%% 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

%% Data directory
data_dir = './mat/';

% Simulink Model name
mdl = 'nass_model';

%% Colors for the figures
colors = colororder;

%% Frequency Vector [Hz]
freqs = logspace(0, 3, 1000);

% HAC Plant


%% Identify the IFF plant dynamics using the Simscape model

% Initialize each Simscape model elements
initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeSimplifiedNanoHexapod();
initializeSample('type', 'cylindrical', 'm', 1);

% Initial Simscape Configuration
initializeSimscapeConfiguration('gravity', false);
initializeDisturbances('enable', false);
initializeLoggingConfiguration('log', 'none');
initializeController('type', 'open-loop');
initializeReferences();

% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Controller'],     1, 'input');                  io_i = io_i + 1; % Actuator Inputs [N]
io(io_i) = linio([mdl, '/Tracking Error'], 1, 'openoutput', [], 'EdL');  io_i = io_i + 1; % Strut errors [m]

%% Identify HAC Plant without using IFF
initializeSample('type', 'cylindrical', 'm', 1);
G_m1 = linearize(mdl, io);
G_m1.InputName  = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
G_m1.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6'};

initializeSample('type', 'cylindrical', 'm', 25);
G_m25 = linearize(mdl, io);
G_m25.InputName  = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
G_m25.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6'};

initializeSample('type', 'cylindrical', 'm', 50);
G_m50 = linearize(mdl, io);
G_m50.InputName  = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
G_m50.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6'};

%% Effect of Rotation
initializeSample('type', 'cylindrical', 'm', 1);
initializeReferences(...
    'Rz_type', 'rotating', ...
    'Rz_period', 1); % 360 deg/s

G_m1_Rz = linearize(mdl, io, 0.1);
G_m1_Rz.InputName  = {'f1',  'f2',  'f3',  'f4',  'f5',  'f6'};
G_m1_Rz.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6'};



% - Effect of rotation: ref:fig:nass_undamped_plant_effect_Wz
%   Add some coupling at low frequency, but still small at the considered velocity.
%   This is thanks to the relatively stiff nano-hexapod (CF rotating model)
% - Effect of payload mass:
%   Decrease resonance frequencies
%   Increase coupling: ref:fig:nass_undamped_plant_effect_mass
%   => control challenge for high payload masses
% - Other effects such as: Ry tilt angle, Rz spindle position, micro-hexapod position are found to have negligible effect on the plant dynamics.
%   This is thanks to the fact the the plant dynamics is well decoupled from the micro-station dynamics.


figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(freqs, abs(squeeze(freqresp(G_m1(1,1), freqs, 'Hz'))), 'color', colors(1,:), ...
     'DisplayName', '$\epsilon_{\mathcal{L}i}/f_i$, $\Omega = 0$')
plot(freqs, abs(squeeze(freqresp(G_m1_Rz(1,1), freqs, 'Hz'))), 'color', colors(2,:), ...
     'DisplayName', '$\epsilon_{\mathcal{L}i}/f_i$, $\Omega = 360$ deg/s')
plot(freqs, abs(squeeze(freqresp(G_m1(1,2), freqs, 'Hz'))), 'color', [colors(1,:), 0.2], ...
     'DisplayName', '$\epsilon_{\mathcal{L}i}/f_j$')
plot(freqs, abs(squeeze(freqresp(G_m1_Rz(1,2), freqs, 'Hz'))), 'color', [colors(2,:), 0.2], ...
     'DisplayName', '$\epsilon_{\mathcal{L}i}/f_j$')
for i = 1:5
    for j = i+1:6
        plot(freqs, abs(squeeze(freqresp(G_m1(i,j), freqs, 'Hz'))), 'color', [colors(1,:), 0.2], ...
             'HandleVisibility', 'off');
        plot(freqs, abs(squeeze(freqresp(G_m1_Rz(i,j), freqs, 'Hz'))), 'color', [colors(2,:), 0.2], ...
             'HandleVisibility', 'off');
    end
end
for i = 2:6
    plot(freqs, abs(squeeze(freqresp(G_m1(i,i), freqs, 'Hz'))), 'color', colors(1,:), ...
         'HandleVisibility', 'off');
    plot(freqs, abs(squeeze(freqresp(G_m1_Rz(i,i), freqs, 'Hz'))), 'color', colors(2,:), ...
         'HandleVisibility', 'off');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
ylim([1e-11, 2e-5]);
leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
leg.ItemTokenSize(1) = 15;

ax2 = nexttile;
hold on;
for i = 1:6
    plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_m1(i,i), freqs, 'Hz')))), 'color', colors(1,:));
    plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_m1_Rz(i,i), freqs, 'Hz')))), 'color', colors(2,:));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-200, 20]);
yticks([-180:45:180]);

linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);

figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(freqs, abs(squeeze(freqresp(G_m1( 1,1), freqs, 'Hz'))), 'color', colors(1,:), ...
     'DisplayName', '$\epsilon_{\mathcal{L}i}/f_i$, 1 kg')
plot(freqs, abs(squeeze(freqresp(G_m25(1,1), freqs, 'Hz'))), 'color', colors(2,:), ...
     'DisplayName', '$\epsilon_{\mathcal{L}i}/f_i$, 25 kg')
plot(freqs, abs(squeeze(freqresp(G_m50(1,1), freqs, 'Hz'))), 'color', colors(3,:), ...
     'DisplayName', '$\epsilon_{\mathcal{L}i}/f_i$, 50 kg')
for i = 1:5
    for j = i+1:6
        plot(freqs, abs(squeeze(freqresp(G_m1(i,j), freqs, 'Hz'))), 'color', [colors(1,:), 0.2], ...
             'HandleVisibility', 'off');
        plot(freqs, abs(squeeze(freqresp(G_m25(i,j), freqs, 'Hz'))), 'color', [colors(2,:), 0.2], ...
             'HandleVisibility', 'off');
        plot(freqs, abs(squeeze(freqresp(G_m50(i,j), freqs, 'Hz'))), 'color', [colors(3,:), 0.2], ...
             'HandleVisibility', 'off');
    end
end
for i = 2:6
    plot(freqs, abs(squeeze(freqresp(G_m1( i,i), freqs, 'Hz'))), 'color', colors(1,:), ...
         'HandleVisibility', 'off');
    plot(freqs, abs(squeeze(freqresp(G_m25(i,i), freqs, 'Hz'))), 'color', colors(2,:), ...
         'HandleVisibility', 'off');
    plot(freqs, abs(squeeze(freqresp(G_m50(i,i), freqs, 'Hz'))), 'color', colors(3,:), ...
         'HandleVisibility', 'off');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
ylim([1e-11, 2e-5]);
leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;

ax2 = nexttile;
hold on;
for i = 1:6
    plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_m1(i,i), freqs, 'Hz')))), 'color', colors(1,:));
    plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_m25(i,i), freqs, 'Hz')))), 'color', colors(2,:));
    plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_m50(i,i), freqs, 'Hz')))), 'color', colors(3,:));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-200, 20]);
yticks([-180:45:180]);

linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);



% #+name: fig:nass_undamped_plant_effect
% #+caption: Effect of the Spindle's rotational velocity on the positioning plant (\subref{fig:nass_undamped_plant_effect_Wz}) and effect of the payload's mass on the positioning plant (\subref{fig:nass_undamped_plant_effect_mass})
% #+attr_latex: :options [htbp]
% #+begin_figure
% #+attr_latex: :caption \subcaption{\label{fig:nass_undamped_plant_effect_Wz}Effect of rotational velocity $\Omega_z$}
% #+attr_latex: :options {0.48\textwidth}
% #+begin_subfigure
% #+attr_latex: :width 0.95\linewidth
% [[file:figs/nass_undamped_plant_effect_Wz.png]]
% #+end_subfigure
% #+attr_latex: :caption \subcaption{\label{fig:nass_undamped_plant_effect_mass}Effect of payload's mass}
% #+attr_latex: :options {0.48\textwidth}
% #+begin_subfigure
% #+attr_latex: :width 0.95\linewidth
% [[file:figs/nass_undamped_plant_effect_mass.png]]
% #+end_subfigure
% #+end_figure


% - Effect of IFF on the plant ref:fig:nass_comp_undamped_damped_plant_m1
%   Modes are well damped
%   Small coupling increase at low frequency
% - Benefits of using IFF ref:fig:nass_hac_plants
%   with added damping, the set of plants to be controlled (with payloads from 1kg to 50kg) is more easily controlled.
%   Between 10 and 50Hz, the plant dynamics does not vary a lot with the frequency, whereas without active damping, it would be impossible to design a robust controller with bandwidth above 10Hz that is robust to the change of payload


%% Identify HAC Plant without using IFF
initializeReferences(); % No Spindle Rotation
initializeController('type', 'iff'); % Implemented IFF controller
load('nass_K_iff.mat', 'Kiff'); % Load designed IFF controller

% 1kg payload
initializeSample('type', 'cylindrical', 'm', 1);
G_hac_m1 = linearize(mdl, io);
G_hac_m1.InputName  = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
G_hac_m1.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6'};

% 25kg payload
initializeSample('type', 'cylindrical', 'm', 25);
G_hac_m25 = linearize(mdl, io);
G_hac_m25.InputName  = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
G_hac_m25.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6'};

% 50kg payload
initializeSample('type', 'cylindrical', 'm', 50);
G_hac_m50 = linearize(mdl, io);
G_hac_m50.InputName  = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
G_hac_m50.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6'};

% Check stability
if not(isstable(G_hac_m1) && isstable(G_hac_m25) && isstable(G_hac_m50))
    warning('One of HAC plant is not stable')
end

figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(freqs, abs(squeeze(freqresp(G_m1( 1,1), freqs, 'Hz'))), 'color', colors(1,:), ...
     'DisplayName', '$\epsilon_{\mathcal{L}i}/f_i$, OL')
plot(freqs, abs(squeeze(freqresp(G_hac_m1(1,1), freqs, 'Hz'))), 'color', colors(2,:), ...
     'DisplayName', '$\epsilon_{\mathcal{L}i}/f_i$, with IFF')
for i = 1:5
    for j = i+1:6
        plot(freqs, abs(squeeze(freqresp(G_m1(i,j), freqs, 'Hz'))), 'color', [colors(1,:), 0.2], ...
             'HandleVisibility', 'off');
        plot(freqs, abs(squeeze(freqresp(G_hac_m1(i,j), freqs, 'Hz'))), 'color', [colors(2,:), 0.2], ...
             'HandleVisibility', 'off');
    end
end
for i = 2:6
    plot(freqs, abs(squeeze(freqresp(G_m1( i,i), freqs, 'Hz'))), 'color', colors(1,:), ...
         'HandleVisibility', 'off');
    plot(freqs, abs(squeeze(freqresp(G_hac_m1(i,i), freqs, 'Hz'))), 'color', colors(2,:), ...
         'HandleVisibility', 'off');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
ylim([1e-10, 2e-5]);
leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;

ax2 = nexttile;
hold on;
for i = 1:6
    plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_m1(i,i), freqs, 'Hz')))), 'color', colors(1,:));
    plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_hac_m1(i,i), freqs, 'Hz')))), 'color', colors(2,:));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-200, 20]);
yticks([-180:45:180]);

linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);

