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Add index html page
2019-07-12 11:53:59 +02:00
#+TITLE: Simscape Model of the Nano-Active-Stabilization-System
:DRAWER:
#+STARTUP: overview
#+LANGUAGE: en
#+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas
Start the standardize the folder. Add org-mode files.
2019-07-15 11:07:24 +02:00
#+HTML_LINK_HOME: ../index.html
#+HTML_LINK_UP: ./index.html
Add index html page
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/zenburn.css"/>
#+HTML_HEAD: <script type="text/javascript" src="./js/jquery.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="./js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="./js/jquery.stickytableheaders.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="./js/readtheorg.js"></script>
#+HTML_MATHJAX: align: center tagside: right font: TeX
Start the standardize the folder. Add org-mode files.
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#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :output-dir figs
#+PROPERTY: header-args:matlab+ :tangle matlab/modal_frf_coh.m
#+PROPERTY: header-args:matlab+ :mkdirp yes
#+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+ :imagemagick t :fit yes
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
#+PROPERTY: header-args:latex+ :results raw replace :buffer no
#+PROPERTY: header-args:latex+ :eval no-export
#+PROPERTY: header-args:latex+ :exports both
#+PROPERTY: header-args:latex+ :mkdirp yes
#+PROPERTY: header-args:latex+ :output-dir figs
Add index html page
2019-07-12 11:53:59 +02:00
:END:
Start the standardize the folder. Add org-mode files.
2019-07-15 11:07:24 +02:00
- [[file:identification/index.org][Identification of the Micro-Station]]
- [[file:kinematics/index.org][Kinematics of the station]]
- Control
* Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src
* Simulink project
The project can be opened using the =simulinkproject= function:
#+begin_src matlab
simulinkproject('./');
#+end_src
When the project opens, a startup script is ran.
The startup script is defined below and is exported to the =project_startup.m= script.
#+begin_src matlab :eval no :tangle src/project_startup.m
%%
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);
#+end_src
When the project closes, it runs the =project_shutdown.m= script defined below.
#+begin_src matlab :eval no :tangle src/project_shutdown.m
Simulink.fileGenControl('reset');
#+end_src
The project also permits to automatically add defined folder to the path when the project is opened.
* 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.
** Simscape files for identification
|------------------------+----+----+----+------+------|
| Simscape Name | Ty | Ry | Rz | Hexa | NASS |
|------------------------+----+----+----+------+------|
| id micro station | F | F | F | F | |
| id nano station stages | F | F | F | F | F |
| id nano station config | D | D | D | D | F |
| control nano station | D | D | D | D | F |
|------------------------+----+----+----+------+------|
** Inputs
*** Perturbations
|----------+--------------------------------------+------+------|
| Variable | Meaning | Size | Unit |
|----------+--------------------------------------+------+------|
| ~Dw~ | Ground motion | 3 | [m] |
| ~Fg~ | External force applied on granite | 3 | [N] |
| ~Fs~ | External force applied on the Sample | 3 | [N] |
|----------+--------------------------------------+------+------|
*** Measurement Noise
|----------+---------+------+------|
| Variable | Meaning | Size | Unit |
|----------+---------+------+------|
| | | | |
|----------+---------+------+------|
*** Control Inputs
|----------+-------------------------------------------+------+----------|
| Variable | Meaning | Size | Unit |
|----------+-------------------------------------------+------+----------|
| ~Fy~ | Actuation force for Ty | 1 | [N] |
| ~Dy~ | Imposed displacement for Ty | 1 | [m] |
|----------+-------------------------------------------+------+----------|
| ~My~ | Actuation torque for Ry | 1 | [N.m] |
| ~Ry~ | Imposed rotation for Ry | 1 | [rad] |
|----------+-------------------------------------------+------+----------|
| ~Mz~ | Actuation torque for Rz | 1 | [N.m] |
| ~Rz~ | Imposed rotation for Rz | 1 | [rad] |
