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Thomas Dehaeze
2025-04-14 18:38:19 +02:00
parent 3cc2105324
commit 37cd117a8f
859 changed files with 5418446 additions and 0 deletions
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54
C4-test-bench-nano-hexapod/mat/APA300ML_b_out_nodes_3D.txt Normal file
View File

@@ -0,0 +1,54 @@
LIST ALL SELECTED NODES. DSYS= 0
*** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 ***
DISTRIBUTED ANSYS Mechanical Enterprise
00208316 VERSION=WINDOWS x64 11:07:02 MAR 25, 2021 CP= 2.062
Unknown
NODE X Y Z THXY THYZ THZX
840914 0.0000 0.0000 0.28000E-001 0.00 0.00 0.00
840915 0.0000 0.0000 -0.28000E-001 0.00 0.00 0.00
840916 -0.34000E-001 0.0000 0.0000 0.00 0.00 0.00
840917 0.34000E-001 0.0000 0.0000 0.00 0.00 0.00
LIST MASTERS ON ALL SELECTED NODES.
CURRENT DOF SET= UX UY UZ ROTX ROTY ROTZ
*** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 ***
DISTRIBUTED ANSYS Mechanical Enterprise
00208316 VERSION=WINDOWS x64 11:07:02 MAR 25, 2021 CP= 2.188
Unknown
NODE LABEL SUPPORT
840914 UX
840914 UY
840914 UZ
840914 ROTX
840914 ROTY
840914 ROTZ
840915 UX
840915 UY
840915 UZ
840915 ROTX
840915 ROTY
840915 ROTZ
840916 UX
840916 UY
840916 UZ
840916 ROTX
840916 ROTY
840916 ROTZ
840917 UX
840917 UY
840917 UZ
840917 ROTX
840917 ROTY
840917 ROTZ

36
C4-test-bench-nano-hexapod/mat/full_APA300ML_K.CSV Normal file
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61
C4-test-bench-nano-hexapod/mat/full_APA300ML_out_nodes_3D.txt Normal file
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@@ -0,0 +1,61 @@
LIST ALL SELECTED NODES. DSYS= 0
*** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 ***
DISTRIBUTED ANSYS Mechanical Enterprise
00208316 VERSION=WINDOWS x64 10:10:05 MAR 26, 2021 CP= 2.188
Unknown
NODE X Y Z THXY THYZ THZX
1 0.0000 0.0000 0.28000E-001 0.00 0.00 0.00
1228810 0.0000 0.0000 -0.28000E-001 0.00 0.00 0.00
1228811 -0.30000E-001 0.0000 0.0000 0.00 0.00 0.00
1228812 0.10000E-001 0.0000 0.0000 0.00 0.00 0.00
1228813 0.30000E-001 0.0000 0.0000 0.00 0.00 0.00
LIST MASTERS ON ALL SELECTED NODES.
CURRENT DOF SET= UX UY UZ ROTX ROTY ROTZ
*** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 ***
DISTRIBUTED ANSYS Mechanical Enterprise
00208316 VERSION=WINDOWS x64 10:10:05 MAR 26, 2021 CP= 2.188
Unknown
NODE LABEL SUPPORT
1 UX
1 UY
1 UZ
1 ROTX
1 ROTY
1 ROTZ
1228810 UX
1228810 UY
1228810 UZ
1228810 ROTX
1228810 ROTY
1228810 ROTZ
1228811 UX
1228811 UY
1228811 UZ
1228811 ROTX
1228811 ROTY
1228811 ROTZ
1228812 UX
1228812 UY
1228812 UZ
1228812 ROTX
1228812 ROTY
1228812 ROTZ
1228813 UX
1228813 UY
1228813 UZ
1228813 ROTX
1228813 ROTY
1228813 ROTZ

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C4-test-bench-nano-hexapod/src/extractNodes.m Normal file
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function [int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes(filename)
% extractNodes -
%
% Syntax: [n_xyz, nodes] = extractNodes(filename)
%
% Inputs:
% - filename - relative or absolute path of the file that contains the Matrix
%
% Outputs:
% - n_xyz -
% - nodes - table containing the node numbers and corresponding dof of the interfaced DoFs
arguments
filename
end
fid = fopen(filename,'rt');
if fid == -1
error('Error opening the file');
end
n_xyz = []; % Contains nodes coordinates
n_i = []; % Contains nodes indices
n_num = []; % Contains node numbers
n_dof = {}; % Contains node directions
while 1
% Read a line
nextline = fgetl(fid);
% End of the file
if ~isstr(nextline), break, end
% Line just before the list of nodes coordinates
if contains(nextline, 'NODE') && ...
contains(nextline, 'X') && ...
contains(nextline, 'Y') && ...
