1396 lines
49 KiB
Org Mode
1396 lines
49 KiB
Org Mode
#+TITLE: Subsystems used for the Simscape Models
|
|
:DRAWER:
|
|
#+STARTUP: overview
|
|
|
|
#+LANGUAGE: en
|
|
#+EMAIL: dehaeze.thomas@gmail.com
|
|
#+AUTHOR: Dehaeze Thomas
|
|
|
|
#+HTML_LINK_HOME: ../index.html
|
|
#+HTML_LINK_UP: ../index.html
|
|
|
|
#+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
|
|
|
|
#+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 no
|
|
#+PROPERTY: header-args:matlab+ :mkdirp yes
|
|
|
|
#+PROPERTY: header-args:shell :eval no-export
|
|
|
|
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/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
|
|
:END:
|
|
|
|
* Introduction :ignore:
|
|
* General Subsystems
|
|
<<sec:helping functions>>
|
|
** Generate Reference Signals
|
|
:PROPERTIES:
|
|
:header-args:matlab+: :tangle ../src/initializeReferences.m
|
|
:header-args:matlab+: :comments none :mkdirp yes :eval no
|
|
:END:
|
|
<<sec:initializeReferences>>
|
|
|
|
This Matlab function is accessible [[file:../src/initializeInputs.m][here]].
|
|
|
|
*** Function Declaration and Documentation
|
|
#+begin_src matlab
|
|
function [ref] = initializeReferences(args)
|
|
#+end_src
|
|
|
|
*** Optional Parameters
|
|
#+begin_src matlab
|
|
arguments
|
|
% Sampling Frequency [s]
|
|
args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-3
|
|
% Maximum simulation time [s]
|
|
args.Tmax (1,1) double {mustBeNumeric, mustBePositive} = 100
|
|
% Either "constant" / "triangular" / "sinusoidal"
|
|
args.Dy_type char {mustBeMember(args.Dy_type,{'constant', 'triangular', 'sinusoidal'})} = 'constant'
|
|
% Amplitude of the displacement [m]
|
|
args.Dy_amplitude (1,1) double {mustBeNumeric} = 0
|
|
% Period of the displacement [s]
|
|
args.Dy_period (1,1) double {mustBeNumeric, mustBePositive} = 1
|
|
% Either "constant" / "triangular" / "sinusoidal"
|
|
args.Ry_type char {mustBeMember(args.Ry_type,{'constant', 'triangular', 'sinusoidal'})} = 'constant'
|
|
% Amplitude [rad]
|
|
args.Ry_amplitude (1,1) double {mustBeNumeric} = 0
|
|
% Period of the displacement [s]
|
|
args.Ry_period (1,1) double {mustBeNumeric, mustBePositive} = 1
|
|
% Either "constant" / "rotating"
|
|
args.Rz_type char {mustBeMember(args.Rz_type,{'constant', 'rotating'})} = 'constant'
|
|
% Initial angle [rad]
|
|
args.Rz_amplitude (1,1) double {mustBeNumeric} = 0
|
|
% Period of the rotating [s]
|
|
args.Rz_period (1,1) double {mustBeNumeric, mustBePositive} = 1
|
|
% For now, only constant is implemented
|
|
args.Dh_type char {mustBeMember(args.Dh_type,{'constant'})} = 'constant'
|
|
% Initial position [m,m,m,rad,rad,rad] of the top platform (Pitch-Roll-Yaw Euler angles)
|
|
args.Dh_pos (6,1) double {mustBeNumeric} = zeros(6, 1), ...
