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