From f0b424fb5c20fcbe7cb98bda478c95457882d06c Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Tue, 8 Oct 2019 11:13:38 +0200 Subject: [PATCH] Add links to all html pages --- active_damping/index.html | 264 +++++ active_damping/index.org | 2 +- analysis/index.html | 264 +++++ control/index.html | 264 +++++ control/index.org | 2 +- hac_lac/index.html | 264 +++++ hac_lac/index.org | 2 +- identification/index.html | 329 ++++++ index.html | 2246 +------------------------------------ index.org | 7 +- kinematics/index.html | 271 +++++ kinematics/index.org | 2 +- 12 files changed, 1672 insertions(+), 2245 deletions(-) create mode 100644 active_damping/index.html create mode 100644 analysis/index.html create mode 100644 control/index.html create mode 100644 hac_lac/index.html create mode 100644 identification/index.html create mode 100644 kinematics/index.html diff --git a/active_damping/index.html b/active_damping/index.html new file mode 100644 index 0000000..286ecb9 --- /dev/null +++ b/active_damping/index.html @@ -0,0 +1,264 @@ + + + + + + + +Active Damping + + + + + + + + + + + + + +
+ UP + | + HOME +
+

Active Damping

+
+
+

Author: Dehaeze Thomas

+

Created: 2019-10-08 mar. 11:13

+

Validate

+
+ + diff --git a/active_damping/index.org b/active_damping/index.org index d1b042c..15e2fdd 100644 --- a/active_damping/index.org +++ b/active_damping/index.org @@ -1,4 +1,4 @@ -#+TITLE: +#+TITLE: Active Damping :DRAWER: #+STARTUP: overview diff --git a/analysis/index.html b/analysis/index.html new file mode 100644 index 0000000..1010839 --- /dev/null +++ b/analysis/index.html @@ -0,0 +1,264 @@ + + + + + + + +Some analysis + + + + + + + + + + + + + +
+ UP + | + HOME +
+

Some analysis

+
+
+

Author: Dehaeze Thomas

+

Created: 2019-10-08 mar. 11:13

+

Validate

+
+ + diff --git a/control/index.html b/control/index.html new file mode 100644 index 0000000..1301dd2 --- /dev/null +++ b/control/index.html @@ -0,0 +1,264 @@ + + + + + + + +Control of the NASS + + + + + + + + + + + + + +
+ UP + | + HOME +
+

Control of the NASS

+
+
+

Author: Dehaeze Thomas

+

Created: 2019-10-08 mar. 11:13

+

Validate

+
+ + diff --git a/control/index.org b/control/index.org index d1b042c..fb9f4f4 100644 --- a/control/index.org +++ b/control/index.org @@ -1,4 +1,4 @@ -#+TITLE: +#+TITLE: Control of the NASS :DRAWER: #+STARTUP: overview diff --git a/hac_lac/index.html b/hac_lac/index.html new file mode 100644 index 0000000..42a78c0 --- /dev/null +++ b/hac_lac/index.html @@ -0,0 +1,264 @@ + + + + + + + +HAC-LAC + + + + + + + + + + + + + +
+ UP + | + HOME +
+

HAC-LAC

+
+
+

Author: Dehaeze Thomas

+

Created: 2019-10-08 mar. 11:13

+

Validate

+
+ + diff --git a/hac_lac/index.org b/hac_lac/index.org index d1b042c..13a3733 100644 --- a/hac_lac/index.org +++ b/hac_lac/index.org @@ -1,4 +1,4 @@ -#+TITLE: +#+TITLE: HAC-LAC :DRAWER: #+STARTUP: overview diff --git a/identification/index.html b/identification/index.html new file mode 100644 index 0000000..7652f1f --- /dev/null +++ b/identification/index.html @@ -0,0 +1,329 @@ + + + + + + + +Identification + + + + + + + + + + + + + +
+ UP + | + HOME +
+

Identification

+ + +

+The goal here is to make an identification of the micro-station in order to compare the model with the measurements on the real micro-station. +

+ +

+In order to do so: +

+ + +

+For the excitation, we can choose the same excitation points as the one used for the modal test. +For the measurement points, we can choose the Center of Mass of each solid body. +The center of mass of each solid body is not easily defined using Simscape. +Indeed, we can define the center of mass of any solid body but not of multiple solid bodies. However, one solid body is composed of multiple STEP files. +One solution could be to use one STEP file for one solid body. +However, the position of the center of mass can be exported using simulink and then defined on Simscape. +

+ +
+

+All the files (data and Matlab scripts) are accessible here. +

+ +
+ +
+

1 Identification of the micro-station

+
+
+
simulinkproject('../');
+
+
+ +
+
open sim_micro_station_id.slx
+
+
+
+
+ +
+

2 Plot the obtained transfer functions

+
+
+

3 Compare with the modal measurements

+
+
+

4 Modal Identification of the micro station

+
+
+
+

Author: Dehaeze Thomas

+

Created: 2019-10-08 mar. 11:13

+

Validate

+
+ + diff --git a/index.html b/index.html index f9f30cc..0a7075f 100644 --- a/index.html +++ b/index.html @@ -3,12 +3,12 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + -Simscape Model of the Nano-Active-Stabilization-System +‎ - + - - - - - - - -
- UP - | - HOME -
-

Simscape Model of the Nano-Active-Stabilization-System

- - - - -
-

1 Simulink project

-
-

-The project can be opened using the simulinkproject function: -

- -
-
simulinkproject('./');
-
-
- -

-When the project opens, a startup script is ran. -The startup script is defined below and is exported to the project_startup.m script. -

-
-
%%
-freqs = logspace(-1, 3, 1000);
-save_fig = false;
-save('./mat/config.mat', 'freqs', 'save_fig');
-
-%%
-project = simulinkproject;
-projectRoot = project.RootFolder;
-
-myCacheFolder = fullfile(projectRoot, '.SimulinkCache');
-myCodeFolder = fullfile(projectRoot, '.SimulinkCode');
-
-Simulink.fileGenControl('set',...
-    'CacheFolder', myCacheFolder,...
-    'CodeGenFolder', myCodeFolder,...
-    'createDir', true);
-
-
- -

-When the project closes, it runs the project_shutdown.m script defined below. -

-
-
Simulink.fileGenControl('reset');
-
-
- -

-The project also permits to automatically add defined folder to the path when the project is opened. -

-
-
- -
-

2 Notes

-
-

-Step files are exported from SolidWorks and imported into Simscape. -Each step file is then considered as a solid body. -Inertia and mass matrices are computed from the density of the material and the geometry as defined by the step file. -

-
- -
-

2.1 Simscape files for identification

-
- - - --- -- -- -- -- -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Simscape NameTyRyRzHexaNASS
id micro stationFFFF 
id nano station stagesFFFFF
id nano station configDDDDF
control nano stationDDDDF
-
-
- -
-

2.2 Inputs

-
-
-
-

2.2.1 Perturbations

-
- - - --- -- -- -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
VariableMeaningSizeUnit
DwGround motion3[m]
FgExternal force applied on granite3[N]
FsExternal force applied on the Sample3[N]
-
-
- -
-

2.2.2 Measurement Noise

-
- - - --- -- -- -- - - - - - - - - - - - - - - - - -
VariableMeaningSizeUnit
    
-
-
- -
-

2.2.3 Control Inputs

-
- - - --- -- -- -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
VariableMeaningSizeUnit
FyActuation force for Ty1[N]
DyImposed displacement for Ty1[m]
MyActuation torque for Ry1[N.m]
RyImposed rotation for Ry1[rad]
MzActuation torque for Rz1[N.m]
RzImposed rotation for Rz1[rad]
FhActuation force/torque for hexapod (cart)6[N, N.m]
FhlActuation force/torque for hexapod (legs)6[N]
DhImposed position for hexapod (cart)6[m, rad]
RmPosition of the two masses2[rad]
FnActuation force for the NASS (cart)6[N, N.m]
FnlActuation force for the NASS's legs6[N]
DnImposed position for the NASS (cart)6[m, rad]
-
-
-
- -
-

2.3 Outputs

-
- - - --- -- -- -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
VariableMeaningSizeUnit
DgmAbsolute displacement of the granite3[m]
VgmAbsolute Velocity of the granite3[m/s]
DymMeasured displacement of Ty1[m]
RymMeasured rotation of Ry1[rad]
RzmMeasured rotation of Rz1[rad]
DhmMeasured position of hexapod (cart)6[m, rad]
FnlmMeasured force of NASS's legs6[N]
DnlmMeasured elongation of NASS's legs6[m]
DnmMeasured position of NASS w.r.t NASS's base6[m, rad]
VnmMeasured absolute velocity of NASS platform6[m/s, rad/s]
VnlmMeasured absolute velocity of NASS's legs6[m/s]
DsmPosition of Sample w.r.t. granite frame6[m, rad]
-
-
-
- -
-

3 Simulink files

-
-

-Few different Simulink files are used: -

-
    -
  • kinematics
    • -
  • identification - micro station
    • -
  • identification - nano station
    • -
  • control
    • -
-
-
- -
-

