Cleaning of the files. Add script for identification with varying mass

analyze_jacobian.m

@@ -1,3 +1,6 @@
+%% Script Description
+% 
+
 figure;
 plot(d_meas.Time, d.Data-d_meas.Data)
 

identification_cart.m

@@ -11,17 +11,17 @@ initializeNanoHexapod();
 %%
 initializeSample(struct('mass', 0));
 
-G_cart_0 = getPlantCart();
+G_cart_0 = identifyPlantCart();
 
 %%
 initializeSample(struct('mass', 10));
 
-G_cart_10 = getPlantCart();
+G_cart_10 = identifyPlantCart();
 
 %%
 initializeSample(struct('mass', 50));
 
-G_cart_50 = getPlantCart();
+G_cart_50 = identifyPlantCart();
 
 %%
 freqs = logspace(1, 4, 1000);
@@ -54,30 +54,3 @@ exportFig('hexapod_cart_coupling', 'normal-normal')
 
 %% Save identify transfer functions
 save('./mat/G_cart.mat', 'G_cart_0', 'G_cart_10', 'G_cart_50');
-
-%% Centralized control (Cartesian coordinates)
-% Input/Output definition
-io(1) = linio([mdl, '/F_legs'],1,'input');
-io(2) = linio([mdl, '/Stewart_Platform'],2,'output');
-
-% Run the linearization
-G_legs_raw = linearize(mdl,io, 0);
-
-G_legs = preprocessIdTf(G_legs_raw, 10, 10000);
-
-% Input/Output names
-G_legs.InputName  = {'F1', 'F2', 'F3', 'M4', 'M5', 'M6'};
-G_legs.OutputName = {'D1', 'D2', 'D3', 'R4', 'R5', 'R6'};
-
-% Bode Plot of the linearized function
-freqs = logspace(2, 4, 1000);
-
-bodeFig({G_legs(1, 1)}, freqs, struct('phase', true))
-legend({'$F_i \rightarrow D_i$'})
-exportFig('hexapod_legs', 'normal-normal')
-
-bodeFig({G_legs(1, 1), G_legs(2, 1)}, freqs, struct('phase', true))
-legend({'$F_i \rightarrow D_i$', '$F_i \rightarrow D_j$'})
-exportFig('hexapod_legs_coupling', 'normal-normal')
-
-save('mat/G_legs.mat', 'G_legs');

identification_legs.m

@@ -0,0 +1,45 @@
+%% Script Description
+% Script used to identify the transfer functions of the
+% Stewart platform (from actuator to displacement)
+
+%%
+clear; close all; clc;
+
+%%
+initializeNanoHexapod();
+
+%%
+initializeSample(struct('mass', 0));
+
+G_legs_0 = identifyPlantLegs();
+
+%%
+initializeSample(struct('mass', 10));
+
+G_legs_10 = identifyPlantLegs();
+
+%%
+initializeSample(struct('mass', 50));
+
+G_legs_50 = identifyPlantLegs();
+
+%%
+freqs = logspace(1, 4, 1000);
+
+bodeFig({G_legs_0(1, 1), G_legs_10(1, 1), G_legs_50(1, 1)}, freqs, struct('phase', true))
+legend({'$F_i \rightarrow D_i$ - $M = 0Kg$', '$F_i \rightarrow D_i$ - $M = 10Kg$', '$F_i \rightarrow D_i$ - $M = 50Kg$'})
+legend('location', 'southwest')
+
+exportFig('hexapod_legs_mass', 'normal-tall')
+
+%%
+freqs = logspace(1, 4, 1000);
+
+bodeFig({G_legs_0(1, 2), G_legs_10(1, 2), G_legs_50(1, 2)}, freqs, struct('phase', true))
+legend({'$F_i \rightarrow D_j$ - $M = 0Kg$', '$F_i \rightarrow D_j$ - $M = 10Kg$', '$F_i \rightarrow D_j$ - $M = 50Kg$'})
+legend('location', 'southwest')
+
+exportFig('hexapod_legs_coupling_mass', 'normal-tall')
+
+%% Save identify transfer functions
+save('./mat/G_legs.mat', 'G_legs_0', 'G_legs_10', 'G_legs_50');

