXWIT7lTF3 zg=y!0_%6zk{5AypTbV$APaK zJMUyZiKElt9Lj4aVRhOc%jC*98=LYNV&0S5c_t*Gg^D<~qgL2B?dqM-8|+eWZy;=A z;it0+ys4^#m4;FgijoxYVm}wg?{SWq)NUG%oQ<69;Qrt*Zm1iy1w`LVau_aFp`$)0 znDq3U`QehLQRQlENTEKI2!`+IKf5vQasLU9j}AJflcCBhYdGTGD>Bk2o@J%j;wU9- zMhM(>W?_r%Wy@ht7b}y4g_r%Z3#ox(R-r>xwrI@uCBosi>sBVVm~XmwpyqnU77fs} z)SZHvZGeRNOQ?k5B_Q!y*CEnpD`qr^Ydq6=8Nccn#lP}ge&(CdBK4kA3~?`3yMj(s z5N!6(d)X*4Z1jT*xZ(a+MV+~-6oziMbqCvQb%WMlHiW{1_65@2Cb<2*fxB?E8LHAQ zL(RtZ%Dm9lE>LeZmdntsr%%EDvoC-Vz1cCk_r}d!&!*V-4$7Am*OH$+>=Uo30#a0A zf*GtiL_Y4mb58%6Z*^isBY)=?5S8Q>?Vq&Q5k0q|0|5dug$M$I4FYVl!v&0KImB&q zqP&0WB)dLX@7DY|s~L|DABA{)1R-$H+7|?8YI_rVeY_w5>zF6(js8{y0l~~(e zC}+WHpm+1eWg^H*IYWk(f-Co#0wiHLI$|w8$@1mO>YC@3rFoCdKZB)J%}pqPk+EfJ zD~tq(g4$uz7M^QoGvM4r+7zJsJrV=lq*MfwVprXqxBpCp`98p`EL~#U0*a!rD1oqR zuS{6Dj0Xq&C-^N*+7yL3*_cQZtK0yoYZs3O9~H`T!^crc$J-03*U3tgq6we0>hM&3 zCMU(vUN@Pe1ua{oiAc!THV5#EhgZ#^AgBh@3k6-ii$}LiCLD{lO{E9(JIiV3C$E3s%NxLy~V0HFEPOnUAf)W zNzWp%FOINVuq6Tp;46SVK!GKNM~a#OirlYZG}`5o2ZkV2&1s^#B#&NwIIL8CpI`3b zJZi&GP3e=G_fX`dwlah=?WvLeQWG@9E{*6Kg*^5OdS`G+F%Ia~=3DTyfKlKFGH5kG zAX#D#{h^V#o>aREy%=6mNsc=sfygyQFoyO3A3-WCh*{^C_znQ>TS=-yT-hnilK)wp zkR_H%6D_kbRdp^l+~rM%`8Qd_4i?btm>uH1gH!;QK+w9~43z6nW(zcmuBOGdrIaZ| zDV{_6GKqx{nN|z+Ng=s5j}Mt@ntlW$p4|=s1L5LB6Y0_)ufc*X^p(X| zk?~-j_RvBX=E(p?%u#_9FHF7=4<+rY#sOVIH9M$%ie}&9-)>D6G9#+9^E=z1&hgTR zu4nR_su3x(Bao8}Xs_zb7pr5xT8|A|>avQG{D$C~4h=*_TUKLO=Vh;Lkv&h`)wOjG z?P#^GvC#_1HiZLI2Y@){IvHBuwYSVHI|gT2?WL=G<9`5HTM=ZwwMc_K3?Re)flv#9 zGLu+>>wZX3qgus7H0g!RVG`ODoGCgZO;$6G&_crvovXXm5PR`4Sk)Mg^;&6|Sq)Q-TlOQ;cy z@cD3dvhJr&J|gK>_|O{L7B7M*-He>I*;XQ71C_zBWali}UOiQvnI1+55NER|ivoGm z+1pKrlcbj_g(+&)X~p$c#N$;p9yPVMOY^t2rOr_RjpHK5(_aRFxr zFRnYBiSPdJa4D8tUu5`GN=uTtmlGNJuCguK7{LC zA>zO94vnvtC35@t5l>pXfv zMOO2W0?sxeNqWdtIb@lV5CFKG*7v$ON5^e|*>Hq)m;9_HamZ6gpe7K%S`0aWH1sMA z_j$}7)l?a-$$fJ82w^GCWLLxIPO@FIs!6xuxwaZ?y*5$<6tQmREMv{`MY;?GjXOa> zQrFE7?-8A!P`BfY1jX4_jO@l3As{M$!&w@<79?u0 zqg`~epG-zXl)rnBMLPvghYOt|CRfCq3>5VS`VlRX3< zbd(GvzJ6((fG+)md5qQt+^sUFmehIhuY14jmt;<+-;diC;hvNa+Te9!e#xbgO~6Ea zIZq|MVA!rZSL?pdp5R76TVR}<;v=3hodpT`k)$`0n{ua!G79Lm%WaaSI_#fChT-i- zqGG`jWe%*BYx9SILP+sH)-_>uju!PnH_kO&tnrsl#(cP8gahX?HBCZWH@gj%W<{8d z$gfLb^o#~`<8(gg zoyw#vilf8y&IM?_G+7KCSdUeTycCP#mvqJ5?n6A4x=(yT%aQBf>zbp;gMcn?fX%6+ zilG7BP%*9WRKm3(fH;q!Z1BLjv%$auQIx)f$cTP1<1rnMdF8)8D+Kyq=H_4V(&A-Z zUu7dx@znPO28JcbU3p2y?`1);C>-?0{{JW*u zytJ@db|Mm-^ePy2M`~5T>m}_%%ZDS)*B+1Y$F4XYw5#A*N>s{$3tI4O2>)qJ1++V6 zR?h>=o7kwa)ujnbo)VUbQ_V-p_@o}Tq|S~)_}WE?8W1zYFEO;zF#-g|UWnwY0ImuL zbTlo-Y7=08i{S_LlsVV{>^oAIF6uSd0KxUrSBvI)O(JA!f>MLz?Q%fegJ%(rBNoMgK;I}2YY3WP|3p~@Z4GIJiRq@QS1_I z((nQDFQl0Uz|rp`IHEiZ@!*}}m3pixF4Xn6(Cp-#BU&J&2`T=`Wv#;}^C=b_tvL4d z@#x~nqoIOtDr93WU(QF}CR1ZB{#Z?Ho_)(Yg9Sq!78I%}6^N2zvFYmxsA3&4zf z-i}}cjf2e@I3YLQOz^@P6CROVMM&!JNz4OK1o66hLqQ=O!56$BxS^oZ$6k(}Zp*WJ z6+v-6CC7h**FW%KOF%40pGKYNlr^!DH#|Zm2*jX#lpCyB+ctGAXX^KeFKk{A473hU z$peMmULT9!pf;^?h5?_=@mRz3^q|VIhDJ5xPQ$yn+|n@|>SeiGVj}j!lr23p%cHCs zjMg^0zq(R%*K>qZ+aql~^}*&V!8`#9LY(5f`Ezo=jK8vw4LWOQ?3fUTVXQzY(6Ow0 z&9l#5bU$oPY(!a!>LkBa7b;pug5FSO1U@lGlXUv!DT9viHQAv16)sX$8<>s-QKU(_ zVR2Ks8&!n(wZJkR2)kmhq=}YFd1rEpDs>EK+H3qN7+n|PL_<6^Cwp|8JthL+#LNen zc-Xo>uGr6hpztEpw?|B2Fqp1IYekF5}e`baG?HXkfYu~S%M!K5MGa7OQ=ashj zvO;moPvJ_3@o0L9pEG{WFh3N3E4H<-B9*02ArYG&R&R48rNd23iSW*a