contains(nextline, 'Z')
while 1
nextline = fgetl(fid);
if nextline < 0, break, end
c = sscanf(nextline, ' %f');
if isempty(c), break, end
n_xyz = [n_xyz; c(2:4)'];
n_i = [n_i; c(1)];
end
end
if nextline < 0, break, end
% Line just before the list of node DOF
if contains(nextline, 'NODE LABEL')
while 1
nextline = fgetl(fid);
if nextline < 0, break, end
c = sscanf(nextline, ' %d %s');
if isempty(c), break, end
n_num = [n_num; c(1)];
n_dof{length(n_dof)+1} = char(c(2:end)');
end
nodes = table(n_num, string(n_dof'), 'VariableNames', {'node_i', 'node_dof'});
end
if nextline < 0, break, end
end
fclose(fid);
int_i = unique(nodes.('node_i')); % indices of interface nodes
% Extract XYZ coordinates of only the interface nodes
if length(n_xyz) > 0 && length(n_i) > 0
int_xyz = n_xyz(logical(sum(n_i.*ones(1, length(int_i)) == int_i', 2)), :);
else
int_xyz = n_xyz;
end

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function [nano_hexapod] = initializeNanoHexapod(args)
arguments
%% Bottom Flexible Joints
args.flex_bot_type char {mustBeMember(args.flex_bot_type,{'2dof', '3dof', '4dof', 'flexible'})} = '4dof'
args.flex_bot_kRx (6,1) double {mustBeNumeric} = ones(6,1)*5 % X bending stiffness [Nm/rad]
args.flex_bot_kRy (6,1) double {mustBeNumeric} = ones(6,1)*5 % Y bending stiffness [Nm/rad]
args.flex_bot_kRz (6,1) double {mustBeNumeric} = ones(6,1)*260 % Torsionnal stiffness [Nm/rad]
args.flex_bot_kz (6,1) double {mustBeNumeric} = ones(6,1)*7e7 % Axial Stiffness [N/m]
args.flex_bot_cRx (6,1) double {mustBeNumeric} = ones(6,1)*0.001 % X bending Damping [Nm/(rad/s)]
args.flex_bot_cRy (6,1) double {mustBeNumeric} = ones(6,1)*0.001 % Y bending Damping [Nm/(rad/s)]
args.flex_bot_cRz (6,1) double {mustBeNumeric} = ones(6,1)*0.001 % Torsionnal Damping [Nm/(rad/s)]
args.flex_bot_cz (6,1) double {mustBeNumeric} = ones(6,1)*0.001 % Axial Damping [N/(m/s)]
%% Top Flexible Joints
args.flex_top_type char {mustBeMember(args.flex_top_type,{'2dof', '3dof', '4dof', 'flexible'})} = '4dof'
args.flex_top_kRx (6,1) double {mustBeNumeric} = ones(6,1)*5 % X bending stiffness [Nm/rad]
args.flex_top_kRy (6,1) double {mustBeNumeric} = ones(6,1)*5 % Y bending stiffness [Nm/rad]
args.flex_top_kRz (6,1) double {mustBeNumeric} = ones(6,1)*260 % Torsionnal stiffness [Nm/rad]
args.flex_top_kz (6,1) double {mustBeNumeric} = ones(6,1)*7e7 % Axial Stiffness [N/m]
args.flex_top_cRx (6,1) double {mustBeNumeric} = ones(6,1)*0.001 % X bending Damping [Nm/(rad/s)]
args.flex_top_cRy (6,1) double {mustBeNumeric} = ones(6,1)*0.001 % Y bending Damping [Nm/(rad/s)]
args.flex_top_cRz (6,1) double {mustBeNumeric} = ones(6,1)*0.001 % Torsionnal Damping [Nm/(rad/s)]
args.flex_top_cz (6,1) double {mustBeNumeric} = ones(6,1)*0.001 % Axial Damping [N/(m/s)]
%% Jacobian - Location of frame {A} and {B}
args.MO_B (1,1) double {mustBeNumeric} = 150e-3 % Height of {B} w.r.t. {M} [m]
%% Relative Motion Sensor
args.motion_sensor_type char {mustBeMember(args.motion_sensor_type,{'struts', 'plates'})} = 'struts'
%% Top Plate
args.top_plate_type char {mustBeMember(args.top_plate_type,{'rigid', 'flexible'})} = 'rigid'
args.top_plate_xi (1,1) double {mustBeNumeric} = 0.01 % Damping Ratio
%% Actuators
args.actuator_type char {mustBeMember(args.actuator_type,{'2dof', 'flexible frame', 'flexible'})} = 'flexible'
args.actuator_Ga (6,1) double {mustBeNumeric} = zeros(6,1) % Actuator gain [N/V]
args.actuator_Gs (6,1) double {mustBeNumeric} = zeros(6,1) % Sensor gain [V/m]
% For 2DoF
args.actuator_k (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*380000
args.actuator_ke (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*4952605
args.actuator_ka (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*2476302
args.actuator_c (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*5
args.actuator_ce (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*100
args.actuator_ca (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*50
args.actuator_Leq (6,1) double {mustBeNumeric} = ones(6,1)*0.056 % [m]
% For Flexible Frame
args.actuator_ks (6,1) double {mustBeNumeric} = ones(6,1)*235e6 % Stiffness of one stack [N/m]
args.actuator_cs (6,1) double {mustBeNumeric} = ones(6,1)*1e1 % Stiffness of one stack [N/m]
% Misalignment
args.actuator_d_align (6,3) double {mustBeNumeric} = zeros(6,3) % [m]
args.actuator_xi (1,1) double {mustBeNumeric} = 0.01 % Damping Ratio
%% Controller
args.controller_type char {mustBeMember(args.controller_type,{'none', 'iff', 'dvf', 'hac-iff-struts'})} = 'none'
end
nano_hexapod = struct();
nano_hexapod.flex_bot = struct();
switch args.flex_bot_type
case '2dof'
nano_hexapod.flex_bot.type = 1;
case '3dof'
nano_hexapod.flex_bot.type = 2;
case '4dof'
nano_hexapod.flex_bot.type = 3;
case 'flexible'
nano_hexapod.flex_bot.type = 4;
end
nano_hexapod.flex_bot.kRx = args.flex_bot_kRx; % X bending stiffness [Nm/rad]
nano_hexapod.flex_bot.kRy = args.flex_bot_kRy; % Y bending stiffness [Nm/rad]
nano_hexapod.flex_bot.kRz = args.flex_bot_kRz; % Torsionnal stiffness [Nm/rad]
nano_hexapod.flex_bot.kz = args.flex_bot_kz; % Axial stiffness [N/m]
nano_hexapod.flex_bot.cRx = args.flex_bot_cRx; % [Nm/(rad/s)]
nano_hexapod.flex_bot.cRy = args.flex_bot_cRy; % [Nm/(rad/s)]
nano_hexapod.flex_bot.cRz = args.flex_bot_cRz; % [Nm/(rad/s)]
nano_hexapod.flex_bot.cz = args.flex_bot_cz; %[N/(m/s)]
nano_hexapod.flex_top = struct();
switch args.flex_top_type
case '2dof'
nano_hexapod.flex_top.type = 1;
case '3dof'
nano_hexapod.flex_top.type = 2;