4 Simulink Library

-
-

-A simulink library is developed in order to share elements between the different simulink files. -

-
- -
-

4.1 inputs

-
- -
-

4.2 nasslibrary

-
- -
-

4.3 poserrorwrtnassbase

-
- -
-

4.4 QuaternionToAngles

-
- -
-

4.5 RotationMatrixToAngle

-
-
- -
-

5 Scripts

-
-
-
-

5.1 Simulation Initialization

-
-

- -

- -

-This Matlab script is accessible here. -

- -

-This script runs just before the simulation is started. -It is used to load the simulation configuration and the controllers used for the simulation. -

- -
-
%% Load all the data used for the simulation
-load('./mat/sim_conf.mat');
-
-%% Load Controller
-load('./mat/controllers.mat');
-
-
-
-
-
- -
-

6 Functions

-
-
-
-

6.1 computePsdDispl

-
-

- -

- -

-This Matlab function is accessible here. -

- -
-
function [psd_object] = computePsdDispl(sys_data, t_init, n_av)
-    i_init = find(sys_data.time > t_init, 1);
-
-    han_win = hanning(ceil(length(sys_data.Dx(i_init:end, :))/n_av));
-    Fs = 1/sys_data.time(2);
-
-    [pdx, f] = pwelch(sys_data.Dx(i_init:end, :), han_win, [], [], Fs);
-    [pdy, ~] = pwelch(sys_data.Dy(i_init:end, :), han_win, [], [], Fs);
-    [pdz, ~] = pwelch(sys_data.Dz(i_init:end, :), han_win, [], [], Fs);
-
-    [prx, ~] = pwelch(sys_data.Rx(i_init:end, :), han_win, [], [], Fs);
-    [pry, ~] = pwelch(sys_data.Ry(i_init:end, :), han_win, [], [], Fs);
-    [prz, ~] = pwelch(sys_data.Rz(i_init:end, :), han_win, [], [], Fs);
-
-    psd_object = struct(...
-        'f',  f,   ...
-        'dx', pdx, ...
-        'dy', pdy, ...
-        'dz', pdz, ...
-        'rx', prx, ...
-        'ry', pry, ...
-        'rz', prz);
-end
-
-
-
-
-
-

6.2 computeSetpoint

-
-

- -

- -

-This Matlab function is accessible here. -

- -
-
function setpoint = computeSetpoint(ty, ry, rz)
-%%
-setpoint = zeros(6, 1);
-
-%% Ty
-Ty = [1 0 0 0  ;
-      0 1 0 ty ;
-      0 0 1 0  ;
-      0 0 0 1 ];
-
-% Tyinv = [1 0 0  0  ;
-%          0 1 0 -ty ;
-%          0 0 1  0  ;
-%          0 0 0  1 ];
-
-%% Ry
-Ry = [ cos(ry) 0 sin(ry) 0 ;
-      0       1 0       0 ;
-      -sin(ry) 0 cos(ry) 0 ;
-      0        0 0       1 ];
-
-% TMry = Ty*Ry*Tyinv;
-
-%% Rz
-Rz = [cos(rz) -sin(rz) 0 0 ;
-      sin(rz)  cos(rz) 0 0 ;
-      0        0       1 0 ;
-      0        0       0 1 ];
-
-% TMrz = Ty*TMry*Rz*TMry'*Tyinv;
-
-%% All stages
-% TM = TMrz*TMry*Ty;
-
-TM = Ty*Ry*Rz;
-
-[thetax, thetay, thetaz] = RM2angle(TM(1:3, 1:3));
-
-setpoint(1:3) = TM(1:3, 4);
-setpoint(4:6) = [thetax, thetay, thetaz];
-
-%% Custom Functions
-function [thetax, thetay, thetaz] = RM2angle(R)
-    if abs(abs(R(3, 1)) - 1) > 1e-6 % R31 != 1 and R31 != -1
-        thetay = -asin(R(3, 1));
-        thetax = atan2(R(3, 2)/cos(thetay), R(3, 3)/cos(thetay));
-        thetaz = atan2(R(2, 1)/cos(thetay), R(1, 1)/cos(thetay));
-    else
-        thetaz = 0;
-        if abs(R(3, 1)+1) < 1e-6 % R31 = -1
-            thetay = pi/2;
-            thetax = thetaz + atan2(R(1, 2), R(1, 3));
-        else
-            thetay = -pi/2;
-            thetax = -thetaz + atan2(-R(1, 2), -R(1, 3));
-        end
-    end
-end
-end
-
-
-
-
-
-

6.3 converErrorBasis

-
-

- -

- -

-This Matlab function is accessible here. -

- -
-
function error_nass = convertErrorBasis(pos, setpoint, ty, ry, rz)
-% convertErrorBasis -
-%
-% Syntax: convertErrorBasis(p_error, ty, ry, rz)
-%
-% Inputs:
-%    - p_error - Position error of the sample w.r.t. the granite [m, rad]
-%    - ty - Measured translation of the Ty stage [m]
-%    - ry - Measured rotation of the Ry stage [rad]
-%    - rz - Measured rotation of the Rz stage [rad]
-%
-% Outputs:
-%    - P_nass - Position error of the sample w.r.t. the NASS base [m]
-%    - R_nass - Rotation error of the sample w.r.t. the NASS base [rad]
-%
-% Example:
-%
-
-%% If line vector => column vector
-if size(pos, 2) == 6
-    pos = pos';
-end
-
-if size(setpoint, 2) == 6
-    setpoint = setpoint';
-end
-
-%% Position of the sample in the frame fixed to the Granite
-P_granite = [pos(1:3); 1]; % Position [m]
-R_granite = [setpoint(1:3); 1]; % Reference [m]
-
-%% Transformation matrices of the stages
-% T-y
-TMty = [1 0 0 0  ;
-        0 1 0 ty ;
-        0 0 1 0  ;
-        0 0 0 1 ];
-
-% R-y
-TMry = [ cos(ry) 0 sin(ry) 0 ;
-        0       1 0       0 ;
-        -sin(ry) 0 cos(ry) 0 ;
-        0        0 0       1 ];
-
-% R-z
-TMrz = [cos(rz) -sin(rz) 0 0 ;
-        sin(rz)  cos(rz) 0 0 ;
-        0        0       1 0 ;
-        0        0       0 1 ];
-
-%% Compute Point coordinates in the new reference fixed to the NASS base
-% P_nass = TMrz*TMry*TMty*P_granite;
-P_nass = TMrz\TMry\TMty\P_granite;
-R_nass = TMrz\TMry\TMty\R_granite;
-
-dx = R_nass(1)-P_nass(1);
-dy = R_nass(2)-P_nass(2);
-dz = R_nass(3)-P_nass(3);
-
-%% Compute new basis vectors linked to the NASS base
-% ux_nass = TMrz*TMry*TMty*[1; 0; 0; 0];
-% ux_nass = ux_nass(1:3);
-% uy_nass = TMrz*TMry*TMty*[0; 1; 0; 0];
-% uy_nass = uy_nass(1:3);
-% uz_nass = TMrz*TMry*TMty*[0; 0; 1; 0];
-% uz_nass = uz_nass(1:3);
-
-ux_nass = TMrz\TMry\TMty\[1; 0; 0; 0];
-ux_nass = ux_nass(1:3);
-uy_nass = TMrz\TMry\TMty\[0; 1; 0; 0];
-uy_nass = uy_nass(1:3);
-uz_nass = TMrz\TMry\TMty\[0; 0; 1; 0];
-uz_nass = uz_nass(1:3);
-
-%% Rotations error w.r.t. granite Frame
-% Rotations error w.r.t. granite Frame
-rx_nass = pos(4);
-ry_nass = pos(5);
-rz_nass = pos(6);
-
-% Rotation matrices of the Sample w.r.t. the Granite
-Mrx_error = [1 0              0 ;
-            0 cos(-rx_nass) -sin(-rx_nass) ;
-            0 sin(-rx_nass)  cos(-rx_nass)];
-
-Mry_error = [ cos(-ry_nass) 0 sin(-ry_nass) ;
-              0             1 0 ;
-            -sin(-ry_nass) 0 cos(-ry_nass)];
-
-Mrz_error = [cos(-rz_nass) -sin(-rz_nass) 0 ;
-            sin(-rz_nass)  cos(-rz_nass) 0 ;
-            0              0             1];
-
-% Rotation matrix of the Sample w.r.t. the Granite
-Mr_error = Mrz_error*Mry_error*Mrx_error;
-
-%% Use matrix to solve
-R = Mr_error/[ux_nass, uy_nass, uz_nass]; % Rotation matrix from NASS base to Sample
-
-[thetax, thetay, thetaz] = RM2angle(R);
-
-error_nass = [dx; dy; dz; thetax; thetay; thetaz];
-
-%% Custom Functions
-function [thetax, thetay, thetaz] = RM2angle(R)
-    if abs(abs(R(3, 1)) - 1) > 1e-6 % R31 != 1 and R31 != -1
-        thetay = -asin(R(3, 1));
-        % thetaybis = pi-thetay;
-        thetax = atan2(R(3, 2)/cos(thetay), R(3, 3)/cos(thetay));
-        % thetaxbis = atan2(R(3, 2)/cos(thetaybis), R(3, 3)/cos(thetaybis));
-        thetaz = atan2(R(2, 1)/cos(thetay), R(1, 1)/cos(thetay));
-        % thetazbis = atan2(R(2, 1)/cos(thetaybis), R(1, 1)/cos(thetaybis));
-    else
-        thetaz = 0;
-        if abs(R(3, 1)+1) < 1e-6 % R31 = -1
-            thetay = pi/2;
-            thetax = thetaz + atan2(R(1, 2), R(1, 3));
-        else
-            thetay = -pi/2;
-            thetax = -thetaz + atan2(-R(1, 2), -R(1, 3));
-        end
-    end
-end
-
-end
-
-
-
-
-
-