%% Comparison of all the undamped FRF and all the damped FRF
figure;
tiledlayout(3, 1, 'TileSpacing', 'compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(freqs, abs(squeeze(freqresp(G_m1(    1,1), freqs, 'Hz'))), 'color', [colors(1,:), 0.5], 'DisplayName', 'Undamped - $\epsilon\mathcal{L}_i/f_i$');
plot(freqs, abs(squeeze(freqresp(G_hac_m1(1,1), freqs, 'Hz'))), 'color', [colors(2,:), 0.5], 'DisplayName', 'Damped - $\epsilon\mathcal{L}_i/f_i^\prime$');
for i = 1:6
    plot(freqs, abs(squeeze(freqresp(G_m1( i,i), freqs, 'Hz'))), 'color', [colors(1,:), 0.5], 'HandleVisibility', 'off');
    plot(freqs, abs(squeeze(freqresp(G_m25(i,i), freqs, 'Hz'))), 'color', [colors(1,:), 0.5], 'HandleVisibility', 'off');
    plot(freqs, abs(squeeze(freqresp(G_m50(i,i), freqs, 'Hz'))), 'color', [colors(1,:), 0.5], 'HandleVisibility', 'off');
end
for i = 1:6
    plot(freqs, abs(squeeze(freqresp(G_hac_m1( i,i), freqs, 'Hz'))), 'color', [colors(2,:), 0.5], 'HandleVisibility', 'off');
    plot(freqs, abs(squeeze(freqresp(G_hac_m25(i,i), freqs, 'Hz'))), 'color', [colors(2,:), 0.5], 'HandleVisibility', 'off');
    plot(freqs, abs(squeeze(freqresp(G_hac_m50(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/N]'); set(gca, 'XTickLabel',[]);
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;
% ylim([1e-8, 1e-4]);

ax2 = nexttile;
hold on;
for i =1:6
    plot(freqs, 180/pi*angle(squeeze(freqresp(G_m1( i,i), freqs, 'Hz'))), 'color', [colors(1,:), 0.5]);
    plot(freqs, 180/pi*angle(squeeze(freqresp(G_m25(i,i), freqs, 'Hz'))), 'color', [colors(1,:), 0.5]);
    plot(freqs, 180/pi*angle(squeeze(freqresp(G_m50(i,i), freqs, 'Hz'))), 'color', [colors(1,:), 0.5]);
end
for i = 1:6
    plot(freqs, 180/pi*angle(squeeze(freqresp(G_hac_m1( i,i), freqs, 'Hz'))), 'color', [colors(2,:), 0.5]);
    plot(freqs, 180/pi*angle(squeeze(freqresp(G_hac_m25(i,i), freqs, 'Hz'))), 'color', [colors(2,:), 0.5]);
    plot(freqs, 180/pi*angle(squeeze(freqresp(G_hac_m50(i,i), freqs, 'Hz'))), 'color', [colors(2,:), 0.5]);
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
ylim([-200, 20]);
yticks([-180:45:180]);

linkaxes([ax1,ax2],'x');
% xlim([1, 5e2]);

% Effect of micro-station compliance

% Micro-Station complex dynamics has almost no effect on the plant dynamics (Figure ref:fig:nass_effect_ustation_compliance):
% - adds some alternating poles and zeros above 100Hz, which should not be an issue for control


%% Identify plant with "rigid" micro-station
initializeGround('type', 'rigid');
initializeGranite('type', 'rigid');
initializeTy('type', 'rigid');
initializeRy('type', 'rigid');
initializeRz('type', 'rigid');
initializeMicroHexapod('type', 'rigid');
initializeSimplifiedNanoHexapod();
initializeSample('type', 'cylindrical', 'm', 25);

initializeReferences();
initializeController('type', 'open-loop'); % Implemented IFF controller
load('nass_K_iff.mat', 'Kiff'); % Load designed IFF controller

% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Controller'],     1, 'input');                  io_i = io_i + 1; % Actuator Inputs [N]
io(io_i) = linio([mdl, '/Tracking Error'], 1, 'openoutput', [], 'EdL');  io_i = io_i + 1; % Strut errors [m]

G_m25_rigid = linearize(mdl, io);
G_m25_rigid.InputName  = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
G_m25_rigid.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6'};

%% Effect of the micro-station limited compliance on the plant dynamics
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(freqs, abs(squeeze(freqresp(G_m25_rigid( 1,1), freqs, 'Hz'))), 'color', colors(1,:), ...
     'DisplayName', '$\epsilon_{\mathcal{L}i}/f_i$, OL')
plot(freqs, abs(squeeze(freqresp(G_m25(1,1), freqs, 'Hz'))), 'color', colors(2,:), ...
     'DisplayName', '$\epsilon_{\mathcal{L}i}/f_i$, with IFF')
for i = 1:5
    for j = i+1:6
        plot(freqs, abs(squeeze(freqresp(G_m25_rigid(i,j), freqs, 'Hz'))), 'color', [colors(1,:), 0.2], ...
             'HandleVisibility', 'off');
        plot(freqs, abs(squeeze(freqresp(G_m25(i,j), freqs, 'Hz'))), 'color', [colors(2,:), 0.2], ...
             'HandleVisibility', 'off');
    end
end
for i = 2:6
    plot(freqs, abs(squeeze(freqresp(G_m25_rigid( i,i), freqs, 'Hz'))), 'color', colors(1,:), ...
         'HandleVisibility', 'off');
    plot(freqs, abs(squeeze(freqresp(G_m25(i,i), freqs, 'Hz'))), 'color', colors(2,:), ...
         'HandleVisibility', 'off');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
ylim([1e-10, 2e-5]);
leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;