case '4dof'
nano_hexapod.flex_top.type = 3;
case 'flexible'
nano_hexapod.flex_top.type = 4;
end
nano_hexapod.flex_top.kRx = args.flex_top_kRx; % X bending stiffness [Nm/rad]
nano_hexapod.flex_top.kRy = args.flex_top_kRy; % Y bending stiffness [Nm/rad]
nano_hexapod.flex_top.kRz = args.flex_top_kRz; % Torsionnal stiffness [Nm/rad]
nano_hexapod.flex_top.kz = args.flex_top_kz; % Axial stiffness [N/m]
nano_hexapod.flex_top.cRx = args.flex_top_cRx; % [Nm/(rad/s)]
nano_hexapod.flex_top.cRy = args.flex_top_cRy; % [Nm/(rad/s)]
nano_hexapod.flex_top.cRz = args.flex_top_cRz; % [Nm/(rad/s)]
nano_hexapod.flex_top.cz = args.flex_top_cz; %[N/(m/s)]
nano_hexapod.motion_sensor = struct();
switch args.motion_sensor_type
case 'struts'
nano_hexapod.motion_sensor.type = 1;
case 'plates'
nano_hexapod.motion_sensor.type = 2;
end
nano_hexapod.actuator = struct();
switch args.actuator_type
case '2dof'
nano_hexapod.actuator.type = 1;
case 'flexible frame'
nano_hexapod.actuator.type = 2;
case 'flexible'
nano_hexapod.actuator.type = 3;
end
%% Actuator gain [N/V]
if all(args.actuator_Ga == 0)
switch args.actuator_type
case '2dof'
nano_hexapod.actuator.Ga = ones(6,1)*(-2.5796);
case 'flexible frame'
nano_hexapod.actuator.Ga = ones(6,1); % TODO
case 'flexible'
nano_hexapod.actuator.Ga = ones(6,1)*23.2;
end
else
nano_hexapod.actuator.Ga = args.actuator_Ga; % Actuator gain [N/V]
end
%% Sensor gain [V/m]
if all(args.actuator_Gs == 0)
switch args.actuator_type
case '2dof'
nano_hexapod.actuator.Gs = ones(6,1)*466664;
case 'flexible frame'
nano_hexapod.actuator.Gs = ones(6,1); % TODO
case 'flexible'
nano_hexapod.actuator.Gs = ones(6,1)*(-4898341);
end
else
nano_hexapod.actuator.Gs = args.actuator_Gs; % Sensor gain [V/m]
end
switch args.actuator_type
case '2dof'
nano_hexapod.actuator.k = args.actuator_k; % [N/m]
nano_hexapod.actuator.ke = args.actuator_ke; % [N/m]
nano_hexapod.actuator.ka = args.actuator_ka; % [N/m]
nano_hexapod.actuator.c = args.actuator_c; % [N/(m/s)]
nano_hexapod.actuator.ce = args.actuator_ce; % [N/(m/s)]
nano_hexapod.actuator.ca = args.actuator_ca; % [N/(m/s)]
nano_hexapod.actuator.Leq = args.actuator_Leq; % [m]
case 'flexible frame'
nano_hexapod.actuator.K = readmatrix('APA300ML_b_mat_K.CSV'); % Stiffness Matrix
nano_hexapod.actuator.M = readmatrix('APA300ML_b_mat_M.CSV'); % Mass Matrix
nano_hexapod.actuator.P = extractNodes('APA300ML_b_out_nodes_3D.txt'); % Node coordinates [m]
nano_hexapod.actuator.ks = args.actuator_ks; % Stiffness of one stack [N/m]
nano_hexapod.actuator.cs = args.actuator_cs; % Damping of one stack [N/m]
nano_hexapod.actuator.xi = args.actuator_xi; % Damping ratio
case 'flexible'
nano_hexapod.actuator.K = readmatrix('full_APA300ML_K.CSV'); % Stiffness Matrix
nano_hexapod.actuator.M = readmatrix('full_APA300ML_M.CSV'); % Mass Matrix
nano_hexapod.actuator.P = extractNodes('full_APA300ML_out_nodes_3D.txt'); % Node coordiantes [m]
nano_hexapod.actuator.d_align = args.actuator_d_align; % Misalignment
nano_hexapod.actuator.xi = args.actuator_xi; % Damping ratio
end
nano_hexapod.geometry = struct();
Fa = [[-86.05, -74.78, 22.49],
[ 86.05, -74.78, 22.49],
[ 107.79, -37.13, 22.49],
[ 21.74, 111.91, 22.49],
[-21.74, 111.91, 22.49],
[-107.79, -37.13, 22.49]]'*1e-3; % Ai w.r.t. {F} [m]
Mb = [[-28.47, -106.25, -22.50],
[ 28.47, -106.25, -22.50],
[ 106.25, 28.47, -22.50],
[ 77.78, 77.78, -22.50],
[-77.78, 77.78, -22.50],
[-106.25, 28.47, -22.50]]'*1e-3; % Bi w.r.t. {M} [m]
Fb = Mb + [0; 0; 95e-3]; % Bi w.r.t. {F} [m]
si = Fb - Fa;
si = si./vecnorm(si); % Normalize
Fc = [[-29.362, -105.765, 52.605]
[ 29.362, -105.765, 52.605]
[ 106.276, 27.454, 52.605]
[ 76.914, 78.31, 52.605]
[-76.914, 78.31, 52.605]
[-106.276, 27.454, 52.605]]'*1e-3; % Meas pos w.r.t. {F}
Mc = Fc - [0; 0; 95e-3]; % Meas pos w.r.t. {M}
nano_hexapod.geometry.Fa = Fa;
nano_hexapod.geometry.Fb = Fb;
nano_hexapod.geometry.Fc = Fc;
nano_hexapod.geometry.Mb = Mb;
nano_hexapod.geometry.Mc = Mc;
nano_hexapod.geometry.si = si;
nano_hexapod.geometry.MO_B = args.MO_B;
Bb = Mb - [0; 0; args.MO_B];
nano_hexapod.geometry.J = [nano_hexapod.geometry.si', cross(Bb, nano_hexapod.geometry.si)'];
switch args.motion_sensor_type
case 'struts'
nano_hexapod.geometry.Js = nano_hexapod.geometry.J;
case 'plates'
Bc = Mc - [0; 0; args.MO_B];
nano_hexapod.geometry.Js = [nano_hexapod.geometry.si', cross(Bc, nano_hexapod.geometry.si)'];
end
nano_hexapod.top_plate = struct();
switch args.top_plate_type
case 'rigid'
nano_hexapod.top_plate.type = 1;
case 'flexible'
nano_hexapod.top_plate.type = 2;
nano_hexapod.top_plate.R_flex = ...
{[ 0.53191886726305 0.4795690716524 0.69790817745892
-0.29070157897799 0.8775041341865 -0.38141720787774
-0.79533320729697 0 0.60617249143351 ],
[ 0.53191886726305 -0.4795690716524 -0.69790817745892
0.29070157897799 0.8775041341865 -0.38141720787774
0.79533320729697 0 0.60617249143351 ],
[-0.01420448131633 -0.9997254079576 -0.01863709726680
0.60600604129104 -0.0234330681729 0.79511481512719
-0.79533320729697 0 0.60617249143351 ],
[-0.51771438594672 -0.5201563363051 0.67927108019212
0.31530446231304 -0.8540710660135 -0.41369760724945
0.79533320729697 0 0.60617249143351 ],
[-0.51771438594671 0.5201563363052 -0.67927108019211
-0.31530446231304 -0.8540710660135 -0.41369760724945
-0.79533320729697 0 0.60617249143351 ],
[-0.01420448131632 0.9997254079576 0.01863709726679
-0.60600604129104 -0.0234330681729 0.79511481512719
0.79533320729697 0 0.60617249143351 ] };
nano_hexapod.top_plate.R_enc = ...