6.4 generateDiagPidControl

-
-

- -

- -

-This Matlab function is accessible here. -

- -
-
function [K] = generateDiagPidControl(G, fs)
-    %%
-    pid_opts = pidtuneOptions(...
-        'PhaseMargin', 50, ...
-        'DesignFocus', 'disturbance-rejection');
-
-    %%
-    K = tf(zeros(6));
-
-    for i = 1:6
-        input_name = G.InputName(i);
-        output_name = G.OutputName(i);
-        K(i, i) = tf(pidtune(minreal(G(output_name, input_name)), 'PIDF', 2*pi*fs, pid_opts));
-    end
-
-    K.InputName = G.OutputName;
-    K.OutputName = G.InputName;
-end
-
-
-
-
-
-

6.5 identifyPlant

-
-

- -

- -

-This Matlab function is accessible here. -

- -
-
function [sys] = identifyPlant(opts_param)
-    %% Default values for opts
-    opts = struct();
-
-    %% Populate opts with input parameters
-    if exist('opts_param','var')
-        for opt = fieldnames(opts_param)'
-            opts.(opt{1}) = opts_param.(opt{1});
-        end
-    end
-
-    %% Options for Linearized
-    options = linearizeOptions;
-    options.SampleTime = 0;
-
-    %% Name of the Simulink File
-    mdl = 'sim_nano_station_id';
-
-    %% Input/Output definition
-    io(1) = linio([mdl, '/Fn'],   1, 'input'); % Cartesian forces applied by NASS
-    io(2) = linio([mdl, '/Dw'],   1, 'input'); % Ground Motion
-    io(3) = linio([mdl, '/Fs'],   1, 'input'); % External forces on the sample
-    io(4) = linio([mdl, '/Fnl'],  1, 'input'); % Forces applied on the NASS's legs
-    io(5) = linio([mdl, '/Dsm'],  1, 'output'); % Displacement of the sample
-    io(6) = linio([mdl, '/Fnlm'], 1, 'output'); % Force sensor in NASS's legs
-    io(7) = linio([mdl, '/Dnlm'], 1, 'output'); % Displacement of NASS's legs
-    io(8) = linio([mdl, '/Es'],   1, 'output'); % Position Error w.r.t. NASS base
-
-    %% Run the linearization
-    G = linearize(mdl, io, 0);
-    G.InputName  = {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz', ...
-                    'Dgx', 'Dgy', 'Dgz', ...
-                    'Fsx', 'Fsy', 'Fsz', 'Msx', 'Msy', 'Msz', ...
-                    'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
-    G.OutputName = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz', ...
-                    'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6', ...
-                    'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6', ...
-                    'Edx', 'Rdy', 'Edz', 'Erx', 'Ery', 'Erz'};
-
-    %% Create the sub transfer functions
-    % From forces applied in the cartesian frame to displacement of the sample in the cartesian frame
-    sys.G_cart = minreal(G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'}));
-    % From ground motion to Sample displacement
-    sys.G_gm   = minreal(G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'Dgx', 'Dgy', 'Dgz'}));
-    % From direct forces applied on the sample to displacement of the sample
-    sys.G_fs   = minreal(G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'Fsx', 'Fsy', 'Fsz', 'Msx', 'Msy', 'Msz'}));
-    % From forces applied on NASS's legs to force sensor in each leg
-    sys.G_iff  = minreal(G({'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}));
-    % From forces applied on NASS's legs to displacement of each leg
-    sys.G_dleg = minreal(G({'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}));
-    % From forces applied on NASS's legs to displacement of each leg
-    sys.G_plant = minreal(G({'Edx', 'Rdy', 'Edz', 'Erx', 'Ery', 'Erz'}, {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'}));
-end
-
-
-
-
-
-

6.6 runSimulation

-
-

- -

- -

-This Matlab function is accessible here. -

- -
-
function [] = runSimulation(sys_name, sys_mass, ctrl_type, act_damp)
-    %% Load the controller and save it for the simulation
-    if strcmp(ctrl_type, 'cl') && strcmp(act_damp, 'none')
-      K_obj = load('./mat/K_fb.mat');
-      K = K_obj.(sprintf('K_%s_%s', sys_mass, sys_name)); %#ok
-      save('./mat/controllers.mat', 'K');
-    elseif strcmp(ctrl_type, 'cl') && strcmp(act_damp, 'iff')
-      K_obj = load('./mat/K_fb_iff.mat');
-      K = K_obj.(sprintf('K_%s_%s_iff', sys_mass, sys_name)); %#ok
-      save('./mat/controllers.mat', 'K');
-    elseif strcmp(ctrl_type, 'ol')
-      K = tf(zeros(6)); %#ok
-      save('./mat/controllers.mat', 'K');
-    else
-      error('ctrl_type should be cl or ol');
-    end
-
-    %% Active Damping
-    if strcmp(act_damp, 'iff')
-      K_iff_crit = load('./mat/K_iff_crit.mat');
-      K_iff = K_iff_crit.(sprintf('K_iff_%s_%s', sys_mass, sys_name)); %#ok
-      save('./mat/controllers.mat', 'K_iff', '-append');
-    elseif strcmp(act_damp, 'none')
-      K_iff = tf(zeros(6)); %#ok
-      save('./mat/controllers.mat', 'K_iff', '-append');
-    end
-
-    %%
-    if strcmp(sys_name, 'pz')
-      initializeNanoHexapod(struct('actuator', 'piezo'));
-    elseif strcmp(sys_name, 'vc')
-      initializeNanoHexapod(struct('actuator', 'lorentz'));
-    else
-      error('sys_name should be pz or vc');
-    end
-
-    if strcmp(sys_mass, 'light')
-      initializeSample(struct('mass', 1));
-    elseif strcmp(sys_mass, 'heavy')
-      initializeSample(struct('mass', 50));
-    else
-      error('sys_mass should be light or heavy');
-    end
-
-    %% Run the simulation
-    sim('sim_nano_station_ctrl.slx');
-
-    %% Split the Dsample matrix into vectors
-    [Dx, Dy, Dz, Rx, Ry, Rz] = matSplit(Es.Data, 1); %#ok
-    time = Dsample.Time; %#ok
-
-    %% Save the result
-    filename = sprintf('sim_%s_%s_%s_%s', sys_mass, sys_name, ctrl_type, act_damp);
-    save(sprintf('./mat/%s.mat', filename), ...
-        'time', 'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz', 'K');
-end
-
-
-
-
-
-
-

7 Initialize Elements

-
-
-
-

7.1 Simulation Configuration

-
-

- -

- -

-This Matlab function is accessible here. -

- -
-
function [] = initializeSimConf(opts_param)
-    %% Default values for opts
-    opts = struct('Ts',      1e-4,  ... % Sampling time [s]
-                  'Tsim',    10,    ... % Simulation time [s]
-                  'cl_time', 0,     ... % Close Loop time [s]
-                  'gravity', false  ... % Gravity along the z axis
-    );
-
-    %% Populate opts with input parameters
-    if exist('opts_param','var')
-        for opt = fieldnames(opts_param)'
-            opts.(opt{1}) = opts_param.(opt{1});
-        end
-    end
-
-    %%
-    sim_conf = struct();
-
-    %%
-    sim_conf.Ts = opts.Ts;
-    sim_conf.Tsim = opts.Tsim;
-    sim_conf.cl_time = opts.cl_time;
-
-    %% Gravity
-    if opts.gravity
-        sim_conf.g = -9.8; %#ok
-    else
-        sim_conf.g = 0; %#ok
-    end
-
-    %% Save
-    save('./mat/sim_conf.mat', 'sim_conf');
-end
-
-
-
-
- -
-

7.2 Experiment

-
-

- -

- -

-This Matlab function is accessible here. -

- -
-
function [] = initializeExperiment(exp_name, sys_mass)
-    if strcmp(exp_name, 'tomography')
-        opts_sim = struct(...
-            'Tsim',    5, ...
-            'cl_time', 5  ...
-        );
-        initializeSimConf(opts_sim);
-
-        if strcmp(sys_mass, 'light')
-            opts_inputs = struct(...
-                'Dw', true,  ...
-                'Rz', 60     ... % rpm
-            );
-        elseif strcpm(sys_mass, 'heavy')
-            opts_inputs = struct(...
-                'Dw', true,  ...
-                'Rz', 1     ... % rpm
-            );
-        else
-            error('sys_mass should be light or heavy');
-        end
-
-        initializeInputs(opts_inputs);
-    else
-        error('exp_name is only configured for tomography');
-    end
-end
-
-
-
-
- -
-

