226 lines
8.2 KiB
Matlab
226 lines
8.2 KiB
Matlab
%% 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
|
|
|
|
%% Colors for the figures
|
|
colors = colororder;
|
|
|
|
%% Uniaxial Simscape model name
|
|
mdl = 'nass_uniaxial_model';
|
|
|
|
%% Frequency Vector [Hz]
|
|
freqs = logspace(0, 3, 1000);
|
|
|
|
%% Load the micro-station parameters
|
|
load('uniaxial_micro_station_parameters.mat')
|
|
|
|
% Nano-Hexapod Parameters
|
|
% The parameters for the nano-hexapod and sample are:
|
|
% - $m_s$ the sample mass that can vary from 1kg up to 50kg
|
|
% - $m_n$ the nano-hexapod mass which is set to 15kg
|
|
% - $k_n$ the nano-hexapod stiffness, which can vary depending on the chosen architecture/technology
|
|
|
|
% As a first example, let's choose a nano-hexapod stiffness of $10\,N/\mu m$ and a sample mass of 10kg.
|
|
|
|
|
|
%% Nano-Hexapod Parameters
|
|
mn = 15; % [kg]
|
|
kn = 1e7; % [N/m]
|
|
cn = 2*0.01*sqrt(mn*kn); % [N/(m/s)]
|
|
|
|
%% Sample Mass
|
|
ms = 10; % [kg]
|
|
|
|
% Obtained Dynamic Response
|
|
% The sensitivity to disturbances (i.e. $x_f$, $f_t$ and $f_s$) are shown in Figure ref:fig:uniaxial_sensitivity_dist_first_params.
|
|
% The /plant/ (i.e. the transfer function from actuator force $f$ to measured displacement $d$) is shown in Figure ref:fig:uniaxial_plant_first_params.
|
|
|
|
% #+begin_important
|
|
% For further analysis, 9 configurations are considered: three nano-hexapod stiffnesses ($k_n = 0.01\,N/\mu m$, $k_n = 1\,N/\mu m$ and $k_n = 100\,N/\mu m$) combined with three sample's masses ($m_s = 1\,kg$, $m_s = 25\,kg$ and $m_s = 50\,kg$).
|
|
% #+end_important
|
|
|
|
|
|
%% Use 1DoF Nano-Hexpod model
|
|
model_config = struct();
|
|
model_config.nhexa = "1dof";
|
|
model_config.controller = "open_loop";
|
|
|
|
%% Identify the transfer function from disturbances and force actuator to d
|
|
clear io; io_i = 1;
|
|
io(io_i) = linio([mdl, '/controller'], 1, 'openinput'); io_i = io_i + 1; % Force Actuator
|
|
io(io_i) = linio([mdl, '/fs'], 1, 'openinput'); io_i = io_i + 1; % Force applied on the sample
|
|
io(io_i) = linio([mdl, '/micro_station/xf'], 1, 'openinput'); io_i = io_i + 1; % Floor Motion
|
|
io(io_i) = linio([mdl, '/micro_station/ft'], 1, 'openinput'); io_i = io_i + 1; % Stage disturbances
|
|
io(io_i) = linio([mdl, '/d'] , 1, 'openoutput'); io_i = io_i + 1; % Metrology
|
|
|
|
%% Perform the model extraction
|
|
G_ol = linearize(mdl, io, 0.0);
|
|
G_ol.InputName = {'f', 'fs', 'xf', 'ft'};
|
|
G_ol.OutputName = {'d'};
|
|
|
|
%% Sensitivity to disturbances
|
|
figure;
|
|
tiledlayout(1, 3, 'TileSpacing', 'Compact', 'Padding', 'None');
|
|
|
|
ax1 = nexttile();
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G_ol('d', 'fs'), freqs, 'Hz'))));
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
ylabel('Amplitude $d/f_{s}$ [m/N]'); xlabel('Frequency [Hz]');
|
|
xticks([1e0, 1e1, 1e2]);
|
|
|
|
ax2 = nexttile();