ax2 = nexttile;
hold on;
for i = 1:6
    plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_m25_rigid(i,i), freqs, 'Hz')))), 'color', colors(1,:));
    plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_m25(i,i), freqs, 'Hz')))), 'color', colors(2,:));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-200, 20]);
yticks([-180:45:180]);

linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);

% Higher or lower nano-hexapod stiffness?

% *Goal*: confirm the analysis with simpler models (uniaxial and 3DoF) that a nano-hexapod stiffness of $\approx 1\,N/\mu m$ should give better performances than a very stiff or very soft nano-hexapod.

% - *Stiff nano-hexapod*:
%   uniaxial model: high nano-hexapod stiffness induce coupling between the nano-hexapod and the micro-station dynamics.
%   considering the complex dynamics of the micro-station as shown by the modal analysis, that would result in a complex system to control
%   To show that, a nano-hexapod with actuator stiffness equal to 100N/um is initialized, payload of 25kg.
%   The dynamics from $\bm{f}$ to $\bm{\epsilon}_{\mathcal{L}}$ is identified and compared to the case where the micro-station is infinitely rigid (figure ref:fig:nass_stiff_nano_hexapod_coupling_ustation):
%   - Coupling induced by the micro-station: much more complex and difficult to model / predict
%   - Similar to what was predicted using the uniaxial model
% - *Soft nano-hexapod*:
%   Nano-hexapod with stiffness of 0.01N/um is initialized, payload of 25kg.
%   Dynamics is identified with no spindle rotation, and with spindle rotation of 36deg/s and 360deg/s (Figure ref:fig:nass_soft_nano_hexapod_effect_Wz)
%   - Rotation as huge effect on the dynamics: unstable for high rotational velocities, added coupling due to gyroscopic effects, and change of resonance frequencies as a function of the rotational velocity
%   - Simple 3DoF rotating model is helpful to understand the complex effect of the rotation => similar conclusion
%   - Say that controlling the frame of the struts is not adapted with a soft nano-hexapod, but we should rather control in the frame matching the center of mass of the payload, but we would still obtain large coupling and change of dynamics due to gyroscopic effects.


%% Identify Dynamics with a Stiff nano-hexapod (100N/um)

% Initialize each Simscape model elements
initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeSimplifiedNanoHexapod('actuator_k', 1e8, 'actuator_kp', 0, 'actuator_c', 1e3);
initializeSample('type', 'cylindrical', 'm', 25);

% Initial Simscape Configuration
initializeSimscapeConfiguration('gravity', false);
initializeDisturbances('enable', false);
initializeLoggingConfiguration('log', 'none');
initializeController('type', 'open-loop');
initializeReferences();

% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Controller'],     1, 'input');                  io_i = io_i + 1; % Actuator Inputs [N]
io(io_i) = linio([mdl, '/Tracking Error'], 1, 'openoutput', [], 'EdL');  io_i = io_i + 1; % Strut errors [m]

% Identify Plant
G_m25_pz = linearize(mdl, io);
G_m25_pz.InputName  = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
G_m25_pz.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6'};

%% Compare with Nano-Hexapod alone (rigid micro-station)
initializeGround('type', 'rigid');
initializeGranite('type', 'rigid');
initializeTy('type', 'rigid');
initializeRy('type', 'rigid');
initializeRz('type', 'rigid');
initializeMicroHexapod('type', 'rigid');

% Identify Plant
G_m25_pz_rigid = linearize(mdl, io);
G_m25_pz_rigid.InputName  = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
G_m25_pz_rigid.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6'};

%% Stiff nano-hexapod - Coupling with the micro-station
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(freqs, abs(squeeze(freqresp(G_m25_pz_rigid(1,1), freqs, 'Hz'))), 'color', colors(1,:), ...
     'DisplayName', '$\epsilon_{\mathcal{L}i}/f_i$ - Rigid')
plot(freqs, abs(squeeze(freqresp(G_m25_pz(1,1), freqs, 'Hz'))), 'color', colors(2,:), ...
     'DisplayName', '$\epsilon_{\mathcal{L}i}/f_i$ - $\mu$-station')
plot(freqs, abs(squeeze(freqresp(G_m25_pz_rigid(1,2), freqs, 'Hz'))), 'color', [colors(1,:), 0.1], ...
     'DisplayName', '$\epsilon_{\mathcal{L}i}/f_j$ - Rigid')
plot(freqs, abs(squeeze(freqresp(G_m25_pz(1,2), freqs, 'Hz'))), 'color', [colors(2,:), 0.1], ...
     'DisplayName', '$\epsilon_{\mathcal{L}i}/f_j$ - $\mu$-station')
for i = 1:5
    for j = i+1:6
        plot(freqs, abs(squeeze(freqresp(G_m25_pz_rigid(i,j), freqs, 'Hz'))), 'color', [colors(1,:), 0.1], ...
             'HandleVisibility', 'off');
        plot(freqs, abs(squeeze(freqresp(G_m25_pz(i,j), freqs, 'Hz'))), 'color', [colors(2,:), 0.1], ...
             'HandleVisibility', 'off');
    end
end
for i = 2:6
    plot(freqs, abs(squeeze(freqresp(G_m25_pz_rigid(i,i), freqs, 'Hz'))), 'color', colors(1,:), ...
         'HandleVisibility', 'off');
    plot(freqs, abs(squeeze(freqresp(G_m25_pz(i,i), freqs, 'Hz'))), 'color', colors(2,:), ...
         'HandleVisibility', 'off');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
ylim([1e-12, 3e-7]);
leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;