7.3 Inputs

-
-

- -

- -

-This Matlab function is accessible here. -

- -
-
function [inputs] = initializeInputs(opts_param)
-    %% Default values for opts
-    opts = struct(   ...
-        'Dw', false, ...
-        'Dy', false, ...
-        'Ry', false, ...
-        'Rz', false, ...
-        'Dh', false, ...
-        'Rm', false, ...
-        'Dn', false  ...
-    );
-
-    %% Populate opts with input parameters
-    if exist('opts_param','var')
-        for opt = fieldnames(opts_param)'
-            opts.(opt{1}) = opts_param.(opt{1});
-        end
-    end
-
-    %% Load Sampling Time and Simulation Time
-    load('./mat/sim_conf.mat', 'sim_conf');
-
-    %% Define the time vector
-    t = 0:sim_conf.Ts:sim_conf.Tsim;
-
-    %% Ground motion - Dw
-    if islogical(opts.Dw) && opts.Dw == true
-        load('./mat/perturbations.mat', 'Wxg');
-        Dw = 1/sqrt(2)*100*random('norm', 0, 1, length(t), 3);
-        Dw(:, 1) = lsim(Wxg, Dw(:, 1), t);
-        Dw(:, 2) = lsim(Wxg, Dw(:, 2), t);
-        Dw(:, 3) = lsim(Wxg, Dw(:, 3), t);
-    elseif islogical(opts.Dw) && opts.Dw == false
-        Dw = zeros(length(t), 3);
-    else
-        Dw = opts.Dw;
-    end
-
-    %% Translation stage - Dy
-    if islogical(opts.Dy) && opts.Dy == true
-        Dy = zeros(length(t), 1);
-    elseif islogical(opts.Dy) && opts.Dy == false
-        Dy = zeros(length(t), 1);
-    else
-        Dy = opts.Dy;
-    end
-
-    %% Tilt Stage - Ry
-    if islogical(opts.Ry) && opts.Ry == true
-        Ry = 3*(2*pi/360)*sin(2*pi*0.2*t);
-    elseif islogical(opts.Ry) && opts.Ry == false
-        Ry = zeros(length(t), 1);
-    elseif isnumeric(opts.Ry) && length(opts.Ry) == 1
-        Ry = opts.Ry*(2*pi/360)*ones(length(t), 1);
-    else
-        Ry = opts.Ry;
-    end
-
-    %% Spindle - Rz
-    if islogical(opts.Rz) && opts.Rz == true
-        Rz = 2*pi*0.5*t;
-    elseif islogical(opts.Rz) && opts.Rz == false
-        Rz = zeros(length(t), 1);
-    elseif isnumeric(opts.Rz) && length(opts.Rz) == 1
-        Rz = opts.Rz*(2*pi/60)*t;
-    else
-        Rz = opts.Rz;
-    end
-
-    %% Micro Hexapod - Dh
-    if islogical(opts.Dh) && opts.Dh == true
-        Dh = zeros(length(t), 6);
-    elseif islogical(opts.Dh) && opts.Dh == false
-        Dh = zeros(length(t), 6);
-    else
-        Dh = opts.Dh;
-    end
-
-    %% Axis Compensation - Rm
-    if islogical(opts.Rm)
-        Rm = zeros(length(t), 2);
-        Rm(:, 2) = pi*ones(length(t), 1);
-    else
-        Rm = opts.Rm;
-    end
-
-    %% Nano Hexapod - Dn
-    if islogical(opts.Dn) && opts.Dn == true
-        Dn = zeros(length(t), 6);
-    elseif islogical(opts.Dn) && opts.Dn == false
-        Dn = zeros(length(t), 6);
-    else
-        Dn = opts.Dn;
-    end
-
-    %% Setpoint - Ds
-    Ds = zeros(length(t), 6);
-    for i = 1:length(t)
-        Ds(i, :) = computeSetpoint(Dy(i), Ry(i), Rz(i));
-    end
-
-    %% External Forces applied on the Granite
-    Fg = zeros(length(t), 3);
-
-    %% External Forces applied on the Sample
-    Fs = zeros(length(t), 6);
-
-    %% Create the input Structure that will contain all the inputs
-    inputs = struct( ...
-        'Ts', sim_conf.Ts,       ...
-        'Dw', timeseries(Dw, t), ...
-        'Dy', timeseries(Dy, t), ...
-        'Ry', timeseries(Ry, t), ...
-        'Rz', timeseries(Rz, t), ...
-        'Dh', timeseries(Dh, t), ...
-        'Rm', timeseries(Rm, t), ...
-        'Dn', timeseries(Dn, t), ...
-        'Ds', timeseries(Ds, t), ...
-        'Fg', timeseries(Fg, t), ...
-        'Fs', timeseries(Fs, t)  ...
-    );
-
-    %% Save
-    save('./mat/inputs.mat', 'inputs');
-
-    %% Custom Functions
-    function setpoint = computeSetpoint(ty, ry, rz)
-    %%
-    setpoint = zeros(6, 1);
-
-    %% Ty
-    TMTy = [1 0 0 0  ;
-          0 1 0 ty ;
-          0 0 1 0  ;
-          0 0 0 1 ];
-
-    %% Ry
-    TMRy = [ cos(ry) 0 sin(ry) 0 ;
-          0       1 0       0 ;
-          -sin(ry) 0 cos(ry) 0 ;
-          0        0 0       1 ];
-
-    %% Rz
-    TMRz = [cos(rz) -sin(rz) 0 0 ;
-          sin(rz)  cos(rz) 0 0 ;
-          0        0       1 0 ;
-          0        0       0 1 ];
-
-    %% All stages
-    TM = TMTy*TMRy*TMRz;
-
-    [thetax, thetay, thetaz] = RM2angle(TM(1:3, 1:3));
-
-    setpoint(1:3) = TM(1:3, 4);
-    setpoint(4:6) = [thetax, thetay, thetaz];
-
-    %% Custom Functions
-    function [thetax, thetay, thetaz] = RM2angle(R)
-        if abs(abs(R(3, 1)) - 1) > 1e-6 % R31 != 1 and R31 != -1
-            thetay = -asin(R(3, 1));
-            thetax = atan2(R(3, 2)/cos(thetay), R(3, 3)/cos(thetay));
-            thetaz = atan2(R(2, 1)/cos(thetay), R(1, 1)/cos(thetay));
-        else
-            thetaz = 0;
-            if abs(R(3, 1)+1) < 1e-6 % R31 = -1
-                thetay = pi/2;
-                thetax = thetaz + atan2(R(1, 2), R(1, 3));
-            else
-                thetay = -pi/2;
-                thetax = -thetaz + atan2(-R(1, 2), -R(1, 3));
-            end
-        end
-    end
-    end
-end
-
-
-
-
- -
-

7.4 Ground

-
-

- -

- -

-This Matlab function is accessible here. -

- -
-
function [ground] = initializeGround()
-    %%
-    ground = struct();
-
-    ground.shape = [2, 2, 0.5]; % [m]
-    ground.density = 2800; % [kg/m3]
-    ground.color = [0.5, 0.5, 0.5];
-
-    %% Save
-    save('./mat/stages.mat', 'ground', '-append');
-end
-
-
-
-
- -
-

7.5 Granite

-
-

- -

- -

-This Matlab function is accessible here. -

- -
-
function [granite] = initializeGranite()
-    %%
-    granite = struct();
-
-    %% Static Properties
-    granite.density = 2800; % [kg/m3]
-    granite.volume  = 0.72; % [m3] TODO - should
-    granite.mass    = granite.density*granite.volume; % [kg]
-    granite.color   = [1 1 1];
-    granite.STEP    = './STEPS/granite/granite.STEP';
-
-    %% Dynamical Properties
-    granite.k.x = 1e8; % [N/m]
-    granite.c.x = 1e4; % [N/(m/s)]
-
-    granite.k.y = 1e8; % [N/m]
-    granite.c.y = 1e4; % [N/(m/s)]
-
-    granite.k.z = 1e8; % [N/m]
-    granite.c.z = 1e4; % [N/(m/s)]
-
-    %% Positioning parameters
-    granite.sample_pos = 0.8; % Z-offset for the initial position of the sample [m]
-
-    %% Save
-    save('./mat/stages.mat', 'granite', '-append');
-end
-
-
-
-
- -
-