{ [-0.877504134186525 -0.479569071652412 0
0.479569071652412 -0.877504134186525 0
0 0 1 ],
[ 0.877504134186525 -0.479569071652413 0
0.479569071652413 0.877504134186525 0
0 0 1 ],
[ 0.023433068172945 0.999725407957606 0
-0.999725407957606 0.023433068172945 0
0 0 1 ],
[-0.854071066013566 -0.520156336305202 0
0.520156336305202 -0.854071066013566 0
0 0 1 ],
[ 0.854071066013574 -0.520156336305191 0
0.520156336305191 0.854071066013574 0
0 0 1 ],
[-0.023433068172958 0.999725407957606 0
-0.999725407957606 -0.023433068172958 0
0 0 1 ] };
nano_hexapod.top_plate.K = readmatrix('top_plate_K_6.CSV'); % Stiffness Matrix
nano_hexapod.top_plate.M = readmatrix('top_plate_M_6.CSV'); % Mass Matrix
nano_hexapod.top_plate.P = extractNodes('top_plate_out_nodes_3D_qua.txt'); % Node coordiantes [m]
nano_hexapod.top_plate.xi = args.top_plate_xi; % Damping ratio
end

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%% test_nhexa_1_suspended_table.m
%% Clear Workspace and Close figures
clear; close all; clc;
%% Intialize Laplace variable
s = zpk('s');
%% Path for functions, data and scripts
addpath('./mat/'); % Path for Data
addpath('./src/'); % Path for functions
addpath('./STEPS/'); % Path for STEPS
addpath('./subsystems/'); % Path for Subsystems Simulink files
%% Initialize Parameters for Simscape model
table_type = 'Rigid'; % On top of vibration table
device_type = 'None'; % On top of vibration table
payload_num = 0; % No Payload
% Simulink Model name
mdl = 'test_nhexa_simscape';
%% Colors for the figures
colors = colororder;
%% Frequency Vector
freqs = logspace(log10(10), log10(2e3), 1000);
%% Configure Simscape Model
table_type = 'Suspended'; % On top of vibration table
device_type = 'None'; % No device on the vibration table
payload_num = 0; % No Payload
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1;
io(io_i) = linio([mdl, '/F_v'], 1, 'openoutput'); io_i = io_i + 1;
%% Run the linearization
G = linearize(mdl, io);
G.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
G.OutputName = {'Vdx', 'Vdy', 'Vdz', 'Vrx', 'Vry', 'Vrz'};
%% Compute the resonance frequencies
ws = eig(G.A);
ws = ws(imag(ws) > 0);

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%% test_nhexa_2_dynamics.m
% Identification of the nano-hexapod dynamics from u to de and to Vs
% Encoders are fixed to the plates
%% Clear Workspace and Close figures
clear; close all; clc;
%% Intialize Laplace variable
s = zpk('s');
%% Path for functions, data and scripts
addpath('./mat/'); % Path for Data
addpath('./src/'); % Path for functions
addpath('./STEPS/'); % Path for STEPS
addpath('./subsystems/'); % Path for Subsystems Simulink files
%% Colors for the figures
colors = colororder;
%% Frequency Vector
freqs = logspace(log10(10), log10(2e3), 1000);
%% Identification of the transfer function from u to de and from u to Vs without payload
% Load identification data
load('test_nhexa_identification_data_mass_0.mat', 'data');
% Setup useful variables
Ts = 1e-4; % Sampling Time [s]
Nfft = floor(1/Ts); % Number of points for the FFT computation
win = hanning(Nfft); % Hanning window
Noverlap = floor(Nfft/2); % Overlap between frequency analysis
% And we get the frequency vector
[~, f] = tfestimate(data{1}.u, data{1}.de, win, Noverlap, Nfft, 1/Ts);
% Transfer function from u to de
G_de = zeros(length(f), 6, 6);
for i = 1:6
G_de(:,:,i) = tfestimate(data{i}.u, data{i}.de, win, Noverlap, Nfft, 1/Ts);
end
% Transfer function from u to Vs
G_Vs = zeros(length(f), 6, 6);
for i = 1:6
G_Vs(:,:,i) = tfestimate(data{i}.u, data{i}.Vs, win, Noverlap, Nfft, 1/Ts);
end
%% Bode plot for the transfer function from u to de
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
ax1 = nexttile([2,1]);
hold on;
for i = 1:5
for j = i+1:6
plot(f, abs(G_de(:, i, j)), 'color', [0, 0, 0, 0.2], ...
'HandleVisibility', 'off');
end
end
for i =1:6
set(gca,'ColorOrderIndex',i)
plot(f, abs(G_de(:,i, i)), ...
'DisplayName', sprintf('$d_{e,%i}/u_%i$', i, i));
end
plot(f, abs(G_de(:, 1, 2)), 'color', [0, 0, 0, 0.2], ...
'DisplayName', '$d_{e,i}/u_j$');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/V]'); set(gca, 'XTickLabel',[]);
ylim([1e-8, 5e-4]);
leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 4);
leg.ItemTokenSize(1) = 15;
ax2 = nexttile;
hold on;
for i =1:6
set(gca,'ColorOrderIndex',i)
plot(f, 180/pi*angle(G_de(:,i, i)));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
yticks(-360:90:360);
linkaxes([ax1,ax2],'x');
xlim([10, 2e3]);
%% Bode plot of the IFF Plant (transfer function from u to Vs)
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
ax1 = nexttile([2,1]);
hold on;
for i = 1:5
for j = i+1:6
plot(f, abs(G_Vs(:, i, j)), 'color', [0, 0, 0, 0.2], ...
'HandleVisibility', 'off');
end
end
for i =1:6
set(gca,'ColorOrderIndex',i)
plot(f, abs(G_Vs(:,i , i)), ...
'DisplayName', sprintf('$V_{s%i}/u_%i$', i, i));
end
plot(f, abs(G_Vs(:, 1, 2)), 'color', [0, 0, 0, 0.2], ...