|
|
% For now, only constant is implemented
|
|
args.Rm_type char {mustBeMember(args.Rm_type,{'constant'})} = 'constant'
|
|
% Initial position of the two masses
|
|
args.Rm_pos (2,1) double {mustBeNumeric} = [0; pi]
|
|
% For now, only constant is implemented
|
|
args.Dn_type char {mustBeMember(args.Dn_type,{'constant'})} = 'constant'
|
|
% Initial position [m,m,m,rad,rad,rad] of the top platform
|
|
args.Dn_pos (6,1) double {mustBeNumeric} = zeros(6,1)
|
|
end
|
|
#+end_src
|
|
|
|
|
|
*** Initialize Parameters
|
|
#+begin_src matlab
|
|
%% Set Sampling Time
|
|
Ts = args.Ts;
|
|
Tmax = args.Tmax;
|
|
|
|
%% Low Pass Filter to filter out the references
|
|
s = zpk('s');
|
|
w0 = 2*pi*10;
|
|
xi = 1;
|
|
H_lpf = 1/(1 + 2*xi/w0*s + s^2/w0^2);
|
|
#+end_src
|
|
|
|
*** Translation Stage
|
|
#+begin_src matlab
|
|
%% Translation stage - Dy
|
|
t = 0:Ts:Tmax; % Time Vector [s]
|
|
Dy = zeros(length(t), 1);
|
|
Dyd = zeros(length(t), 1);
|
|
Dydd = zeros(length(t), 1);
|
|
switch args.Dy_type
|
|
case 'constant'
|
|
Dy(:) = args.Dy_amplitude;
|
|
Dyd(:) = 0;
|
|
Dydd(:) = 0;
|
|
case 'triangular'
|
|
% This is done to unsure that we start with no displacement
|
|
Dy_raw = args.Dy_amplitude*sawtooth(2*pi*t/args.Dy_period,1/2);
|
|
i0 = find(t>=args.Dy_period/4,1);
|
|
Dy(1:end-i0+1) = Dy_raw(i0:end);
|
|
Dy(end-i0+2:end) = Dy_raw(end); % we fix the last value
|
|
|
|
% The signal is filtered out
|
|
Dy = lsim(H_lpf, Dy, t);
|
|
Dyd = lsim(H_lpf*s, Dy, t);
|
|
Dydd = lsim(H_lpf*s^2, Dy, t);
|
|
case 'sinusoidal'
|
|
Dy(:) = args.Dy_amplitude*sin(2*pi/args.Dy_period*t);
|
|
Dyd = args.Dy_amplitude*2*pi/args.Dy_period*cos(2*pi/args.Dy_period*t);
|
|
Dydd = -args.Dy_amplitude*(2*pi/args.Dy_period)^2*sin(2*pi/args.Dy_period*t);
|
|
otherwise
|
|
warning('Dy_type is not set correctly');
|
|
end
|
|
|
|
Dy = struct('time', t, 'signals', struct('values', Dy), 'deriv', Dyd, 'dderiv', Dydd);
|
|
#+end_src
|
|
|
|
*** Tilt Stage
|
|
#+begin_src matlab
|
|
%% Tilt Stage - Ry
|
|
t = 0:Ts:Tmax; % Time Vector [s]
|
|
Ry = zeros(length(t), 1);
|
|
Ryd = zeros(length(t), 1);
|
|
Rydd = zeros(length(t), 1);
|
|
|
|
switch args.Ry_type
|
|
case 'constant'
|
|
Ry(:) = args.Ry_amplitude;
|
|
Ryd(:) = 0;
|
|
Rydd(:) = 0;
|
|
case 'triangular'
|
|
Ry_raw = args.Ry_amplitude*sawtooth(2*pi*t/args.Ry_period,1/2);
|
|
i0 = find(t>=args.Ry_period/4,1);
|
|
Ry(1:end-i0+1) = Ry_raw(i0:end);
|
|
Ry(end-i0+2:end) = Ry_raw(end); % we fix the last value
|
|
|
|
% The signal is filtered out
|
|
Ry = lsim(H_lpf, Ry, t);
|
|
Ryd = lsim(H_lpf*s, Ry, t);
|
|
Rydd = lsim(H_lpf*s^2, Ry, t);
|
|
case 'sinusoidal'
|
|
Ry(:) = args.Ry_amplitude*sin(2*pi/args.Ry_period*t);
|
|
|
|
Ryd = args.Ry_amplitude*2*pi/args.Ry_period*cos(2*pi/args.Ry_period*t);
|
|
Rydd = -args.Ry_amplitude*(2*pi/args.Ry_period)^2*sin(2*pi/args.Ry_period*t);
|
|
otherwise
|
|
warning('Ry_type is not set correctly');
|
|
end
|
|
|
|
Ry = struct('time', t, 'signals', struct('values', Ry), 'deriv', Ryd, 'dderiv', Rydd);
|
|
#+end_src
|
|
|
|
*** Spindle
|
|
#+begin_src matlab
|
|
%% Spindle - Rz
|
|
t = 0:Ts:Tmax; % Time Vector [s]
|
|
Rz = zeros(length(t), 1);
|
|
Rzd = zeros(length(t), 1);
|
|
Rzdd = zeros(length(t), 1);
|
|
|
|
switch args.Rz_type
|
|
case 'constant'
|
|
Rz(:) = args.Rz_amplitude;
|
|
Rzd(:) = 0;
|
|
Rzdd(:) = 0;
|
|
case 'rotating'
|
|
Rz(:) = args.Rz_amplitude+2*pi/args.Rz_period*t;
|
|
|
|
% The signal is filtered out
|
|
Rz = lsim(H_lpf, Rz, t);
|
|
Rzd = lsim(H_lpf*s, Rz, t);
|
|
Rzdd = lsim(H_lpf*s^2, Rz, t);
|
|
otherwise
|
|
warning('Rz_type is not set correctly');
|
|
end
|
|
|
|
Rz = struct('time', t, 'signals', struct('values', Rz), 'deriv', Rzd, 'dderiv', Rzdd);
|
|
#+end_src
|
|
|
|
*** Micro Hexapod
|
|
#+begin_src matlab
|
|
%% Micro-Hexapod
|
|
t = [0, Ts];
|
|
Dh = zeros(length(t), 6);
|
|
Dhl = zeros(length(t), 6);
|
|
|
|
switch args.Dh_type
|
|
case 'constant'
|
|
Dh = [args.Dh_pos, args.Dh_pos];
|
|
|
|
load('mat/stages.mat', 'micro_hexapod');
|
|
|
|
AP = [args.Dh_pos(1) ; args.Dh_pos(2) ; args.Dh_pos(3)];
|
|
|
|
tx = args.Dh_pos(4);
|
|
ty = args.Dh_pos(5);
|
|
tz = args.Dh_pos(6);
|
|
|
|
ARB = [cos(tz) -sin(tz) 0;
|
|
sin(tz) cos(tz) 0;
|
|
0 0 1]*...