7.6 Translation Stage

-
-

- -

- -

-This Matlab function is accessible here. -

- -
-
function [ty] = initializeTy(opts_param)
-    %% Default values for opts
-    opts = struct('rigid', false);
-
-    %% Populate opts with input parameters
-    if exist('opts_param','var')
-        for opt = fieldnames(opts_param)'
-            opts.(opt{1}) = opts_param.(opt{1});
-        end
-    end
-
-    %%
-    ty = struct();
-
-    %% Y-Translation - Static Properties
-    % Ty Granite frame
-    ty.granite_frame.density = 7800; % [kg/m3]
-    ty.granite_frame.color   = [0.753 1 0.753];
-    ty.granite_frame.STEP    = './STEPS/Ty/Ty_Granite_Frame.STEP';
-    % Guide Translation Ty
-    ty.guide.density         = 7800; % [kg/m3]
-    ty.guide.color           = [0.792 0.820 0.933];
-    ty.guide.STEP            = './STEPS/ty/Ty_Guide.STEP';
-    % Ty - Guide_Translation12
-    ty.guide12.density       = 7800; % [kg/m3]
-    ty.guide12.color         = [0.792 0.820 0.933];
-    ty.guide12.STEP          = './STEPS/Ty/Ty_Guide_12.STEP';
-    % Ty - Guide_Translation11
-    ty.guide11.density       = 7800; % [kg/m3]
-    ty.guide11.color         = [0.792 0.820 0.933];
-    ty.guide11.STEP          = './STEPS/ty/Ty_Guide_11.STEP';
-    % Ty - Guide_Translation22
-    ty.guide22.density       = 7800; % [kg/m3]
-    ty.guide22.color         = [0.792 0.820 0.933];
-    ty.guide22.STEP          = './STEPS/ty/Ty_Guide_22.STEP';
-    % Ty - Guide_Translation21
-    ty.guide21.density       = 7800; % [kg/m3]
-    ty.guide21.color         = [0.792 0.820 0.933];
-    ty.guide21.STEP          = './STEPS/Ty/Ty_Guide_21.STEP';
-    % Ty - Plateau translation
-    ty.frame.density         = 7800; % [kg/m3]
-    ty.frame.color           = [0.792 0.820 0.933];
-    ty.frame.STEP            = './STEPS/ty/Ty_Stage.STEP';
-    % Ty Stator Part
-    ty.stator.density        = 5400; % [kg/m3]
-    ty.stator.color          = [0.792 0.820 0.933];
-    ty.stator.STEP           = './STEPS/ty/Ty_Motor_Stator.STEP';
-    % Ty Rotor Part
-    ty.rotor.density         = 5400; % [kg/m3]
-    ty.rotor.color           = [0.792 0.820 0.933];
-    ty.rotor.STEP            = './STEPS/ty/Ty_Motor_Rotor.STEP';
-
-    ty.m = 250; % TODO [kg]
-
-    %% Y-Translation - Dynamicals Properties
-    if opts.rigid
-        ty.k.ax  = 1e10; % Axial Stiffness for each of the 4 guidance (y) [N/m]
-    else
-        ty.k.ax  = 1e7/4; % Axial Stiffness for each of the 4 guidance (y) [N/m]
-    end
-    ty.k.rad = 9e9/4; % Radial Stiffness for each of the 4 guidance (x-z) [N/m]
-
-    ty.c.ax  = 100*(1/5)*sqrt(ty.k.ax/ty.m);
-    ty.c.rad = 100*(1/5)*sqrt(ty.k.rad/ty.m);
-
-    %% Save
-    save('./mat/stages.mat', 'ty', '-append');
-end
-
-
-
-
- -
-

7.7 Tilt Stage

-
-

- -

- -

-This Matlab function is accessible here. -

- -
-
function [ry] = initializeRy(opts_param)
-    %% Default values for opts
-    opts = struct('rigid', false);
-
-    %% Populate opts with input parameters
-    if exist('opts_param','var')
-        for opt = fieldnames(opts_param)'
-            opts.(opt{1}) = opts_param.(opt{1});
-        end
-    end
-
-    %%
-    ry = struct();
-
-    %% Tilt Stage - Static Properties
-    % Ry - Guide for the tilt stage
-    ry.guide.density = 7800; % [kg/m3]
-    ry.guide.color   = [0.792 0.820 0.933];
-    ry.guide.STEP    = './STEPS/ry/Tilt_Guide.STEP';
-    % Ry - Rotor of the motor
-    ry.rotor.density = 2400; % [kg/m3]
-    ry.rotor.color   = [0.792 0.820 0.933];
-    ry.rotor.STEP    = './STEPS/ry/Tilt_Motor_Axis.STEP';
-    % Ry - Motor
-    ry.motor.density = 3200; % [kg/m3]
-    ry.motor.color   = [0.792 0.820 0.933];
-    ry.motor.STEP    = './STEPS/ry/Tilt_Motor.STEP';
-    % Ry - Plateau Tilt
-    ry.stage.density = 7800; % [kg/m3]
-    ry.stage.color   = [0.792 0.820 0.933];
-    ry.stage.STEP    = './STEPS/ry/Tilt_Stage.STEP';
-
-    ry.m = 200; % TODO [kg]
-
-    %% Tilt Stage - Dynamical Properties
-    if opts.rigid
-        ry.k.tilt = 1e10; % Rotation stiffness around y [N*m/deg]
-    else
-        ry.k.tilt = 1e4; % Rotation stiffness around y [N*m/deg]
-    end
-
-    ry.k.h    = 357e6/4; % Stiffness in the direction of the guidance [N/m]
-    ry.k.rad  = 555e6/4; % Stiffness in the top direction [N/m]
-    ry.k.rrad = 238e6/4; % Stiffness in the side direction [N/m]
-
-    ry.c.h    = 10*(1/5)*sqrt(ry.k.h/ry.m);
-    ry.c.rad  = 10*(1/5)*sqrt(ry.k.rad/ry.m);
-    ry.c.rrad = 10*(1/5)*sqrt(ry.k.rrad/ry.m);
-    ry.c.tilt = 10*(1/1)*sqrt(ry.k.tilt/ry.m);
-
-    %% Positioning parameters
-    ry.z_offset = 0.58178; % Z-Offset so that the center of rotation matches the sample center [m]
-
-    %% Save
-    save('./mat/stages.mat', 'ry', '-append');
-end
-
-
-
-
- -
-

7.8 Spindle

-
-

- -

- -

-This Matlab function is accessible here. -

- -
-
function [rz] = initializeRz(opts_param)
-    %% Default values for opts
-    opts = struct('rigid', false);
-
-    %% Populate opts with input parameters
-    if exist('opts_param','var')
-        for opt = fieldnames(opts_param)'
-            opts.(opt{1}) = opts_param.(opt{1});
-        end
-    end
-
-    %%
-    rz = struct();
-
-    %% Spindle - Static Properties
-    % Spindle - Slip Ring
-    rz.slipring.density = 7800; % [kg/m3]
-    rz.slipring.color   = [0.792 0.820 0.933];
-    rz.slipring.STEP    = './STEPS/rz/Spindle_Slip_Ring.STEP';
-    % Spindle - Rotor
-    rz.rotor.density    = 7800; % [kg/m3]
-    rz.rotor.color      = [0.792 0.820 0.933];
-    rz.rotor.STEP       = './STEPS/rz/Spindle_Rotor.STEP';
-    % Spindle - Stator
-    rz.stator.density   = 7800; % [kg/m3]
-    rz.stator.color     = [0.792 0.820 0.933];
-    rz.stator.STEP      = './STEPS/rz/Spindle_Stator.STEP';
-
-    % Estimated mass of the mooving part
-    rz.m = 250; % [kg]
-
-    %% Spindle - Dynamical Properties
-    % Estimated stiffnesses
-    rz.k.ax   = 2e9; % Axial Stiffness [N/m]
-    rz.k.rad  = 7e8; % Radial Stiffness [N/m]
-    rz.k.rot  = 100e6*2*pi/360; % Rotational Stiffness [N*m/deg]
-
-    if opts.rigid
-        rz.k.tilt = 1e10; % Vertical Rotational Stiffness [N*m/deg]
-    else
-        rz.k.tilt = 1e2; % TODO what value should I put? [N*m/deg]
-    end
-
-    % TODO
-    rz.c.ax   = 2*sqrt(rz.k.ax/rz.m);
-    rz.c.rad  = 2*sqrt(rz.k.rad/rz.m);
-    rz.c.tilt = 100*sqrt(rz.k.tilt/rz.m);
-    rz.c.rot  = 100*sqrt(rz.k.rot/rz.m);
-
-    %% Save
-    save('./mat/stages.mat', 'rz', '-append');
-end
-
-
-
-
- -
-