ax2 = nexttile;
hold on;
for i = 1:6
    plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_m25_pz_rigid(i,i), freqs, 'Hz')))), 'color', colors(1,:));
    plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_m25_pz(i,i), freqs, 'Hz')))), 'color', colors(2,:));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-200, 20]);
yticks([-180:45:180]);

linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);

%% Identify Dynamics with a Soft nano-hexapod (0.01N/um)
initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeSimplifiedNanoHexapod('actuator_k', 1e4, 'actuator_kp', 0, 'actuator_c', 1);

% Initialize each Simscape model elements
initializeSample('type', 'cylindrical', 'm', 25); % 25kg payload
initializeController('type', 'open-loop');

% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Controller'],     1, 'input');                  io_i = io_i + 1; % Actuator Inputs [N]
io(io_i) = linio([mdl, '/Tracking Error'], 1, 'openoutput', [], 'EdL');  io_i = io_i + 1; % Strut errors [m]

% Identify the dynamics without rotation
initializeReferences();
G_m1_vc = linearize(mdl, io);
G_m1_vc.InputName  = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
G_m1_vc.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6'};

% Identify the dynamics with 36 deg/s rotation
initializeReferences(...
    'Rz_type', 'rotating', ...
    'Rz_period', 10); % 36 deg/s

G_m1_vc_Rz_slow = linearize(mdl, io, 0.1);
G_m1_vc_Rz_slow.InputName  = {'f1',  'f2',  'f3',  'f4',  'f5',  'f6'};
G_m1_vc_Rz_slow.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6'};

% Identify the dynamics with 360 deg/s rotation
initializeReferences(...
    'Rz_type', 'rotating', ...
    'Rz_period', 1); % 360 deg/s

G_m1_vc_Rz_fast = linearize(mdl, io, 0.1);
G_m1_vc_Rz_fast.InputName  = {'f1',  'f2',  'f3',  'f4',  'f5',  'f6'};
G_m1_vc_Rz_fast.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6'};

%% Soft Nano-Hexapod - effect of rotational velocity on the dynamics
f = logspace(-1,2,200);
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(f, abs(squeeze(freqresp(G_m1_vc(1,1), f, 'Hz'))), 'color', colors(1,:), ...
     'DisplayName', '$f_{ni}/f_i$ - $\Omega_z = 0$')
plot(f, abs(squeeze(freqresp(G_m1_vc_Rz_slow(1,1), f, 'Hz'))), 'color', colors(2,:), ...
     'DisplayName', '$f_{ni}/f_i$ - $\Omega_z = 36$ deg/s')
plot(f, abs(squeeze(freqresp(G_m1_vc_Rz_fast(1,1), f, 'Hz'))), 'color', colors(3,:), ...
     'DisplayName', '$f_{ni}/f_i$ - $\Omega_z = 360$ deg/s')
for i = 1:5
    for j = i+1:6
        plot(f, abs(squeeze(freqresp(G_m1_vc(i,j), f, 'Hz'))), 'color', [colors(1,:), 0.2], ...
             'HandleVisibility', 'off');
        plot(f, abs(squeeze(freqresp(G_m1_vc_Rz_slow(i,j), f, 'Hz'))), 'color', [colors(2,:), 0.2], ...
             'HandleVisibility', 'off');
        plot(f, abs(squeeze(freqresp(G_m1_vc_Rz_fast(i,j), f, 'Hz'))), 'color', [colors(3,:), 0.2], ...
             'HandleVisibility', 'off');
    end
end
for i = 2:6
    plot(f, abs(squeeze(freqresp(G_m1_vc(i,i), f, 'Hz'))), 'color', colors(1,:), ...
         'HandleVisibility', 'off');
end
for i = 2:6
    plot(f, abs(squeeze(freqresp(G_m1_vc_Rz_slow(i,i), f, 'Hz'))), 'color', colors(2,:), ...
         'HandleVisibility', 'off');
end
for i = 2:6
    plot(f, abs(squeeze(freqresp(G_m1_vc_Rz_fast(i,i), f, 'Hz'))), 'color', colors(3,:), ...
         'HandleVisibility', 'off');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
ylim([1e-9, 1e-2]);
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;

ax2 = nexttile;
hold on;
for i = 1:6
    plot(f, 180/pi*angle(squeeze(freqresp(G_m1_vc(i,i), f, 'Hz'))), 'color', colors(1,:));
    plot(f, 180/pi*angle(squeeze(freqresp(G_m1_vc_Rz_slow(i,i), f, 'Hz'))), 'color', colors(2,:));
    plot(f, 180/pi*angle(squeeze(freqresp(G_m1_vc_Rz_fast(i,i), f, 'Hz'))), 'color', colors(3,:));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-180, 180]);
yticks([-180:90:180]);

linkaxes([ax1,ax2],'x');
xlim([f(1), f(end)]);