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0 0 1 ]; - Rn(1:3, 1:3) = Rnx*Rny*Rnz; + Rn(1:3, 1:3) = Rnz*Rny*Rnx; %% Total Homogeneous transformation WTr = Rty*Rry*Rrz*Rh*Rn; diff --git a/src/initializeGranite.m b/src/initializeGranite.m index a4623d4..21c21fa 100644 --- a/src/initializeGranite.m +++ b/src/initializeGranite.m @@ -1,7 +1,8 @@ function [granite] = initializeGranite(args) arguments - args.type char {mustBeMember(args.type,{'rigid', 'flexible', 'none', 'modal-analysis'})} = 'flexible' + args.type char {mustBeMember(args.type,{'rigid', 'flexible', 'none', 'modal-analysis', 'init'})} = 'flexible' + args.Foffset logical {mustBeNumericOrLogical} = true args.density (1,1) double {mustBeNumeric, mustBeNonnegative} = 2800 % Density [kg/m3] args.x0 (1,1) double {mustBeNumeric} = 0 % Rest position of the Joint in the X direction [m] args.y0 (1,1) double {mustBeNumeric} = 0 % Rest position of the Joint in the Y direction [m] @@ -19,23 +20,23 @@ switch args.type granite.type = 2; case 'modal-analysis' granite.type = 3; + case 'init' + granite.type = 4; end granite.density = args.density; % [kg/m3] granite.STEP = './STEPS/granite/granite.STEP'; -granite.k.x = 4e9; % [N/m] -granite.k.y = 3e8; % [N/m] -granite.k.z = 8e8; % [N/m] - -granite.c.x = 4.0e5; % [N/(m/s)] -granite.c.y = 1.1e5; % [N/(m/s)] -granite.c.z = 9.0e5; % [N/(m/s)] - -granite.x0 = args.x0; -granite.y0 = args.y0; -granite.z0 = args.z0; - granite.sample_pos = 0.8; % [m] +granite.K = [4e9; 3e8; 8e8]; % [N/m] +granite.C = [4.0e5; 1.1e5; 9.0e5]; % [N/(m/s)] + +if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init') + load('mat/Foffset.mat', 'Fgm'); + granite.Deq = -Fgm'./granite.K; +else + granite.Deq = zeros(6,1); +end + save('./mat/stages.mat', 'granite', '-append'); diff --git a/src/initializeLoggingConfiguration.m b/src/initializeLoggingConfiguration.m index 76b6c06..5d46e58 100644 --- a/src/initializeLoggingConfiguration.m +++ b/src/initializeLoggingConfiguration.m @@ -1,7 +1,7 @@ function [] = initializeLoggingConfiguration(args) arguments - args.log char {mustBeMember(args.log,{'none', 'all'})} = 'none' + args.log char {mustBeMember(args.log,{'none', 'all', 'forces'})} = 'none' args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-3 end @@ -12,6 +12,8 @@ switch args.log conf_log.type = 0; case 'all' conf_log.type = 1; + case 'forces' + conf_log.type = 2; end conf_log.Ts = args.Ts; diff --git a/src/initializeMicroHexapod.m b/src/initializeMicroHexapod.m index a0b3a25..9204995 100644 --- a/src/initializeMicroHexapod.m +++ b/src/initializeMicroHexapod.m @@ -1,7 +1,7 @@ function [micro_hexapod] = initializeMicroHexapod(args) arguments - args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis'})} = 'flexible' + args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible' % initializeFramesPositions args.H (1,1) double {mustBeNumeric, mustBePositive} = 350e-3 args.MO_B (1,1) double {mustBeNumeric} = 270e-3 @@ -32,8 +32,8 @@ arguments % inverseKinematics args.AP (3,1) double {mustBeNumeric} = zeros(3,1) args.ARB (3,3) double {mustBeNumeric} = eye(3) - % Equilibrium position of each leg - args.dLeq (6,1) double {mustBeNumeric} = zeros(6,1) + % Force that stiffness of each joint should apply at t=0 + args.Foffset logical {mustBeNumericOrLogical} = true end micro_hexapod = initializeFramesPositions('H', args.H, 'MO_B', args.MO_B); @@ -47,7 +47,12 @@ micro_hexapod = computeJacobian(micro_hexapod); micro_hexapod.Li = Li; micro_hexapod.dLi = dLi; -micro_hexapod.dLeq = args.dLeq; +if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init') + load('mat/Foffset.mat', 'Fhm'); + micro_hexapod.dLeq = -Fhm'./args.Ki; +else + micro_hexapod.dLeq = zeros(6,1); +end switch args.type case 'none' @@ -58,6 +63,8 @@ switch args.type micro_hexapod.type = 2; case 'modal-analysis' micro_hexapod.type = 3; + case 'init' + micro_hexapod.type = 4; end save('./mat/stages.mat', 'micro_hexapod', '-append'); diff --git a/src/initializeMirror.m b/src/initializeMirror.m index 5c3ae2c..3ff845c 100644 --- a/src/initializeMirror.m +++ b/src/initializeMirror.m @@ -15,23 +15,23 @@ switch args.type mirror.type = 1; end -mirror.h = 50; % Height of the mirror [mm] +mirror.h = 0.05; % Height of the mirror [m] -mirror.thickness = 25; % Thickness of the plate supporting the sample [mm] +mirror.thickness = 0.025; % Thickness of the plate supporting the sample [m] -mirror.hole_rad = 120; % radius of the hole in the mirror [mm] +mirror.hole_rad = 0.120; % radius of the hole in the mirror [m] -mirror.support_rad = 100; % radius of the support plate [mm] +mirror.support_rad = 0.1; % radius of the support plate [m] -% point of interest offset in z (above the top surfave) [mm] +% point of interest offset in z (above the top surfave) [m] switch args.type case 'none' - mirror.jacobian = 200; + mirror.jacobian = 0.20; case 'rigid' - mirror.jacobian = 200 - mirror.h; + mirror.jacobian = 0.20 - mirror.h; end -mirror.rad = 180; % radius of the mirror (at the bottom surface) [mm] +mirror.rad = 0.180; % radius of the mirror (at the bottom surface) [m] mirror.density = 2400; % Density of the material [kg/m3] diff --git a/src/initializePosError.m b/src/initializePosError.m