%% 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');