|----------+-------------------------------------------+------+----------|
| ~Fh~ | Actuation force/torque for hexapod (cart) | 6 | [N, N.m] |
| ~Fhl~ | Actuation force/torque for hexapod (legs) | 6 | [N] |
| ~Dh~ | Imposed position for hexapod (cart) | 6 | [m, rad] |
|----------+-------------------------------------------+------+----------|
| ~Rm~ | Position of the two masses | 2 | [rad] |
|----------+-------------------------------------------+------+----------|
| ~Fn~ | Actuation force for the NASS (cart) | 6 | [N, N.m] |
| ~Fnl~ | Actuation force for the NASS's legs | 6 | [N] |
| ~Dn~ | Imposed position for the NASS (cart) | 6 | [m, rad] |
|----------+-------------------------------------------+------+----------|
** Outputs
|----------+---------------------------------------------+------+--------------|
| Variable | Meaning | Size | Unit |
|----------+---------------------------------------------+------+--------------|
| ~Dgm~ | Absolute displacement of the granite | 3 | [m] |
| ~Vgm~ | Absolute Velocity of the granite | 3 | [m/s] |
|----------+---------------------------------------------+------+--------------|
| ~Dym~ | Measured displacement of Ty | 1 | [m] |
|----------+---------------------------------------------+------+--------------|
| ~Rym~ | Measured rotation of Ry | 1 | [rad] |
|----------+---------------------------------------------+------+--------------|
| ~Rzm~ | Measured rotation of Rz | 1 | [rad] |
|----------+---------------------------------------------+------+--------------|
| ~Dhm~ | Measured position of hexapod (cart) | 6 | [m, rad] |
|----------+---------------------------------------------+------+--------------|
| ~Fnlm~ | Measured force of NASS's legs | 6 | [N] |
| ~Dnlm~ | Measured elongation of NASS's legs | 6 | [m] |
| ~Dnm~ | Measured position of NASS w.r.t NASS's base | 6 | [m, rad] |
| ~Vnm~ | Measured absolute velocity of NASS platform | 6 | [m/s, rad/s] |
| ~Vnlm~ | Measured absolute velocity of NASS's legs | 6 | [m/s] |
|----------+---------------------------------------------+------+--------------|
| ~Dsm~ | Position of Sample w.r.t. granite frame | 6 | [m, rad] |
|----------+---------------------------------------------+------+--------------|
* Simulink files
Few different Simulink files are used:
- kinematics
- identification - micro station
- identification - nano station
- control
* Simulink Library
A simulink library is developed in order to share elements between the different simulink files.
** inputs
** nass_library
** pos_error_wrt_nass_base
** QuaternionToAngles
** RotationMatrixToAngle
* Scripts
** Simulation Initialization
:PROPERTIES:
:header-args:matlab+: :tangle src/init_simulation.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:init_simulation>>
This Matlab script is accessible [[file:src/init_simulation.m][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.
#+begin_src matlab
%% Load all the data used for the simulation
load('./mat/sim_conf.mat');
%% Load Controller
load('./mat/controllers.mat');
#+end_src
* Functions
** computePsdDispl
:PROPERTIES:
:header-args:matlab+: :tangle src/computePsdDispl.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:computePsdDispl>>
This Matlab function is accessible [[file:src/computePsdDispl.m][here]].
#+begin_src matlab
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
#+end_src
** computeSetpoint
:PROPERTIES:
:header-args:matlab+: :tangle src/computeSetpoint.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:computeSetpoint>>
This Matlab function is accessible [[file:src/computeSetpoint.m][here]].
#+begin_src matlab
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
#+end_src
** converErrorBasis
:PROPERTIES:
:header-args:matlab+: :tangle src/converErrorBasis.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:converErrorBasis>>
This Matlab function is accessible [[file:src/converErrorBasis.m][here]].
#+begin_src matlab
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
#+end_src
** generateDiagPidControl
:PROPERTIES:
:header-args:matlab+: :tangle src/generateDiagPidControl.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:generateDiagPidControl>>
This Matlab function is accessible [[file:src/generateDiagPidControl.m][here]].