% Controller design

% In this section, a high authority controller is design such that:
% - it is robust to the change of payload mass (i.e. is should be stable for all the damped plants of Figure ref:fig:nass_hac_plants)
% - it has reasonably high bandwidth to give good performances (here 10Hz)

% eqref:eq:nass_robust_hac

% \begin{equation}\label{eq:nass_robust_hac}
%   K_{\text{HAC}}(s) = g_0 \cdot \underbrace{\frac{\omega_c}{s}}_{\text{int}} \cdot \underbrace{\frac{1}{\sqrt{\alpha}}\frac{1 + \frac{s}{\omega_c/\sqrt{\alpha}}}{1 + \frac{s}{\omega_c\sqrt{\alpha}}}}_{\text{lead}} \cdot \underbrace{\frac{1}{1 + \frac{s}{\omega_0}}}_{\text{LPF}}, \quad \left( \omega_c = 2\pi10\,\text{rad/s},\ \alpha = 2,\ \omega_0 = 2\pi80\,\text{rad/s} \right)
% \end{equation}


%% HAC Design
% Wanted crossover
wc = 2*pi*10; % [rad/s]

% Integrator
H_int = wc/s;

% Lead to increase phase margin
a  = 2;  % Amount of phase lead / width of the phase lead / high frequency gain
H_lead = 1/sqrt(a)*(1 + s/(wc/sqrt(a)))/(1 + s/(wc*sqrt(a)));

% Low Pass filter to increase robustness
H_lpf = 1/(1 + s/2/pi/80);

% Gain to have unitary crossover at wc
H_gain = 1./abs(evalfr(G_hac_m50(1,1), 1j*wc));

% Decentralized HAC
Khac = -H_gain  * ... % Gain
        H_int   * ... % Integrator
        H_lead   * ... % Low Pass filter
        H_lpf   * ... % Low Pass filter
        eye(6);       % 6x6 Diagonal

% The designed HAC controller is saved
save('./mat/nass_K_hac.mat', 'Khac');



% - "Decentralized" Loop Gain:
%   Bandwidth around 10Hz
% - Characteristic Loci:
%   Stable for all payloads with acceptable stability margins


%% "Diagonal" loop gain for the High Authority Controller
f = logspace(-1, 2, 1000);
figure;
tiledlayout(3, 1, 'TileSpacing', 'compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(f, abs(squeeze(freqresp(Khac(i,i)*G_hac_m1( i,i), f, 'Hz'))), ...
     'color', [colors(1,:), 0.5], 'DisplayName', '1kg');
plot(f, abs(squeeze(freqresp(Khac(i,i)*G_hac_m25(i,i), f, 'Hz'))), ...
     'color', [colors(2,:), 0.5], 'DisplayName', '25kg');
plot(f, abs(squeeze(freqresp(Khac(i,i)*G_hac_m50(i,i), f, 'Hz'))), ...
     'color', [colors(3,:), 0.5], 'DisplayName', '50kg');
for i = 2:6
    plot(f, abs(squeeze(freqresp(Khac(i,i)*G_hac_m1( i,i), f, 'Hz'))), 'color', [colors(1,:), 0.5], 'HandleVisibility', 'off');
    plot(f, abs(squeeze(freqresp(Khac(i,i)*G_hac_m25(i,i), f, 'Hz'))), 'color', [colors(2,:), 0.5], 'HandleVisibility', 'off');
    plot(f, abs(squeeze(freqresp(Khac(i,i)*G_hac_m50(i,i), f, 'Hz'))), 'color', [colors(3,:), 0.5], 'HandleVisibility', 'off');
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Loop Gain'); set(gca, 'XTickLabel',[]);
ylim([1e-2, 1e2]);
leg = legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;

ax2 = nexttile;
hold on;
for i = 1:6
    plot(f, 180/pi*angle(squeeze(freqresp(-Khac(i,i)*G_hac_m1( i,i), f, 'Hz'))), 'color', [colors(1,:), 0.5]);
    plot(f, 180/pi*angle(squeeze(freqresp(-Khac(i,i)*G_hac_m25(i,i), f, 'Hz'))), 'color', [colors(2,:), 0.5]);
    plot(f, 180/pi*angle(squeeze(freqresp(-Khac(i,i)*G_hac_m50(i,i), f, 'Hz'))), 'color', [colors(3,:), 0.5]);
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
yticks(-360:90:360);
ylim([-180, 180])

linkaxes([ax1,ax2],'x');
xlim([0.1, 100]);

%% Characteristic Loci for the High Authority Controller
Ldet_m1 = zeros(6, length(freqs));
Lmimo_m1 = squeeze(freqresp(-G_hac_m1*Khac, freqs, 'Hz'));
for i_f = 2:length(freqs)
    Ldet_m1(:, i_f) = eig(squeeze(Lmimo_m1(:,:,i_f)));
end
Ldet_m25 = zeros(6, length(freqs));
Lmimo_m25 = squeeze(freqresp(-G_hac_m25*Khac, freqs, 'Hz'));
for i_f = 2:length(freqs)
    Ldet_m25(:, i_f) = eig(squeeze(Lmimo_m25(:,:,i_f)));
end
Ldet_m50 = zeros(6, length(freqs));
Lmimo_m50 = squeeze(freqresp(-G_hac_m50*Khac, freqs, 'Hz'));
for i_f = 2:length(freqs)
    Ldet_m50(:, i_f) = eig(squeeze(Lmimo_m50(:,:,i_f)));
end