|
|
[ cos(ty) 0 sin(ty);
|
|
0 1 0;
|
|
-sin(ty) 0 cos(ty)]*...
|
|
[1 0 0;
|
|
0 cos(tx) -sin(tx);
|
|
0 sin(tx) cos(tx)];
|
|
|
|
[Dhl] = inverseKinematicsHexapod(micro_hexapod, AP, ARB);
|
|
Dhl = [Dhl, Dhl];
|
|
otherwise
|
|
warning('Dh_type is not set correctly');
|
|
end
|
|
|
|
Dh = struct('time', t, 'signals', struct('values', Dh));
|
|
Dhl = struct('time', t, 'signals', struct('values', Dhl));
|
|
#+end_src
|
|
|
|
*** Axis Compensation
|
|
#+begin_src matlab
|
|
%% Axis Compensation - Rm
|
|
t = [0, Ts];
|
|
|
|
Rm = [args.Rm_pos, args.Rm_pos];
|
|
Rm = struct('time', t, 'signals', struct('values', Rm));
|
|
#+end_src
|
|
|
|
*** Nano Hexapod
|
|
#+begin_src matlab
|
|
%% Nano-Hexapod
|
|
t = [0, Ts];
|
|
Dn = zeros(length(t), 6);
|
|
|
|
switch args.Dn_type
|
|
case 'constant'
|
|
Dn = [args.Dn_pos, args.Dn_pos];
|
|
otherwise
|
|
warning('Dn_type is not set correctly');
|
|
end
|
|
|
|
Dn = struct('time', t, 'signals', struct('values', Dn));
|
|
#+end_src
|
|
|
|
*** Save
|
|
#+begin_src matlab
|
|
%% Save
|
|
save('mat/nass_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'Rm', 'Dn', 'Ts');
|
|
end
|
|
#+end_src
|
|
|
|
** Initialize Disturbances
|
|
:PROPERTIES:
|
|
:header-args:matlab+: :tangle ../src/initDisturbances.m
|
|
:header-args:matlab+: :comments none :mkdirp yes
|
|
:header-args:matlab+: :eval no :results none
|
|
:END:
|
|
<<sec:initDisturbances>>
|
|
|
|
This Matlab function is accessible [[file:src/initDisturbances.m][here]].
|
|
|
|
*** Function Declaration and Documentation
|
|
#+begin_src matlab
|
|
function [] = initDisturbances(args)
|
|
% initDisturbances - Initialize the disturbances
|
|
%
|
|
% Syntax: [] = initDisturbances(args)
|
|
%
|
|
% Inputs:
|
|
% - args -
|
|
|
|
#+end_src
|
|
|
|
*** Optional Parameters
|
|
#+begin_src matlab
|
|
arguments
|
|
% Ground Motion - X direction
|
|
args.Dwx logical {mustBeNumericOrLogical} = true
|
|
% Ground Motion - Y direction
|
|
args.Dwy logical {mustBeNumericOrLogical} = true
|
|
% Ground Motion - Z direction
|
|
args.Dwz logical {mustBeNumericOrLogical} = true
|
|
% Translation Stage - X direction
|
|
args.Fty_x logical {mustBeNumericOrLogical} = true
|
|
% Translation Stage - Z direction
|
|
args.Fty_z logical {mustBeNumericOrLogical} = true
|
|
% Spindle - Z direction
|
|
args.Frz_z logical {mustBeNumericOrLogical} = true
|
|
end
|
|
#+end_src
|
|
|
|
|
|
*** Load Data
|
|
#+begin_src matlab
|
|
load('./disturbances/mat/dist_psd.mat', 'dist_f');
|
|
#+end_src
|
|
|
|
We remove the first frequency point that usually is very large.