'DisplayName', '$V_{si}/u_j$');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [V/V]'); set(gca, 'XTickLabel',[]);
leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 4);
leg.ItemTokenSize(1) = 15;
ylim([1e-3, 6e1]);
ax2 = nexttile;
hold on;
for i =1:6
set(gca,'ColorOrderIndex',i)
plot(f, 180/pi*angle(G_Vs(:,i, i)));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
yticks(-360:90:360);
linkaxes([ax1,ax2],'x');
xlim([10, 2e3]);
%% Set to true only if all the FRF matrices should again computed
% from the experimental data
compute_frf = false;
if compute_frf
%% Identification of the FRF matrices from u to de and to Vs
% Load identification Data
meas_added_mass = {...
load('test_nhexa_identification_data_mass_0.mat', 'data'), ....
load('test_nhexa_identification_data_mass_1.mat', 'data'), ....
load('test_nhexa_identification_data_mass_2.mat', 'data'), ....
load('test_nhexa_identification_data_mass_3.mat', 'data')};
% Setup useful variables
Ts = 1e-4; % Sampling Time [s]
Nfft = floor(1/Ts); % Number of points for the FFT computation
win = hanning(Nfft); % Hanning window
Noverlap = floor(Nfft/2); % Overlap between frequency analysis
% And we get the frequency vector
[~, f] = tfestimate(meas_added_mass{1}.data{1}.u, meas_added_mass{1}.data{1}.de, win, Noverlap, Nfft, 1/Ts);
% FRF from u to de
G_de = {};
for i_mass = [0:3]
G_de(i_mass+1) = {zeros(length(f), 6, 6)};
for i_strut = 1:6
G_de{i_mass+1}(:,:,i_strut) = tfestimate(meas_added_mass{i_mass+1}.data{i_strut}.u, meas_added_mass{i_mass+1}.data{i_strut}.de, win, Noverlap, Nfft, 1/Ts);
end
end
% FRF from u to Vs
G_Vs = {};
for i_mass = [0:3]
G_Vs(i_mass+1) = {zeros(length(f), 6, 6)};
for i_strut = 1:6
G_Vs{i_mass+1}(:,:,i_strut) = tfestimate(meas_added_mass{i_mass+1}.data{i_strut}.u, meas_added_mass{i_mass+1}.data{i_strut}.Vs, win, Noverlap, Nfft, 1/Ts);
end
end
% The identified dynamics are then saved for further use.
save('./mat/test_nhexa_identified_frf_masses.mat', 'f', 'G_Vs', 'G_de')
end
%% Load the identified transfer functions
frf_ol = load('test_nhexa_identified_frf_masses.mat', 'f', 'G_Vs', 'G_de');
%% Bode plot for the transfer function from u to de - Several payloads
masses = [0, 13, 26, 39];
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
ax1 = nexttile([2,1]);
hold on;
for i_mass = [0:3]
% Diagonal terms
plot(frf_ol.f, abs(frf_ol.G_de{i_mass+1}(:,1, 1)), 'color', [colors(i_mass+1,:), 0.5], ...
'DisplayName', sprintf('$d_{ei}/u_i$ - %i kg', masses(i_mass+1)));
for i = 2:6
plot(frf_ol.f, abs(frf_ol.G_de{i_mass+1}(:,i, i)), 'color', [colors(i_mass+1,:), 0.5], ...
'HandleVisibility', 'off');
end
% % Off-Diagonal terms
% for i = 1:5
% for j = i+1:6
% plot(frf_ol.f, abs(frf_ol.G_de{i_mass+1}(:,i,j)), 'color', [colors(i_mass+1,:), 0.2], ...
% 'HandleVisibility', 'off');
% end
% end
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/V]'); set(gca, 'XTickLabel',[]);
ylim([1e-8, 5e-4]);
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 2);
leg.ItemTokenSize(1) = 15;
ax2 = nexttile;
hold on;
for i_mass = [0:3]
for i =1:6
plot(frf_ol.f, 180/pi*angle(frf_ol.G_de{i_mass+1}(:,i, i)), 'color', [colors(i_mass+1,:), 0.5]);
end
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
yticks(-360:90:360);
ylim([-90, 180])
linkaxes([ax1,ax2],'x');
xlim([10, 2e3]);
%% Bode plot for the transfer function from u to de
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
ax1 = nexttile([2,1]);
hold on;
for i_mass = [0:3]
% Diagonal terms
plot(frf_ol.f, abs(frf_ol.G_Vs{i_mass+1}(:,1, 1)), 'color', [colors(i_mass+1,:), 0.5], ...
'DisplayName', sprintf('$V_{si}/u_i$ - %i kg', masses(i_mass+1)));
for i = 2:6
plot(frf_ol.f, abs(frf_ol.G_Vs{i_mass+1}(:,i, i)), 'color', [colors(i_mass+1,:), 0.5], ...
'HandleVisibility', 'off');
end
% % Off-Diagonal terms
% for i = 1:5
% for j = i+1:6
% plot(frf_ol.f, abs(frf_ol.G_Vs{i_mass+1}(:,i,j)), 'color', [colors(i_mass+1,:), 0.2], ...
% 'HandleVisibility', 'off');
% end
% end
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [V/V]'); set(gca, 'XTickLabel',[]);
ylim([1e-2, 1e2]);
leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
leg.ItemTokenSize(1) = 15;
ax2 = nexttile;
hold on;
for i_mass = [0:3]
for i =1:6
plot(frf_ol.f, 180/pi*angle(frf_ol.G_Vs{i_mass+1}(:,i, i)), 'color', [colors(i_mass+1,:), 0.5]);
end
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
yticks(-360:90:360);
linkaxes([ax1,ax2],'x');
xlim([10, 2e3]);

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C4-test-bench-nano-hexapod/test_nhexa_3_model.m Normal file
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%% test_nhexa_3_model.m
% Compare the measured dynamics from u to de and to Vs with the Simscape model
%% Clear Workspace and Close figures
clear; close all; clc;
%% Intialize Laplace variable
s = zpk('s');
%% Path for functions, data and scripts
addpath('./mat/'); % Path for Data
addpath('./src/'); % Path for functions
addpath('./STEPS/'); % Path for STEPS
addpath('./subsystems/'); % Path for Subsystems Simulink files
%% Initialize Parameters for Simscape model
table_type = 'Rigid'; % On top of vibration table
device_type = 'None'; % On top of vibration table
payload_num = 0; % No Payload
% Simulink Model name
mdl = 'test_nhexa_simscape';
%% Colors for the figures
colors = colororder;
%% Frequency Vector
freqs = logspace(log10(10), log10(2e3), 1000);
%% Set to true only if all the dynamics should again computed
% from the simscape model
extract_simscape_dynamics = false;
if extract_simscape_dynamics
%% Extract the transfer function matrix from the Simscape model
% Initialization of the Simscape model
table_type = 'Suspended'; % On top of vibration table
device_type = 'Hexapod'; % Nano-Hexapod
payload_num = 0; % No Payload
n_hexapod = initializeNanoHexapod('flex_bot_type', '4dof', ...