new file mode 100644 index 0000000..b0b12ec --- /dev/null +++ b/src/initializePosError.m @@ -0,0 +1,28 @@ +function [] = initializePosError(args) +% initializePosError - Initialize the position errors +% +% Syntax: [] = initializePosError(args) +% +% Inputs: +% - args - + +arguments + args.error logical {mustBeNumericOrLogical} = false + args.Dy (1,1) double {mustBeNumeric} = 0 % [m] + args.Ry (1,1) double {mustBeNumeric} = 0 % [m] + args.Rz (1,1) double {mustBeNumeric} = 0 % [m] +end + +pos_error = struct(); + +if args.error + pos_error.type = 1; +else + pos_error.type = 0; +end + +pos_error.Dy = args.Dy; +pos_error.Ry = args.Ry; +pos_error.Rz = args.Rz; + +save('mat/pos_error.mat', 'pos_error'); diff --git a/src/initializeReferences.m b/src/initializeReferences.m index efc9e30..ea313e4 100644 --- a/src/initializeReferences.m +++ b/src/initializeReferences.m @@ -186,12 +186,34 @@ Dn = zeros(length(t), 6); switch args.Dn_type case 'constant' Dn = [args.Dn_pos, args.Dn_pos]; + + load('mat/stages.mat', 'nano_hexapod'); + + AP = [args.Dn_pos(1) ; args.Dn_pos(2) ; args.Dn_pos(3)]; + + tx = args.Dn_pos(4); + ty = args.Dn_pos(5); + tz = args.Dn_pos(6); + + ARB = [cos(tz) -sin(tz) 0; + sin(tz) cos(tz) 0; + 0 0 1]*... + [ cos(ty) 0 sin(ty); + 0 1 0; + -sin(ty) 0 cos(ty)]*... + [1 0 0; + 0 cos(tx) -sin(tx); + 0 sin(tx) cos(tx)]; + + [~, Dnl] = inverseKinematics(nano_hexapod, 'AP', AP, 'ARB', ARB); + Dnl = [Dnl, Dnl]; otherwise warning('Dn_type is not set correctly'); end Dn = struct('time', t, 'signals', struct('values', Dn)); +Dnl = struct('time', t, 'signals', struct('values', Dnl)); %% Save - save('mat/nass_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'Rm', 'Dn', 'Ts'); + save('mat/nass_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'Rm', 'Dn', 'Dnl', 'Ts'); end diff --git a/src/initializeRy.m b/src/initializeRy.m index 8da87f1..34aa7e9 100644 --- a/src/initializeRy.m +++ b/src/initializeRy.m @@ -1,19 +1,9 @@ function [ry] = initializeRy(args) arguments - args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis'})} = 'flexible' - args.x11 (1,1) double {mustBeNumeric} = 0 % [m] - args.y11 (1,1) double {mustBeNumeric} = 0 % [m] - args.z11 (1,1) double {mustBeNumeric} = 0 % [m] - args.x12 (1,1) double {mustBeNumeric} = 0 % [m] - args.y12 (1,1) double {mustBeNumeric} = 0 % [m] - args.z12 (1,1) double {mustBeNumeric} = 0 % [m] - args.x21 (1,1) double {mustBeNumeric} = 0 % [m] - args.y21 (1,1) double {mustBeNumeric} = 0 % [m] - args.z21 (1,1) double {mustBeNumeric} = 0 % [m] - args.x22 (1,1) double {mustBeNumeric} = 0 % [m] - args.y22 (1,1) double {mustBeNumeric} = 0 % [m] - args.z22 (1,1) double {mustBeNumeric} = 0 % [m] + args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible' + args.Foffset logical {mustBeNumericOrLogical} = true + args.Ry_init (1,1) double {mustBeNumeric} = 0 end ry = struct(); @@ -27,6 +17,8 @@ switch args.type ry.type = 2; case 'modal-analysis' ry.type = 3; + case 'init' + ry.type = 4; end % Ry - Guide for the tilt stage @@ -45,29 +37,18 @@ ry.motor.STEP = './STEPS/ry/Tilt_Motor.STEP'; ry.stage.density = 7800; % [kg/m3] ry.stage.STEP = './STEPS/ry/Tilt_Stage.STEP'; -ry.k.tilt = 1e4; % Rotation stiffness around y [N*m/deg] -ry.k.h = 1e8; % Stiffness in the direction of the guidance [N/m] -ry.k.rad = 1e8; % Stiffness in the top direction [N/m] -ry.k.rrad = 1e8; % Stiffness in the side direction [N/m] - -ry.c.tilt = 2.8e2; -ry.c.h = 2.8e4; -ry.c.rad = 2.8e4; -ry.c.rrad = 2.8e4; - -ry.x0_11 = args.x11; -ry.y0_11 = args.y11; -ry.z0_11 = args.z11; -ry.x0_12 = args.x12; -ry.y0_12 = args.y12; -ry.z0_12 = args.z12; -ry.x0_21 = args.x21; -ry.y0_21 = args.y21; -ry.z0_21 = args.z21; -ry.x0_22 = args.x22; -ry.y0_22 = args.y22; -ry.z0_22 = args.z22; - ry.z_offset = 0.58178; % [m] +ry.Ry_init = args.Ry_init; % [rad] + +ry.K = [3.8e8; 4e8; 3.8e8; 1.2e8; 6e4; 1.2e8]; +ry.C = [1e5; 1e5; 1e5; 3e4; 1e3; 3e4]; + +if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init') + load('mat/Foffset.mat', 'Fym'); + ry.Deq = -Fym'./ry.K; +else + ry.Deq = zeros(6,1); +end + save('./mat/stages.mat', 'ry', '-append'); diff --git a/src/initializeRz.m b/src/initializeRz.m index 6b8922a..6e89a17 100644 --- a/src/initializeRz.m +++ b/src/initializeRz.m @@ -1,12 +1,8 @@ function [rz] = initializeRz(args) arguments - args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis'})} = 'flexible' - args.x0 (1,1) double {mustBeNumeric} = 0 % Equilibrium position of the Joint [m] - args.y0 (1,1) double {mustBeNumeric} = 0 % Equilibrium position of the Joint [m] - args.z0 (1,1) double {mustBeNumeric} = 0 % Equilibrium position of the Joint [m] - args.rx0 (1,1) double {mustBeNumeric} = 0 % Equilibrium position of the Joint [rad] - args.ry0 (1,1) double {mustBeNumeric} = 0 % Equilibrium position of the Joint [rad] + args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible' + args.Foffset logical {mustBeNumericOrLogical} = true end rz = struct(); @@ -20,6 +16,8 @@ switch args.type rz.type = 2; case 'modal-analysis' rz.type = 3; + case 'init' + rz.type = 4; end % Spindle - Slip Ring @@ -34,20 +32,14 @@ rz.rotor.STEP = './STEPS/rz/Spindle_Rotor.STEP'; rz.stator.density = 7800; % [kg/m3] rz.stator.STEP = './STEPS/rz/Spindle_Stator.STEP'; -rz.k.rot = 1e6; % TODO - Rotational Stiffness (Rz) [N*m/deg] -rz.k.tilt = 1e6; % Rotational Stiffness (Rx, Ry) [N*m/deg] -rz.k.ax = 2e9; % Axial Stiffness (Z) [N/m] -rz.k.rad = 7e8; % Radial Stiffness (X, Y) [N/m] +rz.K = [7e8; 7e8; 2e9; 1e7; 1e7; 1e7]; +rz.C = [4e4; 4e4; 7e4; 1e4; 1e4; 1e4]; -rz.c.rot = 1.6e3; -rz.c.tilt = 1.6e3; -rz.c.ax = 7.1e4; -rz.c.rad = 