|
|
#+begin_src matlab :exports none
|
|
dist_f.f = dist_f.f(2:end);
|
|
dist_f.psd_gm = dist_f.psd_gm(2:end);
|
|
dist_f.psd_ty = dist_f.psd_ty(2:end);
|
|
dist_f.psd_rz = dist_f.psd_rz(2:end);
|
|
#+end_src
|
|
|
|
*** Parameters
|
|
We define some parameters that will be used in the algorithm.
|
|
#+begin_src matlab
|
|
Fs = 2*dist_f.f(end); % Sampling Frequency of data is twice the maximum frequency of the PSD vector [Hz]
|
|
N = 2*length(dist_f.f); % Number of Samples match the one of the wanted PSD
|
|
T0 = N/Fs; % Signal Duration [s]
|
|
df = 1/T0; % Frequency resolution of the DFT [Hz]
|
|
% Also equal to (dist_f.f(2)-dist_f.f(1))
|
|
t = linspace(0, T0, N+1)'; % Time Vector [s]
|
|
Ts = 1/Fs; % Sampling Time [s]
|
|
#+end_src
|
|
|
|
*** Ground Motion
|
|
#+begin_src matlab
|
|
phi = dist_f.psd_gm;
|
|
C = zeros(N/2,1);
|
|
for i = 1:N/2
|
|
C(i) = sqrt(phi(i)*df);
|
|
end
|
|
#+end_src
|
|
|
|
#+begin_src matlab
|
|
if args.Dwx
|
|
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
|
|
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
|
|
Cx = [Cx; flipud(conj(Cx(2:end)))];;
|
|
Dwx = N/sqrt(2)*ifft(Cx); % Ground Motion - x direction [m]
|
|
else
|
|
Dwx = zeros(length(t), 1);
|
|
end
|
|
#+end_src
|
|
|
|
#+begin_src matlab
|
|
if args.Dwy
|
|
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
|
|
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
|
|
Cx = [Cx; flipud(conj(Cx(2:end)))];;
|
|
Dwy = N/sqrt(2)*ifft(Cx); % Ground Motion - y direction [m]
|
|
else
|
|
Dwy = zeros(length(t), 1);
|
|
end
|
|
#+end_src
|
|
|
|
#+begin_src matlab
|
|
if args.Dwy
|
|
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
|
|
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
|
|
Cx = [Cx; flipud(conj(Cx(2:end)))];;
|
|
Dwz = N/sqrt(2)*ifft(Cx); % Ground Motion - z direction [m]
|
|
else
|
|
Dwz = zeros(length(t), 1);
|
|
end
|
|
#+end_src
|
|
|
|
*** Translation Stage - X direction
|
|
#+begin_src matlab
|
|
if args.Fty_x
|
|
phi = dist_f.psd_ty; % TODO - we take here the vertical direction which is wrong but approximate
|
|
C = zeros(N/2,1);
|
|
for i = 1:N/2
|
|
C(i) = sqrt(phi(i)*df);
|
|
end
|
|
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
|
|
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
|
|
Cx = [Cx; flipud(conj(Cx(2:end)))];;
|
|
u = N/sqrt(2)*ifft(Cx); % Disturbance Force Ty x [N]
|
|
Fty_x = u;
|
|
else
|
|
Fty_x = zeros(length(t), 1);
|
|
end
|
|
#+end_src
|
|
|
|
*** Translation Stage - Z direction
|
|
#+begin_src matlab
|
|
if args.Fty_z
|
|
phi = dist_f.psd_ty;
|
|
C = zeros(N/2,1);
|
|
for i = 1:N/2
|
|
C(i) = sqrt(phi(i)*df);
|
|
end
|
|
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
|
|
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
|
|
Cx = [Cx; flipud(conj(Cx(2:end)))];;
|
|
u = N/sqrt(2)*ifft(Cx); % Disturbance Force Ty z [N]
|
|
Fty_z = u;
|
|
else
|
|
Fty_z = zeros(length(t), 1);
|
|
end
|
|
#+end_src
|
|
|
|
*** Spindle - Z direction
|
|
#+begin_src matlab
|
|
if args.Frz_z
|
|
phi = dist_f.psd_rz;
|
|
C = zeros(N/2,1);
|
|
for i = 1:N/2
|
|
C(i) = sqrt(phi(i)*df);
|
|
end
|
|
theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