init_simulink.m

@@ -1,2 +1,6 @@
+%% Script Description
+% 
+
+%% Load the sample and the stewart platform
 load('./mat/sample.mat', 'sample')
 load('./mat/stewart.mat', 'stewart')

params_micro_hexapod.m

@@ -1,90 +0,0 @@
-%% Stewart Object
-stewart = struct();
-stewart.h        = 350; % Total height of the platform [mm]
-stewart.jacobian = 435; % Point where the Jacobian is computed => Center of rotation [mm]
-
-%% Bottom Plate
-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
-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];
-
-%% Leg
-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];
-
-%%
-stewart.BP = BP;
-stewart.TP = TP;
-stewart.Leg = Leg;
-stewart.SP = SP;
-
-%%
-stewart = initializeParameters(stewart);
-
-%%
-clear BP TP Leg SP;
-
-%%
-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

params_nano_hexapod.m

@@ -1,90 +0,0 @@
-%% Stewart Object
-stewart = struct();
-stewart.h        = 90;    % Total height of the platform [mm]
-stewart.jacobian = 174.5; % 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]
-Leg.k.ax       = 5e7;   % Stiffness of each leg [N/m]
-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];
-
-%%
-stewart.BP = BP;
-stewart.TP = TP;
-stewart.Leg = Leg;
-stewart.SP = SP;
-
-%%
-stewart = initializeParameters(stewart);
-
-%%
-clear BP TP Leg SP;
-
-%%
-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

plot_max_positions.m

@@ -1,10 +1,16 @@
-%%
+%% Script Description
-run stewart_parameters.m
+% 
-run stewart_init.m
 
 %%
-[X, Y, Z] = getMaxPositions(Leg, J);
+clear; close all; clc;
 
+%%
+init_simulink;
+
+%%
+[X, Y, Z] = getMaxPositions(stewart);
+
+%%
 figure;
 hold on;
 mesh(X, Y, Z);

readme.org

@@ -1,2 +1,5 @@
 * Stewart Platform using Simscape
 
+* TODO Add functions to identify transmissibility and sensitivity
+* TODO Rewrite the script to study the effect of various parameters on the stiffness/stroke/...
+* TODO Rewrite the function to study the jacobian, or delete it.

src/getMaxPositions.m

@@ -1,4 +1,6 @@
-function [X, Y, Z] = getMaxPositions(Leg, J)
+function [X, Y, Z] = getMaxPositions(stewart)
+    Leg = stewart.Leg;
+    J = stewart.J;
     theta = linspace(0, 2*pi, 100);
     phi = linspace(-pi/2 , pi/2, 100);
     dmax = zeros(length(theta), length(phi));

src/identifyPlantCart.m

@@ -1,4 +1,4 @@
-function [G_cart, G_cart_raw] = getPlantCart()
+function [G_cart, G_cart_raw] = identifyPlantCart()
     %% Default values for opts
     opts = struct('f_low', 1,...
                   'f_high', 10000 ...

src/identifyPlantLegs.m

@@ -0,0 +1,35 @@
+function [G_legs, G_legs_raw] = identifyPlantLegs()
+    %% Default values for opts
+    opts = struct('f_low',  1,    ...
+                  'f_high', 10000 ...
+    );
+
+    %% 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 = 'stewart_simscape';
+
+    %% Centralized control (Cartesian coordinates)
+    % Input/Output definition
+    io(1) = linio([mdl, '/F_legs'],          1,'input');
+    io(2) = linio([mdl, '/Stewart_Platform'],2,'output');
+
+    % Run the linearization
+    G_legs_raw = linearize(mdl,io, 0);
+
+    G_legs = preprocessIdTf(G_legs_raw, opts.f_low, opts.f_high);
+
+    % Input/Output names
+    G_legs.InputName  = {'F1', 'F2', 'F3', 'M4', 'M5', 'M6'};
+    G_legs.OutputName = {'D1', 'D2', 'D3', 'R4', 'R5', 'R6'};
+end
+

study_architecture.m

@@ -1,4 +1,8 @@
-%% TODO - rewrite this script
+%% Script Description
+% 
+
+%%
+clear; close all; clc;
 
 %%
 run stewart_parameters.m