#+begin_src matlab
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
#+end_src
** identifyPlant
:PROPERTIES:
:header-args:matlab+: :tangle src/identifyPlant.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:identifyPlant>>
This Matlab function is accessible [[file:src/identifyPlant.m][here]].
#+begin_src matlab
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
#+end_src
** runSimulation
:PROPERTIES:
:header-args:matlab+: :tangle src/runSimulation.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:runSimulation>>
This Matlab function is accessible [[file:src/runSimulation.m][here]].
#+begin_src matlab
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
#+end_src
* Initialize Elements
** Simulation Configuration
:PROPERTIES:
:header-args:matlab+: :tangle src/initializeSimConf.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:initializeSimConf>>
This Matlab function is accessible [[file:src/initializeSimConf.m][here]].
#+begin_src matlab
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
#+end_src
** Experiment
:PROPERTIES:
:header-args:matlab+: :tangle src/initializeExperiment.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:initializeExperiment>>
This Matlab function is accessible [[file:src/initializeExperiment.m][here]].
#+begin_src matlab
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
#+end_src
** Inputs
:PROPERTIES:
:header-args:matlab+: :tangle src/initializeInputs.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:initializeInputs>>
This Matlab function is accessible [[file:src/initializeInputs.m][here]].
#+begin_src matlab
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
#+end_src
** Ground
:PROPERTIES:
:header-args:matlab+: :tangle src/initializeGround.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:initializeGround>>
This Matlab function is accessible [[file:src/initializeGround.m][here]].
#+begin_src matlab
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
#+end_src
** Granite
:PROPERTIES:
:header-args:matlab+: :tangle src/initializeGranite.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:initializeGranite>>
This Matlab function is accessible [[file:src/initializeGranite.m][here]].
#+begin_src matlab
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
#+end_src
** Translation Stage
:PROPERTIES:
:header-args:matlab+: :tangle src/initializeTy.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:initializeTy>>
This Matlab function is accessible [[file:src/initializeTy.m][here]].
#+begin_src matlab
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
#+end_src
** Tilt Stage
:PROPERTIES:
:header-args:matlab+: :tangle src/initializeRy.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:initializeRy>>
This Matlab function is accessible [[file:src/initializeRy.m][here]].
#+begin_src matlab
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
#+end_src
** Spindle
:PROPERTIES:
:header-args:matlab+: :tangle src/initializeRz.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:initializeRz>>
This Matlab function is accessible [[file:src/initializeRz.m][here]].
#+begin_src matlab
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
#+end_src
** Micro Hexapod
:PROPERTIES:
:header-args:matlab+: :tangle src/initializeMicroHexapod.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:initializeMicroHexapod>>
This Matlab function is accessible [[file:src/initializeMicroHexapod.m][here]].
#+begin_src matlab
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
#+end_src
** Center of gravity compensation
:PROPERTIES:
:header-args:matlab+: :tangle src/initializeAxisc.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:initializeAxisc>>
This Matlab function is accessible [[file:src/initializeAxisc.m][here]].
#+begin_src matlab
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
#+end_src
** Mirror
:PROPERTIES:
:header-args:matlab+: :tangle src/initializeMirror.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:initializeMirror>>
This Matlab function is accessible [[file:src/initializeMirror.m][here]].
#+begin_src matlab
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
#+end_src
** Nano Hexapod
:PROPERTIES:
:header-args:matlab+: :tangle src/initializeNanoHexapod.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:initializeNanoHexapod>>
This Matlab function is accessible [[file:src/initializeNanoHexapod.m][here]].
#+begin_src matlab
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
#+end_src
** Sample
:PROPERTIES:
:header-args:matlab+: :tangle src/initializeSample.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:initializeSample>>
This Matlab function is accessible [[file:src/initializeSample.m][here]].
#+begin_src matlab
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
#+end_src
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