|
|
Cx = [0 ; C.*complex(cos(theta),sin(theta))];
|
|
Cx = [Cx; flipud(conj(Cx(2:end)))];;
|
|
u = N/sqrt(2)*ifft(Cx); % Disturbance Force Rz z [N]
|
|
Frz_z = u;
|
|
else
|
|
Frz_z = zeros(length(t), 1);
|
|
end
|
|
#+end_src
|
|
|
|
*** Direct Forces
|
|
#+begin_src matlab
|
|
u = zeros(length(t), 6);
|
|
Fd = u;
|
|
#+end_src
|
|
|
|
*** Set initial value to zero
|
|
#+begin_src matlab
|
|
Dwx = Dwx - Dwx(1);
|
|
Dwy = Dwy - Dwy(1);
|
|
Dwz = Dwz - Dwz(1);
|
|
Fty_x = Fty_x - Fty_x(1);
|
|
Fty_z = Fty_z - Fty_z(1);
|
|
Frz_z = Frz_z - Frz_z(1);
|
|
#+end_src
|
|
|
|
*** Save
|
|
#+begin_src matlab
|
|
save('mat/nass_disturbances.mat', 'Dwx', 'Dwy', 'Dwz', 'Fty_x', 'Fty_z', 'Frz_z', 'Fd', 'Ts', 't');
|
|
#+end_src
|
|
|
|
** Z-Axis Geophone
|
|
:PROPERTIES:
|
|
:header-args:matlab+: :tangle ../src/initializeZAxisGeophone.m
|
|
:header-args:matlab+: :comments none :mkdirp yes :eval no
|
|
:END:
|
|
<<sec:initializeZAxisGeophone>>
|
|
|
|
This Matlab function is accessible [[file:../src/initializeZAxisGeophone.m][here]].
|
|
|
|
#+begin_src matlab
|
|
function [geophone] = initializeZAxisGeophone(args)
|
|
arguments
|
|
args.mass (1,1) double {mustBeNumeric, mustBePositive} = 1e-3 % [kg]
|
|
args.freq (1,1) double {mustBeNumeric, mustBePositive} = 1 % [Hz]
|
|
end
|
|
|
|
%%
|
|
geophone.m = args.mass;
|
|
|
|
%% The Stiffness is set to have the damping resonance frequency
|
|
geophone.k = geophone.m * (2*pi*args.freq)^2;
|
|
|
|
%% We set the damping value to have critical damping
|
|
geophone.c = 2*sqrt(geophone.m * geophone.k);
|
|
|
|
%% Save
|
|
save('./mat/geophone_z_axis.mat', 'geophone');
|
|
end
|
|
#+end_src
|
|
|
|
** Z-Axis Accelerometer
|
|
:PROPERTIES:
|
|
:header-args:matlab+: :tangle ../src/initializeZAxisAccelerometer.m
|
|
:header-args:matlab+: :comments none :mkdirp yes :eval no
|
|
:END:
|
|
<<sec:initializeZAxisAccelerometer>>
|
|
|
|
This Matlab function is accessible [[file:../src/initializeZAxisAccelerometer.m][here]].
|
|
|
|
#+begin_src matlab
|
|
function [accelerometer] = initializeZAxisAccelerometer(args)
|
|
arguments
|
|
args.mass (1,1) double {mustBeNumeric, mustBePositive} = 1e-3 % [kg]
|
|
args.freq (1,1) double {mustBeNumeric, mustBePositive} = 5e2 % [Hz]
|
|
end
|
|
|
|
%%
|
|
accelerometer.m = args.mass;
|
|
|
|
%% The Stiffness is set to have the damping resonance frequency
|
|
accelerometer.k = accelerometer.m * (2*pi*args.freq)^2;
|
|
|
|
%% We set the damping value to have critical damping
|
|
accelerometer.c = 2*sqrt(accelerometer.m * accelerometer.k);
|
|
|
|
%% Save
|
|
save('./mat/accelerometer_z_axis.mat', 'accelerometer');
|
|
end
|
|
#+end_src
|
|
|
|
* Initialize Elements
|
|
:PROPERTIES:
|
|
:ID: a0819dea-8d7a-4d55-b961-2b2ca2312344
|
|
:END:
|
|
<<sec:initialize_elements>>
|
|
** Ground
|
|
:PROPERTIES:
|
|
:header-args:matlab+: :tangle ../src/initializeGround.m
|
|
:header-args:matlab+: :comments none :mkdirp yes :eval no
|
|
: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 none :mkdirp yes :eval no
|
|
:END:
|
|
<<sec:initializeGranite>>
|
|
|
|
This Matlab function is accessible [[file:../src/initializeGranite.m][here]].