7.9 Micro Hexapod

-
-

- -

- -

-This Matlab function is accessible here. -

- -
-
function [micro_hexapod] = initializeMicroHexapod(opts_param)
-    %% Default values for opts
-    opts = struct();
-
-    %% Populate opts with input parameters
-    if exist('opts_param','var')
-        for opt = fieldnames(opts_param)'
-            opts.(opt{1}) = opts_param.(opt{1});
-        end
-    end
-
-    %% Stewart Object
-    micro_hexapod = struct();
-    micro_hexapod.h        = 350; % Total height of the platform [mm]
-%     micro_hexapod.jacobian = 269.26; % Distance from the top platform to the Jacobian point [mm]
-    micro_hexapod.jacobian = 270; % Distance from the top platform to the Jacobian point [mm]
-
-    %% Bottom Plate - Mechanical Design
-    BP = struct();
-
-    BP.rad.int   = 110;   % Internal Radius [mm]
-    BP.rad.ext   = 207.5; % External Radius [mm]
-    BP.thickness = 26;    % Thickness [mm]
-    BP.leg.rad   = 175.5; % Radius where the legs articulations are positionned [mm]
-    BP.leg.ang   = 9.5;   % Angle Offset [deg]
-    BP.density   = 8000;  % Density of the material [kg/m^3]
-    BP.color     = [0.6 0.6 0.6]; % Color [rgb]
-    BP.shape     = [BP.rad.int BP.thickness; BP.rad.int 0; BP.rad.ext 0; BP.rad.ext BP.thickness];
-
-    %% Top Plate - Mechanical Design
-    TP = struct();
-
-    TP.rad.int   = 82;   % Internal Radius [mm]
-    TP.rad.ext   = 150;  % Internal Radius [mm]
-    TP.thickness = 26;   % Thickness [mm]
-    TP.leg.rad   = 118;  % Radius where the legs articulations are positionned [mm]
-    TP.leg.ang   = 12.1; % Angle Offset [deg]
-    TP.density   = 8000; % Density of the material [kg/m^3]
-    TP.color     = [0.6 0.6 0.6]; % Color [rgb]
-    TP.shape     = [TP.rad.int TP.thickness; TP.rad.int 0; TP.rad.ext 0; TP.rad.ext TP.thickness];
-
-    %% Struts
-    Leg = struct();
-
-    Leg.stroke     = 10e-3; % Maximum Stroke of each leg [m]
-    Leg.k.ax       = 5e7;   % Stiffness of each leg [N/m]
-    Leg.ksi.ax     = 3;     % Maximum amplification at resonance []
-    Leg.rad.bottom = 25;    % Radius of the cylinder of the bottom part [mm]
-    Leg.rad.top    = 17;    % Radius of the cylinder of the top part [mm]
-    Leg.density    = 8000;  % Density of the material [kg/m^3]
-    Leg.color.bottom  = [0.5 0.5 0.5]; % Color [rgb]
-    Leg.color.top     = [0.5 0.5 0.5]; % Color [rgb]
-
-    Leg.sphere.bottom = Leg.rad.bottom; % Size of the sphere at the end of the leg [mm]
-    Leg.sphere.top    = Leg.rad.top; % Size of the sphere at the end of the leg [mm]
-    Leg.m             = TP.density*((pi*(TP.rad.ext/1000)^2)*(TP.thickness/1000)-(pi*(TP.rad.int/1000^2))*(TP.thickness/1000))/6; % TODO [kg]
-    Leg = updateDamping(Leg);
-
-
-    %% Sphere
-    SP = struct();
-
-    SP.height.bottom  = 27; % [mm]
-    SP.height.top     = 27; % [mm]
-    SP.density.bottom = 8000; % [kg/m^3]
-    SP.density.top    = 8000; % [kg/m^3]
-    SP.color.bottom   = [0.6 0.6 0.6]; % [rgb]
-    SP.color.top      = [0.6 0.6 0.6]; % [rgb]
-    SP.k.ax           = 0; % [N*m/deg]
-    SP.ksi.ax         = 10;
-
-    SP.thickness.bottom = SP.height.bottom-Leg.sphere.bottom; % [mm]
-    SP.thickness.top    = SP.height.top-Leg.sphere.top; % [mm]
-    SP.rad.bottom       = Leg.sphere.bottom; % [mm]
-    SP.rad.top          = Leg.sphere.top; % [mm]
-    SP.m                = SP.density.bottom*2*pi*((SP.rad.bottom*1e-3)^2)*(SP.height.bottom*1e-3); % TODO [kg]
-
-    SP = updateDamping(SP);
-
-    %%
-    Leg.support.bottom = [0 SP.thickness.bottom; 0 0; SP.rad.bottom 0; SP.rad.bottom SP.height.bottom];
-    Leg.support.top    = [0 SP.thickness.top; 0 0; SP.rad.top 0; SP.rad.top SP.height.top];
-
-    %%
-    micro_hexapod.BP = BP;
-    micro_hexapod.TP = TP;
-    micro_hexapod.Leg = Leg;
-    micro_hexapod.SP = SP;
-
-    %%
-    micro_hexapod = initializeParameters(micro_hexapod);
-
-    %% Save
-    save('./mat/stages.mat', 'micro_hexapod', '-append');
-
-    %%
-    function [element] = updateDamping(element)
-        field = fieldnames(element.k);
-        for i = 1:length(field)
-            element.c.(field{i}) = 1/element.ksi.(field{i})*sqrt(element.k.(field{i})/element.m);
-        end
-    end
-
-    %%
-    function [stewart] = initializeParameters(stewart)
-        %% Connection points on base and top plate w.r.t. World frame at the center of the base plate
-        stewart.pos_base = zeros(6, 3);
-        stewart.pos_top = zeros(6, 3);
-
-        alpha_b = stewart.BP.leg.ang*pi/180; % angle de décalage par rapport à 120 deg (pour positionner les supports bases)
-        alpha_t = stewart.TP.leg.ang*pi/180; % +- offset angle from 120 degree spacing on top
-
-        height = (stewart.h-stewart.BP.thickness-stewart.TP.thickness-stewart.Leg.sphere.bottom-stewart.Leg.sphere.top-stewart.SP.thickness.bottom-stewart.SP.thickness.top)*0.001; % TODO
-
-        radius_b = stewart.BP.leg.rad*0.001; % rayon emplacement support base
-        radius_t = stewart.TP.leg.rad*0.001; % top radius in meters
-
-        for i = 1:3
-          % base points
-          angle_m_b = (2*pi/3)* (i-1) - alpha_b;
-          angle_p_b = (2*pi/3)* (i-1) + alpha_b;
-          stewart.pos_base(2*i-1,:) =  [radius_b*cos(angle_m_b), radius_b*sin(angle_m_b), 0.0];
-          stewart.pos_base(2*i,:) = [radius_b*cos(angle_p_b), radius_b*sin(angle_p_b), 0.0];
-
-          % top points
-          % Top points are 60 degrees offset
-          angle_m_t = (2*pi/3)* (i-1) - alpha_t + 2*pi/6;
-          angle_p_t = (2*pi/3)* (i-1) + alpha_t + 2*pi/6;
-          stewart.pos_top(2*i-1,:) = [radius_t*cos(angle_m_t), radius_t*sin(angle_m_t), height];
-          stewart.pos_top(2*i,:) = [radius_t*cos(angle_p_t), radius_t*sin(angle_p_t), height];
-        end
-
-        % permute pos_top points so that legs are end points of base and top points
-        stewart.pos_top = [stewart.pos_top(6,:); stewart.pos_top(1:5,:)]; %6th point on top connects to 1st on bottom
-        stewart.pos_top_tranform = stewart.pos_top - height*[zeros(6, 2),ones(6, 1)];
-
-        %% leg vectors
-        legs = stewart.pos_top - stewart.pos_base;
-        leg_length = zeros(6, 1);
-        leg_vectors = zeros(6, 3);
-        for i = 1:6
-          leg_length(i) = norm(legs(i,:));
-          leg_vectors(i,:)  = legs(i,:) / leg_length(i);
-        end
-
-        stewart.Leg.lenght = 1000*leg_length(1)/1.5;
-        stewart.Leg.shape.bot = [0 0; ...
-                                stewart.Leg.rad.bottom 0; ...
-                                stewart.Leg.rad.bottom stewart.Leg.lenght; ...
-                                stewart.Leg.rad.top stewart.Leg.lenght; ...
-                                stewart.Leg.rad.top 0.2*stewart.Leg.lenght; ...
-                                0 0.2*stewart.Leg.lenght];
-
-        %% Calculate revolute and cylindrical axes
-        rev1 = zeros(6, 3);
-        rev2 = zeros(6, 3);
-        cyl1 = zeros(6, 3);
-        for i = 1:6
-          rev1(i,:) = cross(leg_vectors(i,:), [0 0 1]);
-          rev1(i,:) = rev1(i,:) / norm(rev1(i,:));
-
-          rev2(i,:) = - cross(rev1(i,:), leg_vectors(i,:));
-          rev2(i,:) = rev2(i,:) / norm(rev2(i,:));
-
-          cyl1(i,:) = leg_vectors(i,:);
-        end
-
-
-        %% Coordinate systems
-        stewart.lower_leg = struct('rotation', eye(3));
-        stewart.upper_leg = struct('rotation', eye(3));
-
-        for i = 1:6
-          stewart.lower_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
-          stewart.upper_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
-        end
-
-        %% Position Matrix
-        stewart.M_pos_base = stewart.pos_base + (height+(stewart.TP.thickness+stewart.Leg.sphere.top+stewart.SP.thickness.top+stewart.jacobian)*1e-3)*[zeros(6, 2),ones(6, 1)];
-
-        %% Compute Jacobian Matrix
-        aa = stewart.pos_top_tranform + (stewart.jacobian - stewart.TP.thickness - stewart.SP.height.top)*1e-3*[zeros(6, 2),ones(6, 1)];
-        stewart.J  = getJacobianMatrix(leg_vectors', aa');
-    end
-
-    function J  = getJacobianMatrix(RM,M_pos_base)
-        % RM: [3x6] unit vector of each leg in the fixed frame
-        % M_pos_base: [3x6] vector of the leg connection at the top platform location in the fixed frame
-        J = zeros(6);
-        J(:, 1:3) = RM';
-        J(:, 4:6) = cross(M_pos_base, RM)';
-    end
-end
-
-
-
-
- -
-