figure;
hold on;
plot(real(squeeze(Ldet_m1(1,:))), imag(squeeze(Ldet_m1(1,:))), ...
        '.', 'color', colors(1, :), ...
        'DisplayName', '1kg');
plot(real(squeeze(Ldet_m1(1,:))),-imag(squeeze(Ldet_m1(1,:))), ...
        '.', 'color', colors(1, :), ...
        'HandleVisibility', 'off');
plot(real(squeeze(Ldet_m25(1,:))), imag(squeeze(Ldet_m25(1,:))), ...
        '.', 'color', colors(2, :), ...
        'DisplayName', '25kg');
plot(real(squeeze(Ldet_m25(1,:))),-imag(squeeze(Ldet_m25(1,:))), ...
        '.', 'color', colors(2, :), ...
        'HandleVisibility', 'off');
plot(real(squeeze(Ldet_m50(1,:))), imag(squeeze(Ldet_m50(1,:))), ...
        '.', 'color', colors(3, :), ...
        'DisplayName', '50kg');
plot(real(squeeze(Ldet_m50(1,:))),-imag(squeeze(Ldet_m50(1,:))), ...
        '.', 'color', colors(3, :), ...
        'HandleVisibility', 'off');
for i = 2:6
    plot(real(squeeze(Ldet_m1(i,:))), imag(squeeze(Ldet_m1(i,:))), ...
            '.', 'color', colors(1, :), ...
            'HandleVisibility', 'off');
    plot(real(squeeze(Ldet_m1(i,:))), -imag(squeeze(Ldet_m1(i,:))), ...
            '.', 'color', colors(1, :), ...
            'HandleVisibility', 'off');

    plot(real(squeeze(Ldet_m25(i,:))), imag(squeeze(Ldet_m25(i,:))), ...
            '.', 'color', colors(2, :), ...
            'HandleVisibility', 'off');
    plot(real(squeeze(Ldet_m25(i,:))), -imag(squeeze(Ldet_m25(i,:))), ...
            '.', 'color', colors(2, :), ...
            'HandleVisibility', 'off');

    plot(real(squeeze(Ldet_m50(i,:))), imag(squeeze(Ldet_m50(i,:))), ...
            '.', 'color', colors(3, :), ...
            'HandleVisibility', 'off');
    plot(real(squeeze(Ldet_m50(i,:))), -imag(squeeze(Ldet_m50(i,:))), ...
            '.', 'color', colors(3, :), ...
            'HandleVisibility', 'off');
end
plot(-1, 0, 'kx', 'HandleVisibility', 'off');
hold off;
set(gca, 'XScale', 'lin'); set(gca, 'YScale', 'lin');
xlabel('Real Part'); ylabel('Imaginary Part');
axis square
xlim([-1.8, 0.2]); ylim([-1, 1]);
leg = legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;

% TODO Sensitivity to disturbances                                :noexport:

% - Compute transfer functions from spindle vertical error to sample vertical error with HAC-IFF
%   Compare without the NASS, and with just IFF
% - Same for horizontal


% Initialize each Simscape model elements
initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeSimplifiedNanoHexapod();
initializeSample('type', 'cylindrical', 'm', 1);

% Initial Simscape Configuration
initializeSimscapeConfiguration('gravity', false);
initializeDisturbances('enable', false);
initializeLoggingConfiguration('log', 'none');
initializeController('type', 'open-loop');
initializeReferences();

% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Frz_y'); io_i = io_i + 1; % Spindle Lateral Vibration [N]
io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Frz_z'); io_i = io_i + 1; % Spindle Vertical Vibration [N]
io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Fdy_z'); io_i = io_i + 1; % Vertical Ground Motion [m]
io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Dwy');   io_i = io_i + 1; % Vertical Ground Motion [m]
io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Dwz');   io_i = io_i + 1; % Vertical Ground Motion [m]
io(io_i) = linio([mdl, '/NASS'],         2, 'output',    [], 'y');     io_i = io_i + 1; % Lateral Displacement [m]
io(io_i) = linio([mdl, '/NASS'],         2, 'output',    [], 'z');     io_i = io_i + 1; % Vertical Displacement [m]

Gd_ol = linearize(mdl, io);
Gd_ol.InputName  = {'Frz_y', 'Frz_z', 'Fdy_z', 'Dwy', 'Dwz'};
Gd_ol.OutputName  = {'Dy', 'Dz'};

initializeController('type', 'iff'); % Implemented IFF controller
load('nass_K_iff.mat', 'Kiff'); % Load designed IFF controller

Gd_iff = linearize(mdl, io);
Gd_iff.InputName  = {'Frz_y', 'Frz_z', 'Fdy_z', 'Dwy', 'Dwz'};
Gd_iff.OutputName  = {'Dy', 'Dz'};

initializeController('type', 'hac-iff'); % Implemented IFF controller
load('nass_K_hac.mat', 'Khac'); % Load designed HAC controller

Gd_hac_iff = linearize(mdl, io);
Gd_hac_iff.InputName  = {'Frz_y', 'Frz_z', 'Fdy_z', 'Dwy', 'Dwz'};
Gd_hac_iff.OutputName  = {'Dy', 'Dz'};

dist = load('ustation_disturbance_psd.mat');



% Spindle, lateral:

figure;
hold on;
plot(freqs, abs(squeeze(freqresp(Gd_ol( 'Dy', 'Frz_y'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Gd_iff('Dy', 'Frz_y'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Gd_hac_iff('Dy', 'Frz_y'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $D_z/F_{R_z,z}$ [m/N]'); xlabel('Frequency [Hz]');
xticks([1e0, 1e1, 1e2]);
xlim([1, 500]);