|
|
|
|
#+begin_src matlab
|
|
function [granite] = initializeGranite(args)
|
|
arguments
|
|
args.rigid logical {mustBeNumericOrLogical} = false
|
|
end
|
|
|
|
%%
|
|
granite = struct();
|
|
|
|
%% Static Properties
|
|
granite.density = 2800; % [kg/m3]
|
|
granite.volume = 0.749; % [m3] TODO - should
|
|
granite.mass = granite.density*granite.volume; % [kg]
|
|
granite.color = [1 1 1];
|
|
granite.STEP = './STEPS/granite/granite.STEP';
|
|
|
|
granite.mass_top = 4000; % [kg] TODO
|
|
|
|
%% Dynamical Properties
|
|
if args.rigid
|
|
granite.k.x = 1e12; % [N/m]
|
|
granite.k.y = 1e12; % [N/m]
|
|
granite.k.z = 1e12; % [N/m]
|
|
granite.k.rx = 1e10; % [N*m/deg]
|
|
granite.k.ry = 1e10; % [N*m/deg]
|
|
granite.k.rz = 1e10; % [N*m/deg]
|
|
else
|
|
granite.k.x = 4e9; % [N/m]
|
|
granite.k.y = 3e8; % [N/m]
|
|
granite.k.z = 8e8; % [N/m]
|
|
granite.k.rx = 1e4; % [N*m/deg]
|
|
granite.k.ry = 1e4; % [N*m/deg]
|
|
granite.k.rz = 1e6; % [N*m/deg]
|
|
end
|
|
|
|
granite.c.x = 0.1*sqrt(granite.mass_top*granite.k.x); % [N/(m/s)]
|
|
granite.c.y = 0.1*sqrt(granite.mass_top*granite.k.y); % [N/(m/s)]
|
|
granite.c.z = 0.5*sqrt(granite.mass_top*granite.k.z); % [N/(m/s)]
|
|
granite.c.rx = 0.1*sqrt(granite.mass_top*granite.k.rx); % [N*m/(deg/s)]
|
|
granite.c.ry = 0.1*sqrt(granite.mass_top*granite.k.ry); % [N*m/(deg/s)]
|
|
granite.c.rz = 0.1*sqrt(granite.mass_top*granite.k.rz); % [N*m/(deg/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 none :mkdirp yes :eval no
|
|
:END:
|
|
<<sec:initializeTy>>
|
|
|
|
This Matlab function is accessible [[file:../src/initializeTy.m][here]].
|
|
|
|
#+begin_src matlab
|
|
function [ty] = initializeTy(args)
|
|
arguments
|
|
args.rigid logical {mustBeNumericOrLogical} = false
|
|
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 = 1000; % TODO [kg]
|
|
|
|
%% Y-Translation - Dynamicals Properties
|
|
if args.rigid
|
|
ty.k.ax = 1e12; % Axial Stiffness for each of the 4 guidance (y) [N/m]
|
|
ty.k.rad = 1e12; % Radial Stiffness for each of the 4 guidance (x-z) [N/m]
|
|
else
|
|
ty.k.ax = 5e8; % Axial Stiffness for each of the 4 guidance (y) [N/m]
|
|
ty.k.rad = 5e7; % Radial Stiffness for each of the 4 guidance (x-z) [N/m]
|
|
end
|
|
|
|
ty.c.ax = 0.1*sqrt(ty.k.ax*ty.m);
|
|
ty.c.rad = 0.1*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 none :mkdirp yes :eval no
|
|
:END:
|
|
<<sec:initializeRy>>
|
|
|
|
This Matlab function is accessible [[file:../src/initializeRy.m][here]].
|
|
|
|
#+begin_src matlab
|
|
function [ry] = initializeRy(args)
|
|
arguments
|
|
args.rigid logical {mustBeNumericOrLogical} = false
|
|
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 = 800; % TODO [kg]
|
|
|
|
%% Tilt Stage - Dynamical Properties
|
|
if args.rigid
|
|
ry.k.tilt = 1e10; % Rotation stiffness around y [N*m/deg]
|
|
ry.k.h = 1e12; % Stiffness in the direction of the guidance [N/m]
|
|
ry.k.rad = 1e12; % Stiffness in the top direction [N/m]
|
|
ry.k.rrad = 1e12; % Stiffness in the side direction [N/m]
|
|
else
|
|
ry.k.tilt = 1e4; % Rotation stiffness around y [N*m/deg]
|
|
ry.k.h = 1e8; % Stiffness in the direction of the guidance [N/m]
|
|
ry.k.rad = 1e8; % Stiffness in the top direction [N/m]
|
|
ry.k.rrad = 1e8; % Stiffness in the side direction [N/m]
|
|
end
|
|
|
|
ry.c.h = 0.1*sqrt(ry.k.h*ry.m);
|
|
ry.c.rad = 0.1*sqrt(ry.k.rad*ry.m);
|
|
ry.c.rrad = 0.1*sqrt(ry.k.rrad*ry.m);
|
|
ry.c.tilt = 0.1*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 none :mkdirp yes :eval no
|
|
:END:
|
|
<<sec:initializeRz>>
|
|
|
|
This Matlab function is accessible [[file:../src/initializeRz.m][here]].