7.10 Center of gravity compensation

-
-

- -

- -

-This Matlab function is accessible here. -

- -
-
function [axisc] = initializeAxisc()
-    %%
-    axisc = struct();
-
-    %% Axis Compensator - Static Properties
-    % Structure
-    axisc.structure.density = 3400; % [kg/m3]
-    axisc.structure.color   = [0.792 0.820 0.933];
-    axisc.structure.STEP    = './STEPS/axisc/axisc_structure.STEP';
-    % Wheel
-    axisc.wheel.density     = 2700; % [kg/m3]
-    axisc.wheel.color       = [0.753 0.753 0.753];
-    axisc.wheel.STEP        = './STEPS/axisc/axisc_wheel.STEP';
-    % Mass
-    axisc.mass.density      = 7800; % [kg/m3]
-    axisc.mass.color        = [0.792 0.820 0.933];
-    axisc.mass.STEP         = './STEPS/axisc/axisc_mass.STEP';
-    % Gear
-    axisc.gear.density      = 7800; % [kg/m3]
-    axisc.gear.color        = [0.792 0.820 0.933];
-    axisc.gear.STEP         = './STEPS/axisc/axisc_gear.STEP';
-
-    axisc.m      = 40; % TODO [kg]
-
-    %% Axis Compensator - Dynamical Properties
-    axisc.k.ax   = 1; % TODO [N*m/deg)]
-    axisc.c.ax   = (1/1)*sqrt(axisc.k.ax/axisc.m);
-
-    %% Save
-    save('./mat/stages.mat', 'axisc', '-append');
-end
-
-
-
-
-
-

7.11 Mirror

-
-

- -

- -

-This Matlab function is accessible here. -

- -
-
function [] = initializeMirror(opts_param)
-    %% Default values for opts
-    opts = struct(...
-        'shape', 'spherical', ... % spherical or conical
-        'angle', 45 ...
-    );
-
-    %% Populate opts with input parameters
-    if exist('opts_param','var')
-        for opt = fieldnames(opts_param)'
-            opts.(opt{1}) = opts_param.(opt{1});
-        end
-    end
-
-    %%
-    mirror = struct();
-    mirror.h = 50; % height of the mirror [mm]
-    mirror.thickness = 25; % Thickness of the plate supporting the sample [mm]
-    mirror.hole_rad = 120; % radius of the hole in the mirror [mm]
-    mirror.support_rad = 100; % radius of the support plate [mm]
-    mirror.jacobian = 150; % point of interest offset in z (above the top surfave) [mm]
-    mirror.rad = 180; % radius of the mirror (at the bottom surface) [mm]
-
-    mirror.density = 2400; % Density of the mirror [kg/m3]
-    mirror.color = [0.4 1.0 1.0]; % Color of the mirror
-
-    mirror.cone_length = mirror.rad*tand(opts.angle)+mirror.h+mirror.jacobian; % Distance from Apex point of the cone to jacobian point
-
-    %% Shape
-    mirror.shape = [...
-        0 mirror.h-mirror.thickness
-        mirror.hole_rad mirror.h-mirror.thickness; ...
-        mirror.hole_rad 0; ...
-        mirror.rad 0 ...
-    ];
-
-    if strcmp(opts.shape, 'spherical')
-        mirror.sphere_radius = sqrt((mirror.jacobian+mirror.h)^2+mirror.rad^2); % Radius of the sphere [mm]
-
-        for z = linspace(0, mirror.h, 101)
-            mirror.shape = [mirror.shape; sqrt(mirror.sphere_radius^2-(z-mirror.jacobian-mirror.h)^2) z];
-        end
-    elseif strcmp(opts.shape, 'conical')
-        mirror.shape = [mirror.shape; mirror.rad+mirror.h/tand(opts.angle) mirror.h];
-    else
-        error('Shape should be either conical or spherical');
-    end
-
-    mirror.shape = [mirror.shape; 0 mirror.h];
-
-    %% Save
-    save('./mat/stages.mat', 'mirror', '-append');
-end
-
-
-
-
- -
-