'flex_top_type', '4dof', ...
'motion_sensor_type', 'plates', ...
'actuator_type', '2dof');
% Identify the FRF matrix from u to [de,Vs]
clear io; io_i = 1;
io(io_i) = linio([mdl, '/u'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs
io(io_i) = linio([mdl, '/de'], 1, 'openoutput'); io_i = io_i + 1; % Encoders
io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; % Encoders
G_de = {};
G_Vs = {};
for i = [0:3]
payload_num = i; % Change the payload on the nano-hexapod
G = exp(-s*1e-4)*linearize(mdl, io, 0.0);
G.InputName = {'u1', 'u2', 'u3', 'u4', 'u5', 'u6'};
G.OutputName = {'de1', 'de2', 'de3', 'de4', 'de5', 'de6', ...
'Vs1', 'Vs2', 'Vs3', 'Vs4', 'Vs5', 'Vs6'};
G_de(i+1) = {G({'de1', 'de2', 'de3', 'de4', 'de5', 'de6'},:)};
G_Vs(i+1) = {G({'Vs1', 'Vs2', 'Vs3', 'Vs4', 'Vs5', 'Vs6'},:)};
end
% Save the identified plants
save('./mat/test_nhexa_simscape_masses.mat', 'G_Vs', 'G_de')
%% The same identification is performed, but this time with
% "flexible" model of the APA
table_type = 'Suspended'; % On top of vibration table
device_type = 'Hexapod'; % Nano-Hexapod
payload_num = 0; % No Payload
n_hexapod = initializeNanoHexapod('flex_bot_type', '4dof', ...
'flex_top_type', '4dof', ...
'motion_sensor_type', 'plates', ...
'actuator_type', 'flexible');
G_de = {};
G_Vs = {};
for i = [0:3]
payload_num = i; % Change the payload on the nano-hexapod
G = exp(-s*1e-4)*linearize(mdl, io, 0.0);
G.InputName = {'u1', 'u2', 'u3', 'u4', 'u5', 'u6'};
G.OutputName = {'de1', 'de2', 'de3', 'de4', 'de5', 'de6', ...
'Vs1', 'Vs2', 'Vs3', 'Vs4', 'Vs5', 'Vs6'};
G_de(i+1) = {G({'de1', 'de2', 'de3', 'de4', 'de5', 'de6'},:)};
G_Vs(i+1) = {G({'Vs1', 'Vs2', 'Vs3', 'Vs4', 'Vs5', 'Vs6'},:)};
end
% Save the identified plants
save('./mat/test_nhexa_simscape_flexible_masses.mat', 'G_Vs', 'G_de')
end
%% Load Simscape Model and measured FRF
sim_ol = load('test_nhexa_simscape_masses.mat', 'G_Vs', 'G_de');
frf_ol = load('test_nhexa_identified_frf_masses.mat', 'f', 'G_Vs', 'G_de');
%% Diagonal elements of the FRF matrix from u to de
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
ax1 = nexttile([2,1]);
hold on;
plot(frf_ol.f, abs(frf_ol.G_de{1}(:,1, 1)), 'color', [colors(1,:),0.5], ...
'DisplayName', '$d_{ei}/u_i$ - FRF')
plot(freqs, abs(squeeze(freqresp(sim_ol.G_de{1}(1,1), freqs, 'Hz'))), 'color', [colors(2,:),0.5], ...
'DisplayName', '$d_{ei}/u_i$ - Model')
for i = 2:6
plot(frf_ol.f, abs(frf_ol.G_de{1}(:,i, i)), 'color', [colors(1,:),0.5], ...
'HandleVisibility', 'off');
plot(freqs, abs(squeeze(freqresp(sim_ol.G_de{1}(i,i), freqs, 'Hz'))), 'color', [colors(2,:),0.5], ...
'HandleVisibility', 'off');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/V]'); set(gca, 'XTickLabel',[]);
ylim([1e-8, 5e-4]);
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;
ax2 = nexttile;
hold on;
for i = 1:6
plot(frf_ol.f, 180/pi*angle(frf_ol.G_de{1}(:,i, i)), 'color', [colors(1,:),0.5]);
plot(freqs, 180/pi*angle(squeeze(freqresp(sim_ol.G_de{1}(i,i), freqs, 'Hz'))), 'color', [colors(2,:),0.5]);
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
%% Diagonal elements of the FRF matrix from u to Vs
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
ax1 = nexttile([2,1]);
hold on;
plot(frf_ol.f, abs(frf_ol.G_Vs{1}(:,1, 1)), 'color', [colors(1,:),0.5], ...
'DisplayName', '$V_{si}/u_i$ - FRF')
plot(freqs, abs(squeeze(freqresp(sim_ol.G_Vs{1}(1,1), freqs, 'Hz'))), 'color', [colors(2,:), 0.5], ...
'DisplayName', '$V_{si}/u_i$ - Model')
for i = 2:6
plot(frf_ol.f, abs(frf_ol.G_Vs{1}(:,i, i)), 'color', [colors(1,:),0.5], ...
'HandleVisibility', 'off');
plot(freqs, abs(squeeze(freqresp(sim_ol.G_Vs{1}(i,i), freqs, 'Hz'))), 'color', [colors(2,:), 0.5], ...