|
|
|
|
#+begin_src matlab
|
|
function [rz] = initializeRz(args)
|
|
arguments
|
|
args.rigid logical {mustBeNumericOrLogical} = false
|
|
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
|
|
|
|
if args.rigid
|
|
rz.k.rot = 1e10; % Rotational Stiffness (Rz) [N*m/deg]
|
|
rz.k.tilt = 1e10; % Rotational Stiffness (Rx, Ry) [N*m/deg]
|
|
rz.k.ax = 1e12; % Axial Stiffness (Z) [N/m]
|
|
rz.k.rad = 1e12; % Radial Stiffness (X, Y) [N/m]
|
|
else
|
|
rz.k.rot = 1e6; % TODO - Rotational Stiffness (Rz) [N*m/deg]
|
|
rz.k.tilt = 1e6; % Rotational Stiffness (Rx, Ry) [N*m/deg]
|
|
rz.k.ax = 2e9; % Axial Stiffness (Z) [N/m]
|
|
rz.k.rad = 7e8; % Radial Stiffness (X, Y) [N/m]
|
|
end
|
|
|
|
% Damping
|
|
rz.c.ax = 0.1*sqrt(rz.k.ax*rz.m);
|
|
rz.c.rad = 0.1*sqrt(rz.k.rad*rz.m);
|
|
rz.c.tilt = 0.1*sqrt(rz.k.tilt*rz.m);
|
|
rz.c.rot = 0.1*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 none :mkdirp yes :eval no
|
|
:END:
|
|
<<sec:initializeMicroHexapod>>
|
|
|
|
This Matlab function is accessible [[file:../src/initializeMicroHexapod.m][here]].
|
|
|
|
#+begin_src matlab
|
|
function [micro_hexapod] = initializeMicroHexapod(args)
|
|
arguments
|
|
args.rigid logical {mustBeNumericOrLogical} = false
|
|
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
|
|
args.ARB (3,3) double {mustBeNumeric} = eye(3)
|
|
end
|
|
|
|
%% Stewart Object
|
|
micro_hexapod = struct();
|
|
micro_hexapod.h = 350; % Total height of the platform [mm]
|
|
micro_hexapod.jacobian = 270; % Distance from the top of the mobile 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]
|
|
if args.rigid
|
|
Leg.k.ax = 1e12; % Stiffness of each leg [N/m]
|
|
else
|
|
Leg.k.ax = 2e7; % Stiffness of each leg [N/m]
|
|
end
|
|
Leg.ksi.ax = 0.1; % Modal damping ksi = 1/2*c/sqrt(km) []
|
|
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);
|
|
|
|
%% Setup equilibrium position of each leg
|
|
micro_hexapod.L0 = inverseKinematicsHexapod(micro_hexapod, args.AP, args.ARB);
|
|
|
|
%% 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}) = 2*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 none :mkdirp yes :eval no
|
|
: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 none :mkdirp yes :eval no
|
|
:END:
|
|
<<sec:initializeMirror>>
|
|
|
|
This Matlab function is accessible [[file:../src/initializeMirror.m][here]].
|
|
|
|
#+begin_src matlab
|
|
function [] = initializeMirror(args)
|
|
arguments
|
|
args.shape char {mustBeMember(args.shape,{'spherical', 'conical'})} = 'spherical'
|
|
args.angle (1,1) double {mustBeNumeric, mustBePositive} = 45
|
|
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(args.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(args.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(args.shape, 'conical')
|
|
mirror.shape = [mirror.shape; mirror.rad+mirror.h/tand(args.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 none :mkdirp yes :eval no
|
|
:END:
|
|
<<sec:initializeNanoHexapod>>
|
|
|
|
This Matlab function is accessible [[file:../src/initializeNanoHexapod.m][here]].