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G_ol('d', 'ft'), freqs, 'Hz'))));
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
ylabel('Amplitude $d/f_{t}$ [m/N]'); xlabel('Frequency [Hz]');
|
|
xticks([1e0, 1e1, 1e2]);
|
|
|
|
ax3 = nexttile();
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G_ol('d', 'xf'), freqs, 'Hz'))));
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
ylabel('Amplitude $d/x_{f}$ [m/m]'); xlabel('Frequency [Hz]');
|
|
xticks([1e0, 1e1, 1e2]);
|
|
|
|
linkaxes([ax1,ax2,ax3],'x');
|
|
xlim([1, 500]);
|
|
|
|
|
|
|
|
% #+name: fig:uniaxial_sensitivity_dist_first_params
|
|
% #+caption: Sensitivity of the relative motion $d$ to disturbances: $f_s$ the direct forces applied on the sample, $f_t$ disturbances from the micro-station stages and $x_f$ the floor motion (from left to right)
|
|
% #+RESULTS:
|
|
% [[file:figs/uniaxial_sensitivity_dist_first_params.png]]
|
|
|
|
|
|
%% Bode Plot of the transfer function from actuator forces to measured displacement by the metrology
|
|
figure;
|
|
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
|
|
|
ax1 = nexttile([2,1]);
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G_ol('d', 'f'), freqs, 'Hz'))));
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
ylabel('Amplitude $d/f$ [m/N]'); set(gca, 'XTickLabel',[]);
|
|
|
|
ax2 = nexttile;
|
|
hold on;
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_ol('d', 'f'), freqs, 'Hz'))));
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
|
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
|
hold off;
|
|
yticks(-360:90:360);
|
|
ylim([-180, 0]);
|
|
|
|
linkaxes([ax1,ax2],'x');
|
|
xlim([1, 500]);
|
|
|
|
% Identification of all combination of stiffnesses / masses :noexport:
|
|
|
|
%% Use 1DoF Nano-Hexpod model
|
|
model_config = struct();
|
|
model_config.nhexa = "1dof";
|
|
model_config.controller = "open_loop";
|
|
|
|
%% Nano-Hexapod Mass
|
|
mn = 15; % Nano-Hexapod mass [kg]
|
|
|
|
%% Identification of all combination of stiffnesses / masses
|
|
clear io; io_i = 1;
|
|
io(io_i) = linio([mdl, '/controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force
|
|
io(io_i) = linio([mdl, '/micro_station/xf'], 1, 'openinput'); io_i = io_i + 1; % Floor Motion
|
|
io(io_i) = linio([mdl, '/micro_station/ft'], 1, 'openinput'); io_i = io_i + 1; % Stage vibrations
|
|
io(io_i) = linio([mdl, '/fs'], 1, 'openinput'); io_i = io_i + 1; % Direct sample forces
|
|
io(io_i) = linio([mdl, '/dL'], 1, 'openoutput'); io_i = io_i + 1; % Relative Motion Sensor
|
|
io(io_i) = linio([mdl, '/fm'], 1, 'openoutput'); io_i = io_i + 1; % Force Sensor
|
|
io(io_i) = linio([mdl, '/vn'] , 1, 'openoutput'); io_i = io_i + 1; % Geophone
|
|
io(io_i) = linio([mdl, '/d'] , 1, 'openoutput'); io_i = io_i + 1; % Metrology Output
|
|
|
|
%% Light Sample
|
|
ms = 1; % Sample Mass [kg]
|
|
|
|
% Voice Coil (i.e. soft) Nano-Hexapod
|
|
kn = 1e4; % Nano-Hexapod Stiffness [N/m]