'HandleVisibility', 'off');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [V/V]'); set(gca, 'XTickLabel',[]);
legend('location', 'southeast');
ax2 = nexttile;
hold on;
for i = 1:6
plot(frf_ol.f, 180/pi*angle(frf_ol.G_Vs{1}(:,i, i)), 'color', [colors(1,:),0.5]);
plot(freqs, 180/pi*angle(squeeze(freqresp(sim_ol.G_Vs{1}(i,i), freqs, 'Hz'))), 'color', [colors(2,:), 0.5]);
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
%% Comparison of the plants (encoder output) when tuning the misalignment
i_input = 1;
figure;
tiledlayout(2, 3, 'TileSpacing', 'tight', 'Padding', 'tight');
ax1 = nexttile();
hold on;
plot(frf_ol.f, abs(frf_ol.G_de{1}(:, 1, i_input)));
plot(freqs, abs(squeeze(freqresp(sim_ol.G_de{1}(1, i_input), freqs, 'Hz'))));
text(54, 4e-4, '$d_{e1}/u_{1}$', 'Horiz','left', 'Vert','top')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
set(gca, 'XTickLabel',[]); ylabel('Amplitude [m/V]');
ax2 = nexttile();
hold on;
plot(frf_ol.f, abs(frf_ol.G_de{1}(:, 2, i_input)));
plot(freqs, abs(squeeze(freqresp(sim_ol.G_de{1}(2, i_input), freqs, 'Hz'))));
text(54, 4e-4, '$d_{e2}/u_{1}$', 'Horiz','left', 'Vert','top')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
set(gca, 'XTickLabel',[]); set(gca, 'YTickLabel',[]);
ax3 = nexttile();
hold on;
plot(frf_ol.f, abs(frf_ol.G_de{1}(:, 3, i_input)), ...
'DisplayName', 'Measurements');
plot(freqs, abs(squeeze(freqresp(sim_ol.G_de{1}(3, i_input), freqs, 'Hz'))), ...
'DisplayName', 'Model (2-DoF APA)');
text(54, 4e-4, '$d_{e3}/u_{1}$', 'Horiz','left', 'Vert','top')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
set(gca, 'XTickLabel',[]); set(gca, 'YTickLabel',[]);
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;
ax4 = nexttile();
hold on;
plot(frf_ol.f, abs(frf_ol.G_de{1}(:, 4, i_input)));
plot(freqs, abs(squeeze(freqresp(sim_ol.G_de{1}(4, i_input), freqs, 'Hz'))));
text(54, 4e-4, '$d_{e4}/u_{1}$', 'Horiz','left', 'Vert','top')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('Amplitude [m/V]');
xticks([50, 100, 200, 400])
ax5 = nexttile();
hold on;
plot(frf_ol.f, abs(frf_ol.G_de{1}(:, 5, i_input)));
plot(freqs, abs(squeeze(freqresp(sim_ol.G_de{1}(5, i_input), freqs, 'Hz'))));
text(54, 4e-4, '$d_{e5}/u_{1}$', 'Horiz','left', 'Vert','top')
hold off;
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xticks([50, 100, 200, 400])
ax6 = nexttile();
hold on;
plot(frf_ol.f, abs(frf_ol.G_de{1}(:, 6, i_input)));
plot(freqs, abs(squeeze(freqresp(sim_ol.G_de{1}(6, i_input), freqs, 'Hz'))));
text(54, 4e-4, '$d_{e6}/u_{1}$', 'Horiz','left', 'Vert','top')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
xticks([50, 100, 200, 400])
linkaxes([ax1,ax2,ax3,ax4,ax5,ax6],'xy');
xlim([50, 5e2]); ylim([1e-8, 5e-4]);
%% Load the plant model with Flexible APA
flex_ol = load('test_nhexa_simscape_flexible_masses.mat', 'G_Vs', 'G_de');
%% Comparison of the plants (encoder output) when tuning the misalignment
i_input = 1;
figure;
tiledlayout(2, 3, 'TileSpacing', 'tight', 'Padding', 'tight');
ax1 = nexttile();
hold on;
plot(frf_ol.f, abs(frf_ol.G_de{1}(:, 1, i_input)));
plot(freqs, abs(squeeze(freqresp(flex_ol.G_de{1}(1, i_input), freqs, 'Hz'))));
text(54, 4e-4, '$d_{e1}/u_{1}$', 'Horiz','left', 'Vert','top')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
set(gca, 'XTickLabel',[]); ylabel('Amplitude [m/V]');
ax2 = nexttile();
hold on;
plot(frf_ol.f, abs(frf_ol.G_de{1}(:, 2, i_input)));
plot(freqs, abs(squeeze(freqresp(flex_ol.G_de{1}(2, i_input), freqs, 'Hz'))));
text(54, 4e-4, '$d_{e2}/u_{1}$', 'Horiz','left', 'Vert','top')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
set(gca, 'XTickLabel',[]); set(gca, 'YTickLabel',[]);
ax3 = nexttile();
hold on;
plot(frf_ol.f, abs(frf_ol.G_de{1}(:, 3, i_input)), ...
'DisplayName', 'Measurements');
plot(freqs, abs(squeeze(freqresp(flex_ol.G_de{1}(3, i_input), freqs, 'Hz'))), ...
'DisplayName', 'Model (Flexible APA)');
text(54, 4e-4, '$d_{e3}/u_{1}$', 'Horiz','left', 'Vert','top')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
set(gca, 'XTickLabel',[]); set(gca, 'YTickLabel',[]);
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;
ax4 = nexttile();
hold on;
plot(frf_ol.f, abs(frf_ol.G_de{1}(:, 4, i_input)));
plot(freqs, abs(squeeze(freqresp(flex_ol.G_de{1}(4, i_input), freqs, 'Hz'))));
text(54, 4e-4, '$d_{e4}/u_{1}$', 'Horiz','left', 'Vert','top')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('Amplitude [m/V]');
xticks([50, 100, 200, 400])
ax5 = nexttile();
hold on;
plot(frf_ol.f, abs(frf_ol.G_de{1}(:, 5, i_input)));
plot(freqs, abs(squeeze(freqresp(flex_ol.G_de{1}(5, i_input), freqs, 'Hz'))));
text(54, 4e-4, '$d_{e5}/u_{1}$', 'Horiz','left', 'Vert','top')
hold off;
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xticks([50, 100, 200, 400])
ax6 = nexttile();
hold on;
plot(frf_ol.f, abs(frf_ol.G_de{1}(:, 6, i_input)));
plot(freqs, abs(squeeze(freqresp(flex_ol.G_de{1}(6, i_input), freqs, 'Hz'))));
text(54, 4e-4, '$d_{e6}/u_{1}$', 'Horiz','left', 'Vert','top')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
xticks([50, 100, 200, 400])
linkaxes([ax1,ax2,ax3,ax4,ax5,ax6],'xy');
xlim([50, 5e2]); ylim([1e-8, 5e-4]);
%% Bode plot for the transfer function from u to de
masses = [0, 13, 26, 39];
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
ax1 = nexttile([2,1]);
hold on;
for i_mass = [0:3]
plot(frf_ol.f, abs(frf_ol.G_de{i_mass+1}(:,1, 1)), 'color', [colors(i_mass+1,:), 0.2], ...