7.12 Nano Hexapod

-
-

- -

- -

-This Matlab function is accessible here. -

- -
-
function [nano_hexapod] = initializeNanoHexapod(opts_param)
-    %% Default values for opts
-    opts = struct('actuator', 'piezo');
-
-    %% Populate opts with input parameters
-    if exist('opts_param','var')
-        for opt = fieldnames(opts_param)'
-            opts.(opt{1}) = opts_param.(opt{1});
-        end
-    end
-
-    %% Stewart Object
-    nano_hexapod = struct();
-    nano_hexapod.h        = 90;  % Total height of the platform [mm]
-    nano_hexapod.jacobian = 175; % Point where the Jacobian is computed => Center of rotation [mm]
-%     nano_hexapod.jacobian = 174.26; % Point where the Jacobian is computed => Center of rotation [mm]
-
-    %% Bottom Plate
-    BP = struct();
-
-    BP.rad.int   = 0;   % Internal Radius [mm]
-    BP.rad.ext   = 150; % External Radius [mm]
-    BP.thickness = 10;  % Thickness [mm]
-    BP.leg.rad   = 100; % Radius where the legs articulations are positionned [mm]
-    BP.leg.ang   = 5;   % Angle Offset [deg]
-    BP.density   = 8000;% Density of the material [kg/m^3]
-    BP.color     = [0.7 0.7 0.7]; % Color [rgb]
-    BP.shape     = [BP.rad.int BP.thickness; BP.rad.int 0; BP.rad.ext 0; BP.rad.ext BP.thickness];
-
-    %% Top Plate
-    TP = struct();
-
-    TP.rad.int   = 0;   % Internal Radius [mm]
-    TP.rad.ext   = 100; % Internal Radius [mm]
-    TP.thickness = 10;  % Thickness [mm]
-    TP.leg.rad   = 90;  % Radius where the legs articulations are positionned [mm]
-    TP.leg.ang   = 5;   % Angle Offset [deg]
-    TP.density   = 8000;% Density of the material [kg/m^3]
-    TP.color     = [0.7 0.7 0.7]; % Color [rgb]
-    TP.shape     = [TP.rad.int TP.thickness; TP.rad.int 0; TP.rad.ext 0; TP.rad.ext TP.thickness];
-
-    %% Leg
-    Leg = struct();
-
-    Leg.stroke     = 80e-6; % Maximum Stroke of each leg [m]
-    if strcmp(opts.actuator, 'piezo')
-        Leg.k.ax   = 1e7;   % Stiffness of each leg [N/m]
-    elseif strcmp(opts.actuator, 'lorentz')
-        Leg.k.ax   = 1e4;   % Stiffness of each leg [N/m]
-    else
-        error('opts.actuator should be piezo or lorentz');
-    end
-    Leg.ksi.ax     = 10;    % Maximum amplification at resonance []
-    Leg.rad.bottom = 12;    % Radius of the cylinder of the bottom part [mm]
-    Leg.rad.top    = 10;    % Radius of the cylinder of the top part [mm]
-    Leg.density    = 8000;  % Density of the material [kg/m^3]
-    Leg.color.bottom  = [0.5 0.5 0.5]; % Color [rgb]
-    Leg.color.top     = [0.5 0.5 0.5]; % Color [rgb]
-
-    Leg.sphere.bottom = Leg.rad.bottom; % Size of the sphere at the end of the leg [mm]
-    Leg.sphere.top    = Leg.rad.top; % Size of the sphere at the end of the leg [mm]
-    Leg.m             = TP.density*((pi*(TP.rad.ext/1000)^2)*(TP.thickness/1000)-(pi*(TP.rad.int/1000^2))*(TP.thickness/1000))/6; % TODO [kg]
-
-    Leg = updateDamping(Leg);
-
-
-    %% Sphere
-    SP = struct();
-
-    SP.height.bottom  = 15; % [mm]
-    SP.height.top     = 15; % [mm]
-    SP.density.bottom = 8000; % [kg/m^3]
-    SP.density.top    = 8000; % [kg/m^3]
-    SP.color.bottom   = [0.7 0.7 0.7]; % [rgb]
-    SP.color.top      = [0.7 0.7 0.7]; % [rgb]
-    SP.k.ax           = 0; % [N*m/deg]
-    SP.ksi.ax         = 3;
-
-    SP.thickness.bottom = SP.height.bottom-Leg.sphere.bottom; % [mm]
-    SP.thickness.top    = SP.height.top-Leg.sphere.top; % [mm]
-    SP.rad.bottom       = Leg.sphere.bottom; % [mm]
-    SP.rad.top          = Leg.sphere.top; % [mm]
-    SP.m                = SP.density.bottom*2*pi*((SP.rad.bottom*1e-3)^2)*(SP.height.bottom*1e-3); % TODO [kg]
-
-    SP = updateDamping(SP);
-
-    %%
-    Leg.support.bottom = [0 SP.thickness.bottom; 0 0; SP.rad.bottom 0; SP.rad.bottom SP.height.bottom];
-    Leg.support.top    = [0 SP.thickness.top; 0 0; SP.rad.top 0; SP.rad.top SP.height.top];
-
-    %%
-    nano_hexapod.BP = BP;
-    nano_hexapod.TP = TP;
-    nano_hexapod.Leg = Leg;
-    nano_hexapod.SP = SP;
-
-    %%
-    nano_hexapod = initializeParameters(nano_hexapod);
-
-    %% Save
-    save('./mat/stages.mat', 'nano_hexapod', '-append');
-
-    %%
-    function [element] = updateDamping(element)
-        field = fieldnames(element.k);
-        for i = 1:length(field)
-            element.c.(field{i}) = 1/element.ksi.(field{i})*sqrt(element.k.(field{i})/element.m);
-        end
-    end
-
-    %%
-    function [stewart] = initializeParameters(stewart)
-        %% Connection points on base and top plate w.r.t. World frame at the center of the base plate
-        stewart.pos_base = zeros(6, 3);
-        stewart.pos_top = zeros(6, 3);
-
-        alpha_b = stewart.BP.leg.ang*pi/180; % angle de décalage par rapport à 120 deg (pour positionner les supports bases)
-        alpha_t = stewart.TP.leg.ang*pi/180; % +- offset angle from 120 degree spacing on top
-
-        height = (stewart.h-stewart.BP.thickness-stewart.TP.thickness-stewart.Leg.sphere.bottom-stewart.Leg.sphere.top-stewart.SP.thickness.bottom-stewart.SP.thickness.top)*0.001; % TODO
-
-        radius_b = stewart.BP.leg.rad*0.001; % rayon emplacement support base
-        radius_t = stewart.TP.leg.rad*0.001; % top radius in meters
-
-        for i = 1:3
-          % base points
-          angle_m_b = (2*pi/3)* (i-1) - alpha_b;
-          angle_p_b = (2*pi/3)* (i-1) + alpha_b;
-          stewart.pos_base(2*i-1,:) =  [radius_b*cos(angle_m_b), radius_b*sin(angle_m_b), 0.0];
-          stewart.pos_base(2*i,:) = [radius_b*cos(angle_p_b), radius_b*sin(angle_p_b), 0.0];
-
-          % top points
-          % Top points are 60 degrees offset
-          angle_m_t = (2*pi/3)* (i-1) - alpha_t + 2*pi/6;
-          angle_p_t = (2*pi/3)* (i-1) + alpha_t + 2*pi/6;
-          stewart.pos_top(2*i-1,:) = [radius_t*cos(angle_m_t), radius_t*sin(angle_m_t), height];
-          stewart.pos_top(2*i,:) = [radius_t*cos(angle_p_t), radius_t*sin(angle_p_t), height];
-        end
-
-        % permute pos_top points so that legs are end points of base and top points
-        stewart.pos_top = [stewart.pos_top(6,:); stewart.pos_top(1:5,:)]; %6th point on top connects to 1st on bottom
-        stewart.pos_top_tranform = stewart.pos_top - height*[zeros(6, 2),ones(6, 1)];
-
-        %% leg vectors
-        legs = stewart.pos_top - stewart.pos_base;
-        leg_length = zeros(6, 1);
-        leg_vectors = zeros(6, 3);
-        for i = 1:6
-          leg_length(i) = norm(legs(i,:));
-          leg_vectors(i,:)  = legs(i,:) / leg_length(i);
-        end
-
-        stewart.Leg.lenght = 1000*leg_length(1)/1.5;
-        stewart.Leg.shape.bot = [0 0; ...
-                                stewart.Leg.rad.bottom 0; ...
-                                stewart.Leg.rad.bottom stewart.Leg.lenght; ...
-                                stewart.Leg.rad.top stewart.Leg.lenght; ...
-                                stewart.Leg.rad.top 0.2*stewart.Leg.lenght; ...
-                                0 0.2*stewart.Leg.lenght];
-
-        %% Calculate revolute and cylindrical axes
-        rev1 = zeros(6, 3);
-        rev2 = zeros(6, 3);
-        cyl1 = zeros(6, 3);
-        for i = 1:6
-          rev1(i,:) = cross(leg_vectors(i,:), [0 0 1]);
-          rev1(i,:) = rev1(i,:) / norm(rev1(i,:));
-
-          rev2(i,:) = - cross(rev1(i,:), leg_vectors(i,:));
-          rev2(i,:) = rev2(i,:) / norm(rev2(i,:));
-
-          cyl1(i,:) = leg_vectors(i,:);
-        end
-
-
-        %% Coordinate systems
-        stewart.lower_leg = struct('rotation', eye(3));
-        stewart.upper_leg = struct('rotation', eye(3));
-
-        for i = 1:6
-          stewart.lower_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
-          stewart.upper_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
-        end
-
-        %% Position Matrix
-        stewart.M_pos_base = stewart.pos_base + (height+(stewart.TP.thickness+stewart.Leg.sphere.top+stewart.SP.thickness.top+stewart.jacobian)*1e-3)*[zeros(6, 2),ones(6, 1)];
-
-        %% Compute Jacobian Matrix
-        aa = stewart.pos_top_tranform + (stewart.jacobian - stewart.TP.thickness - stewart.SP.height.top)*1e-3*[zeros(6, 2),ones(6, 1)];
-        stewart.J  = getJacobianMatrix(leg_vectors', aa');
-    end
-
-    function J  = getJacobianMatrix(RM,M_pos_base)
-        % RM: [3x6] unit vector of each leg in the fixed frame
-        % M_pos_base: [3x6] vector of the leg connection at the top platform location in the fixed frame
-        J = zeros(6);
-        J(:, 1:3) = RM';
-        J(:, 4:6) = cross(M_pos_base, RM)';
-    end
-end
-
-
-
-
- -
-

7.13 Sample

-
-

- -

- -

-This Matlab function is accessible here. -

- -
-
function [sample] = initializeSample(opts_param)
-    %% Default values for opts
-    sample = struct('radius', 100, ...
-                    'height', 300, ...
-                    'mass',   50,  ...
-                    'offset', 0,   ...
-                    'color',  [0.45, 0.45, 0.45] ...
-    );
-
-    %% Populate opts with input parameters
-    if exist('opts_param','var')
-        for opt = fieldnames(opts_param)'
-            sample.(opt{1}) = opts_param.(opt{1});
-        end
-    end
-
-    %%
-    sample.k.x = 1e8;
-    sample.c.x = sqrt(sample.k.x*sample.mass)/10;
-
-    sample.k.y = 1e8;
-    sample.c.y = sqrt(sample.k.y*sample.mass)/10;
-
-    sample.k.z = 1e8;
-    sample.c.z = sqrt(sample.k.y*sample.mass)/10;
-
-    %% Save
-    save('./mat/stages.mat', 'sample', '-append');
-end
-
-
-
-
-
+
-

Author: Dehaeze Thomas

-

Created: 2019-07-15 lun. 11:07

+

Author: Thomas Dehaeze

+

Created: 2019-10-08 mar. 11:10

Validate

diff --git a/index.org b/index.org index 34820f5..157e242 100644 --- a/index.org +++ b/index.org @@ -43,7 +43,12 @@ - [[file:identification/index.org][Identification of the Micro-Station]] - [[file:kinematics/index.org][Kinematics of the station]] -- Control +- [[file:control/index.org][Control]] +- [[file:active_damping/index.org][Active Damping]] +- [[file:analysis/index.org][Plant Analysis]] +- [[file:hac_lac/index.org][HAC LAC]] +- [[file:kinematics/index.org][Kinematics]] +- [[file:modal_test/index.org][Modal Analysis]] * Matlab Init :noexport:ignore: #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) diff --git a/kinematics/index.html b/kinematics/index.html new file mode 100644 index 0000000..0aab43e --- /dev/null +++ b/kinematics/index.html @@ -0,0 +1,271 @@ + + + + + + + +Kinematics of the station + + + + + + + + + + + + + +
+ UP + | + HOME +
+

Kinematics of the station

+ +
+

+All the files (data and Matlab scripts) are accessible here. +

+ +
+
+
+

Author: Dehaeze Thomas

+

Created: 2019-10-08 mar. 11:13

+

Validate

+
+ + diff --git a/kinematics/index.org b/kinematics/index.org index 8f1bdda..03965ac 100644 --- a/kinematics/index.org +++ b/kinematics/index.org @@ -30,7 +30,7 @@ #+PROPERTY: header-args:shell :eval no-export -#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/MEGA/These/LaTeX/}{config.tex}") +#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/These/LaTeX/}{config.tex}") #+PROPERTY: header-args:latex+ :imagemagick t :fit yes #+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150 #+PROPERTY: header-args:latex+ :imoutoptions -quality 100