|
|
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
|
|
G_vc_light = linearize(mdl, io, 0.0);
|
|
G_vc_light.InputName = {'f', 'xf', 'ft', 'fs'};
|
|
G_vc_light.OutputName = {'dL', 'fm', 'vn', 'd'};
|
|
|
|
% APA (i.e. relatively stiff) Nano-Hexapod
|
|
kn = 1e6; % Nano-Hexapod Stiffness [N/m]
|
|
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
|
|
G_md_light = linearize(mdl, io, 0.0);
|
|
G_md_light.InputName = {'f', 'xf', 'ft', 'fs'};
|
|
G_md_light.OutputName = {'dL', 'fm', 'vn', 'd'};
|
|
|
|
% Piezoelectric (i.e. stiff) Nano-Hexapod
|
|
kn = 1e8; % Nano-Hexapod Stiffness [N/m]
|
|
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
|
|
G_pz_light = linearize(mdl, io, 0.0);
|
|
G_pz_light.InputName = {'f', 'xf', 'ft', 'fs'};
|
|
G_pz_light.OutputName = {'dL', 'fm', 'vn', 'd'};
|
|
|
|
%% Mid Sample
|
|
ms = 25; % Sample Mass [kg]
|
|
|
|
% Voice Coil (i.e. soft) Nano-Hexapod
|
|
kn = 1e4; % Nano-Hexapod Stiffness [N/m]
|
|
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
|
|
G_vc_mid = linearize(mdl, io, 0.0);
|
|
G_vc_mid.InputName = {'f', 'xf', 'ft', 'fs'};
|
|
G_vc_mid.OutputName = {'dL', 'fm', 'vn', 'd'};
|
|
|
|
% APA (i.e. relatively stiff) Nano-Hexapod
|
|
kn = 1e6; % Nano-Hexapod Stiffness [N/m]
|
|
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
|
|
G_md_mid = linearize(mdl, io, 0.0);
|
|
G_md_mid.InputName = {'f', 'xf', 'ft', 'fs'};
|
|
G_md_mid.OutputName = {'dL', 'fm', 'vn', 'd'};
|
|
|
|
% Piezoelectric (i.e. stiff) Nano-Hexapod
|
|
kn = 1e8; % Nano-Hexapod Stiffness [N/m]
|
|
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
|
|
G_pz_mid = linearize(mdl, io, 0.0);
|
|
G_pz_mid.InputName = {'f', 'xf', 'ft', 'fs'};
|
|
G_pz_mid.OutputName = {'dL', 'fm', 'vn', 'd'};
|
|
|
|
%% Heavy Sample
|
|
ms = 50; % Sample Mass [kg]
|
|
|
|
% Voice Coil (i.e. soft) Nano-Hexapod
|
|
kn = 1e4; % Nano-Hexapod Stiffness [N/m]
|
|
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
|
|
G_vc_heavy = linearize(mdl, io, 0.0);
|
|
G_vc_heavy.InputName = {'f', 'xf', 'ft', 'fs'};
|
|
G_vc_heavy.OutputName = {'dL', 'fm', 'vn', 'd'};
|
|
|
|
% APA (i.e. relatively stiff) Nano-Hexapod
|
|
kn = 1e6; % Nano-Hexapod Stiffness [N/m]
|
|
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
|
|
G_md_heavy = linearize(mdl, io, 0.0);
|
|
G_md_heavy.InputName = {'f', 'xf', 'ft', 'fs'};
|
|
G_md_heavy.OutputName = {'dL', 'fm', 'vn', 'd'};
|
|
|
|
% Piezoelectric (i.e. stiff) Nano-Hexapod
|
|
kn = 1e8; % Nano-Hexapod Stiffness [N/m]
|
|
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]
|
|
G_pz_heavy = linearize(mdl, io, 0.0);
|
|
G_pz_heavy.InputName = {'f', 'xf', 'ft', 'fs'};
|
|
G_pz_heavy.OutputName = {'dL', 'fm', 'vn', 'd'};
|
|
|
|
%% Save All Identified Plants
|
|
save('./mat/uniaxial_plants.mat', 'G_vc_light', 'G_md_light', 'G_pz_light', ...
|
|
'G_vc_mid', 'G_md_mid', 'G_pz_mid', ...
|
|
'G_vc_heavy', 'G_md_heavy', 'G_pz_heavy');
|