|
|
|
|
#+begin_src matlab
|
|
function [nano_hexapod] = initializeNanoHexapod(args)
|
|
arguments
|
|
args.actuator char {mustBeMember(args.actuator,{'piezo', 'lorentz'})} = 'piezo'
|
|
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
|
|
args.ARB (3,3) double {mustBeNumeric} = eye(3)
|
|
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]
|
|
|
|
%% 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(args.actuator, 'piezo')
|
|
Leg.k.ax = 1e7; % Stiffness of each leg [N/m]
|
|
elseif strcmp(args.actuator, 'lorentz')
|
|
Leg.k.ax = 1e4; % Stiffness of each leg [N/m]
|
|
else
|
|
error('args.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 = 0;
|
|
|
|
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);
|
|
|
|
%% Setup equilibrium position of each leg
|
|
nano_hexapod.L0 = inverseKinematicsHexapod(nano_hexapod, args.AP, args.ARB);
|
|
|
|
%% Save
|
|
save('./mat/stages.mat', 'nano_hexapod', '-append');
|
|
|
|
%%
|
|
function [element] = updateDamping(element)
|
|
field = fieldnames(element.k);
|
|
for i = 1:length(field)
|
|
if element.ksi.(field{i}) > 0
|
|
element.c.(field{i}) = 1/element.ksi.(field{i})*sqrt(element.k.(field{i})/element.m);
|
|
else
|
|
element.c.(field{i}) = 0;
|
|
end
|
|
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
|
|
|
|
** Cedrat Actuator
|
|
:PROPERTIES:
|
|
:header-args:matlab+: :tangle ../src/initializeCedratPiezo.m
|
|
:header-args:matlab+: :comments none :mkdirp yes :eval no
|
|
:END:
|
|
<<sec:initializeCedratPiezo>>
|
|
|
|
This Matlab function is accessible [[file:../src/initializeCedratPiezo.m][here]].
|
|
|
|
#+begin_src matlab
|
|
function [cedrat] = initializeCedratPiezo()
|
|
%% Stewart Object
|
|
cedrat = struct();
|
|
cedrat.k = 10e7; % Linear Stiffness of each "blade" [N/m]
|
|
cedrat.ka = 10e7; % Linear Stiffness of the stack [N/m]
|
|
|
|
cedrat.c = 0.1*sqrt(1*cedrat.k); % [N/(m/s)]
|
|
cedrat.ca = 0.1*sqrt(1*cedrat.ka); % [N/(m/s)]
|
|
|
|
cedrat.L = 80; % Total Width of the Actuator[mm]
|
|
cedrat.H = 45; % Total Height of the Actuator [mm]
|
|
cedrat.L2 = sqrt((cedrat.L/2)^2 + (cedrat.H/2)^2); % Length of the elipsoidal sections [mm]
|
|
cedrat.alpha = 180/pi*atan2(cedrat.L/2, cedrat.H/2); % [deg]
|
|
|
|
%% Save
|
|
save('./mat/stages.mat', 'cedrat', '-append');
|
|
end
|
|
#+end_src
|
|
|
|
** Sample
|
|
:PROPERTIES:
|
|
:header-args:matlab+: :tangle ../src/initializeSample.m
|
|
:header-args:matlab+: :comments none :mkdirp yes :eval no
|
|
:END:
|
|
<<sec:initializeSample>>
|
|
|
|
This Matlab function is accessible [[file:../src/initializeSample.m][here]].
|
|
|
|
#+begin_src matlab
|
|
function [sample] = initializeSample(sample)
|
|
arguments
|
|
sample.radius (1,1) double {mustBeNumeric, mustBePositive} = 100 % [mm]
|
|
sample.height (1,1) double {mustBeNumeric, mustBePositive} = 300 % [mm]
|
|
sample.mass (1,1) double {mustBeNumeric, mustBePositive} = 50 % [kg]
|
|
sample.freq (1,1) double {mustBeNumeric, mustBePositive} = 100 % [Hz]
|
|
sample.offset (1,1) double {mustBeNumeric} = 0 % [mm]
|
|
sample.color (1,3) double {mustBeNumeric} = [0.45, 0.45, 0.45]
|
|
end
|
|
|
|
%%
|
|
sample.k.x = sample.mass * (2*pi * sample.freq)^2;
|
|
sample.c.x = 0.1*sqrt(sample.k.x*sample.mass);
|
|
|
|
sample.k.y = sample.mass * (2*pi * sample.freq)^2;
|
|
sample.c.y = 0.1*sqrt(sample.k.y*sample.mass);
|
|
|
|
sample.k.z = sample.mass * (2*pi * sample.freq)^2;
|
|
sample.c.z = 0.1*sqrt(sample.k.z*sample.mass);
|
|
|
|
%% Save
|
|
save('./mat/stages.mat', 'sample', '-append');
|
|
end
|
|
#+end_src
|