'DisplayName', sprintf('Meas (%i kg)', masses(i_mass+1)));
for i = 2:6
plot(frf_ol.f, abs(frf_ol.G_de{i_mass+1}(:,i, i)), 'color', [colors(i_mass+1,:), 0.2], ...
'HandleVisibility', 'off');
end
set(gca, 'ColorOrderIndex', i_mass+1)
plot(freqs, abs(squeeze(freqresp(sim_ol.G_de{i_mass+1}(1,1), freqs, 'Hz'))), '--', ...
'DisplayName', 'Model');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $d_e/u$ [m/V]'); set(gca, 'XTickLabel',[]);
ylim([5e-8, 1e-3]);
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 2);
leg.ItemTokenSize(1) = 15;
ax2 = nexttile;
hold on;
for i_mass = [0:3]
for i =1:6
plot(frf_ol.f, 180/pi*angle(frf_ol.G_de{i_mass+1}(:,i, i)), 'color', [colors(i_mass+1,:), 0.2]);
end
set(gca, 'ColorOrderIndex', i_mass+1)
plot(freqs, 180/pi*angle(squeeze(freqresp(sim_ol.G_de{i_mass+1}(1,1), freqs, 'Hz'))), '--');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
yticks(-360:45:360);
ylim([-45, 180]);
linkaxes([ax1,ax2],'x');
xlim([20, 2e2]);
xticks([20, 50, 100, 200])
%% Bode plot for the transfer function from u to Vs
masses = [0, 13, 26, 39];
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
ax1 = nexttile([2,1]);
hold on;
for i_mass = 0:3
plot(frf_ol.f, abs(frf_ol.G_Vs{i_mass+1}(:,1, 1)), 'color', [colors(i_mass+1,:), 0.2], ...
'DisplayName', sprintf('Meas (%i kg)', masses(i_mass+1)));
for i = 2:6
plot(frf_ol.f, abs(frf_ol.G_Vs{i_mass+1}(:,i, i)), 'color', [colors(i_mass+1,:), 0.2], ...
'HandleVisibility', 'off');
end
plot(freqs, abs(squeeze(freqresp(sim_ol.G_Vs{i_mass+1}(1,1), freqs, 'Hz'))), '--', 'color', colors(i_mass+1,:), ...
'DisplayName', 'Model');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $V_s/u$ [V/V]'); set(gca, 'XTickLabel',[]);
ylim([1e-3, 1e2]);
leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
leg.ItemTokenSize(1) = 15;
ax2 = nexttile;
hold on;
for i_mass = 0:3
for i =1:6
plot(frf_ol.f, 180/pi*angle(frf_ol.G_Vs{i_mass+1}(:,i, i)), 'color', [colors(i_mass+1,:), 0.2]);
end
plot(freqs, 180/pi*angle(squeeze(freqresp(sim_ol.G_Vs{i_mass+1}(i,i), freqs, 'Hz'))), '--', 'color', colors(i_mass+1,:));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
yticks(-360:90:360);
linkaxes([ax1,ax2],'x');
xlim([20, 2e2]);
xticks([20, 50, 100, 200])
%% Comparison of the plants (encoder output) when tuning the misalignment
i_input = 1;
figure;
tiledlayout(2, 3, 'TileSpacing', 'tight', 'Padding', 'tight');
ax1 = nexttile();
hold on;
plot(frf_ol.f, abs(frf_ol.G_de{4}(:, 1, i_input)));
plot(freqs, abs(squeeze(freqresp(sim_ol.G_de{4}(1, i_input), freqs, 'Hz'))));
text(12, 4e-4, '$d_{e1}/u_{1}$', 'Horiz','left', 'Vert','top')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
set(gca, 'XTickLabel',[]); ylabel('Amplitude [m/V]');
ax2 = nexttile();
hold on;
plot(frf_ol.f, abs(frf_ol.G_de{4}(:, 2, i_input)));
plot(freqs, abs(squeeze(freqresp(sim_ol.G_de{4}(2, i_input), freqs, 'Hz'))));
text(12, 4e-4, '$d_{e2}/u_{1}$', 'Horiz','left', 'Vert','top')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
set(gca, 'XTickLabel',[]); set(gca, 'YTickLabel',[]);
ax3 = nexttile();
hold on;
plot(frf_ol.f, abs(frf_ol.G_de{4}(:, 3, i_input)), ...
'DisplayName', 'Measurements');
plot(freqs, abs(squeeze(freqresp(sim_ol.G_de{4}(3, i_input), freqs, 'Hz'))), ...
'DisplayName', 'Model (2-DoF APA)');
text(12, 4e-4, '$d_{e3}/u_{1}$', 'Horiz','left', 'Vert','top')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
set(gca, 'XTickLabel',[]); set(gca, 'YTickLabel',[]);
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;
ax4 = nexttile();
hold on;
plot(frf_ol.f, abs(frf_ol.G_de{4}(:, 4, i_input)));
plot(freqs, abs(squeeze(freqresp(sim_ol.G_de{4}(4, i_input), freqs, 'Hz'))));
text(12, 4e-4, '$d_{e4}/u_{1}$', 'Horiz','left', 'Vert','top')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('Amplitude [m/V]');
xticks([10, 50, 100, 200, 400])
ax5 = nexttile();
hold on;
plot(frf_ol.f, abs(frf_ol.G_de{4}(:, 5, i_input)));
plot(freqs, abs(squeeze(freqresp(sim_ol.G_de{4}(5, i_input), freqs, 'Hz'))));
text(12, 4e-4, '$d_{e5}/u_{1}$', 'Horiz','left', 'Vert','top')
hold off;
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xticks([10, 50, 100, 200, 400])
ax6 = nexttile();
hold on;
plot(frf_ol.f, abs(frf_ol.G_de{4}(:, 6, i_input)));
plot(freqs, abs(squeeze(freqresp(sim_ol.G_de{4}(6, i_input), freqs, 'Hz'))));
text(12, 4e-4, '$d_{e6}/u_{1}$', 'Horiz','left', 'Vert','top')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
xticks([10, 50, 100, 200, 400])
linkaxes([ax1,ax2,ax3,ax4,ax5,ax6],'xy');
xlim([10, 5e2]); ylim([1e-8, 5e-4]);

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C4-test-bench-nano-hexapod/test_nhexa_simscape.slx Normal file
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