4.2e4; - -rz.x0 = args.x0; -rz.y0 = args.y0; -rz.z0 = args.z0; -rz.rx0 = args.rx0; -rz.ry0 = args.ry0; +if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init') + load('mat/Foffset.mat', 'Fzm'); + rz.Deq = -Fzm'./rz.K; +else + rz.Deq = zeros(6,1); +end save('./mat/stages.mat', 'rz', '-append'); diff --git a/src/initializeSample.m b/src/initializeSample.m index 6dd558a..e6ddb74 100644 --- a/src/initializeSample.m +++ b/src/initializeSample.m @@ -1,15 +1,13 @@ function [sample] = initializeSample(args) arguments - args.type char {mustBeMember(args.type,{'rigid', 'flexible', 'none'})} = 'flexible' - args.radius (1,1) double {mustBeNumeric, mustBePositive} = 0.1 % [m] - args.height (1,1) double {mustBeNumeric, mustBePositive} = 0.3 % [m] - args.mass (1,1) double {mustBeNumeric, mustBePositive} = 50 % [kg] - args.freq (1,1) double {mustBeNumeric, mustBePositive} = 100 % [Hz] - args.offset (1,1) double {mustBeNumeric} = 0 % [m] - args.x0 (1,1) double {mustBeNumeric} = 0 % [m] - args.y0 (1,1) double {mustBeNumeric} = 0 % [m] - args.z0 (1,1) double {mustBeNumeric} = 0 % [m] + args.type char {mustBeMember(args.type,{'rigid', 'flexible', 'none', 'init'})} = 'flexible' + args.radius (1,1) double {mustBeNumeric, mustBePositive} = 0.1 % [m] + args.height (1,1) double {mustBeNumeric, mustBePositive} = 0.3 % [m] + args.mass (1,1) double {mustBeNumeric, mustBePositive} = 50 % [kg] + args.freq (1,1) double {mustBeNumeric, mustBePositive} = 100 % [Hz] + args.offset (1,1) double {mustBeNumeric} = 0 % [m] + args.Foffset logical {mustBeNumericOrLogical} = true end sample = struct(); @@ -21,23 +19,23 @@ switch args.type sample.type = 1; case 'flexible' sample.type = 2; + case 'init' + sample.type = 3; end sample.radius = args.radius; % [m] sample.height = args.height; % [m] -sample.mass = args.mass; % [kg] +sample.mass = args.mass; % [kg] sample.offset = args.offset; % [m] -sample.k.x = sample.mass * (2*pi * args.freq)^2; % [N/m] -sample.k.y = sample.mass * (2*pi * args.freq)^2; % [N/m] -sample.k.z = sample.mass * (2*pi * args.freq)^2; % [N/m] +sample.K = ones(3,1) * sample.mass * (2*pi * args.freq)^2; % [N/m] +sample.C = 0.1 * sqrt(sample.K*sample.mass); % [N/(m/s)] -sample.c.x = 0.1*sqrt(sample.k.x*sample.mass); % [N/(m/s)] -sample.c.y = 0.1*sqrt(sample.k.y*sample.mass); % [N/(m/s)] -sample.c.z = 0.1*sqrt(sample.k.z*sample.mass); % [N/(m/s)] - -sample.x0 = args.x0; % [m] -sample.y0 = args.y0; % [m] -sample.z0 = args.z0; % [m] +if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init') + load('mat/Foffset.mat', 'Fsm'); + sample.Deq = -Fsm'./sample.K; +else + sample.Deq = zeros(3,1); +end save('./mat/stages.mat', 'sample', '-append'); diff --git a/src/initializeTy.m b/src/initializeTy.m index 8209837..5dd580f 100644 --- a/src/initializeTy.m +++ b/src/initializeTy.m @@ -1,15 +1,8 @@ function [ty] = initializeTy(args) arguments - args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis'})} = 'flexible' - args.x11 (1,1) double {mustBeNumeric} = 0 % [m] - args.z11 (1,1) double {mustBeNumeric} = 0 % [m] - args.x21 (1,1) double {mustBeNumeric} = 0 % [m] - args.z21 (1,1) double {mustBeNumeric} = 0 % [m] - args.x12 (1,1) double {mustBeNumeric} = 0 % [m] - args.z12 (1,1) double {mustBeNumeric} = 0 % [m] - args.x22 (1,1) double {mustBeNumeric} = 0 % [m] - args.z22 (1,1) double {mustBeNumeric} = 0 % [m] + args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible' + args.Foffset logical {mustBeNumericOrLogical} = true end ty = struct(); @@ -23,6 +16,8 @@ switch args.type ty.type = 2; case 'modal-analysis' ty.type = 3; + case 'init' + ty.type = 4; end % Ty Granite frame @@ -61,19 +56,14 @@ ty.stator.STEP = './STEPS/ty/Ty_Motor_Stator.STEP'; ty.rotor.density = 5400; % [kg/m3] ty.rotor.STEP = './STEPS/ty/Ty_Motor_Rotor.STEP'; -ty.k.ax = 5e8; % Axial Stiffness for each of the 4 guidance (y) [N/m] -ty.k.rad = 5e7; % Radial Stiffness for each of the 4 guidance (x-z) [N/m] +ty.K = [2e8; 1e8; 2e8; 6e7; 9e7; 6e7]; % [N/m, N*m/rad] +ty.C = [8e4; 5e4; 8e4; 2e4; 3e4; 2e4]; % [N/(m/s), N*m/(rad/s)] -ty.c.ax = 70710; % [N/(m/s)] -ty.c.rad = 22360; % [N/(m/s)] - -ty.x0_11 = args.x11; -ty.z0_11 = args.z11; -ty.x0_12 = args.x12; -ty.z0_12 = args.z12; -ty.x0_21 = args.x21; -ty.z0_21 = args.z21; -ty.x0_22 = args.x22; -ty.z0_22 = args.z22; +if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init') + load('mat/Foffset.mat', 'Ftym'); + ty.Deq = -Ftym'./ty.K; +else + ty.Deq = zeros(6,1); +end save('./mat/stages.mat', 'ty', '-append'); diff --git a/src/inverseKinematicsHexapod.m b/src/inverseKinematicsHexapod.m deleted file mode 100644 index d8b1a90..0000000 --- a/src/inverseKinematicsHexapod.m +++ /dev/null @@ -1,20 +0,0 @@ -function [L] = inverseKinematicsHexapod(hexapod, AP, ARB) -% inverseKinematicsHexapod - Compute the initial position of each leg to have the wanted Hexapod's position -% -% Syntax: inverseKinematicsHexapod(hexapod, AP, ARB) -% -% Inputs: -% - hexapod - Hexapod object containing the geometry of the hexapod -% - AP - Position vector of point OB expressed in frame {A} in [m] -% - ARB - Rotation Matrix expressed in frame {A} - - % Wanted Length of the hexapod's legs [m] - L = zeros(6, 1); - - for i = 1:length(L) - Bbi = hexapod.pos_top_tranform(i, :)' - 1e-3*[0 ; 0 ; hexapod.TP.thickness+hexapod.Leg.sphere.top+hexapod.SP.thickness.top+hexapod.jacobian]; % [m] - Aai = hexapod.pos_base(i, :)' + 1e-3*[0 ; 0 ; hexapod.BP.thickness+hexapod.Leg.sphere.bottom+hexapod.SP.thickness.bottom-hexapod.h-hexapod.jacobian]; % [m] - - L(i) = sqrt(AP'*AP + Bbi'*Bbi + Aai'*Aai - 2*AP'*Aai + 2*AP'*(ARB*Bbi) - 2*(ARB*Bbi)'*Aai); - end -end