% Spindle, vertical:

freqs = logspace(-1,3,1000);
figure;
hold on;
plot(freqs, abs(squeeze(freqresp(Gd_ol( 'Dz', 'Frz_z'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Gd_iff('Dz', 'Frz_z'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Gd_hac_iff('Dz', 'Frz_z'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $D_z/F_{R_z,z}$ [m/N]'); xlabel('Frequency [Hz]');



% Ground motion, vertical:

freqs = logspace(-1,3,1000);
figure;
hold on;
plot(freqs, abs(squeeze(freqresp(Gd_ol( 'Dz', 'Dwz'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Gd_iff('Dz', 'Dwz'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Gd_hac_iff('Dz', 'Dwz'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $D_z/F_{R_z,z}$ [m/N]'); xlabel('Frequency [Hz]');
xticks([1e0, 1e1, 1e2]);
% xlim([1, 500]);



% Ground motion, lateral:

figure;
hold on;
plot(freqs, abs(squeeze(freqresp(Gd_ol( 'Dy', 'Dwy'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Gd_iff('Dy', 'Dwy'), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Gd_hac_iff('Dy', 'Dwy'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $D_y/F_{R_z,z}$ [m/N]'); xlabel('Frequency [Hz]');
xticks([1e0, 1e1, 1e2]);
xlim([1, 500]);



% Noise Budget:

figure;
hold on;
plot(dist.gm_dist.f, sqrt(flip(-cumtrapz(flip(dist.gm_dist.f), flip(dist.gm_dist.pxx_y.*abs(squeeze(freqresp(Gd_ol(  'Dy', 'Dwy'), dist.gm_dist.f, 'Hz'))).^2)))));
plot(dist.gm_dist.f, sqrt(flip(-cumtrapz(flip(dist.gm_dist.f), flip(dist.gm_dist.pxx_y.*abs(squeeze(freqresp(Gd_iff(  'Dy', 'Dwy'), dist.gm_dist.f, 'Hz'))).^2)))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('ASD [m/sqrt(Hz)]'); xlabel('Frequency [Hz]');
xticks([1e0, 1e1, 1e2]);
xlim([1, 500]);

% Tomography experiment

% - Validation of concept with tomography scans at the highest rotational velocity of $\Omega_z = 360\,\text{deg/s}$
% - Compare obtained results with the smallest beam size that is expected with future beamline upgrade: 200nm (horizontal size) x 100nm (vertical size)
% - Take into account the two main sources of disturbances: ground motion, spindle vibrations
%   Other noise sources are not taken into account here as they will be optimized latter (detail design phase): measurement noise, electrical noise for DAC and voltage amplifiers, ...

% The open-loop errors and the closed-loop errors for the tomography scan with the light sample $1\,kg$ are shown in Figure ref:fig:nass_tomo_1kg_60rpm.


% Sample is not centered with the rotation axis
% This is done by offsetfing the micro-hexapod by 0.9um
P_micro_hexapod = [0.9e-6; 0; 0]; % [m]

open(mdl);
set_param(mdl, 'StopTime', '2');

initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod('AP', P_micro_hexapod);
initializeSample('type', 'cylindrical', 'm', 1);

initializeSimscapeConfiguration('gravity', false);
initializeLoggingConfiguration('log', 'all', 'Ts', 1e-3);

initializeDisturbances(...
    'Dw_x',  true, ... % Ground Motion - X direction
    'Dw_y',  true, ... % Ground Motion - Y direction
    'Dw_z',  true, ... % Ground Motion - Z direction
    'Fdy_x', false, ... % Translation Stage - X direction
    'Fdy_z', false, ... % Translation Stage - Z direction
    'Frz_x', true, ... % Spindle - X direction
    'Frz_y', true, ... % Spindle - Y direction
    'Frz_z', true);    % Spindle - Z direction

initializeReferences(...
    'Rz_type', 'rotating', ...
    'Rz_period', 1, ...
    'Dh_pos', [P_micro_hexapod; 0; 0; 0]);

% Open-Loop Simulation without Nano-Hexapod - 1kg payload
initializeSimplifiedNanoHexapod('type', 'none');
initializeController('type', 'open-loop');
sim(mdl);
exp_tomo_ol_m1 = simout;

% Closed-Loop Simulation with NASS
initializeSimplifiedNanoHexapod();
initializeController('type', 'hac-iff');
load('nass_K_iff.mat', 'Kiff');
load('nass_K_hac.mat', 'Khac');

% 1kg payload
initializeSample('type', 'cylindrical', 'm', 1);
sim(mdl);
exp_tomo_cl_m1 = simout;

% 25kg payload
initializeSample('type', 'cylindrical', 'm', 25);
sim(mdl);
exp_tomo_cl_m25 = simout;

% 50kg payload
initializeSample('type', 'cylindrical', 'm', 50);
sim(mdl);
exp_tomo_cl_m50 = simout;

% Slower tomography for high payload mass
% initializeReferences(...
%     'Rz_type', 'rotating', ...
%     'Rz_period', 10, ... % 36deg/s
%     'Dh_pos', [P_micro_hexapod; 0; 0; 0]);
% initializeSample('type', 'cylindrical', 'm', 50);
% set_param(mdl, 'StopTime', '5');
% sim(mdl);
% exp_tomo_cl_m50_slow = simout;

%% Simulation of tomography experiment - 1kg payload - 360deg/s - XY errors
figure;
hold on;
plot(1e6*exp_tomo_ol_m1.y.x.Data, 1e6*exp_tomo_ol_m1.y.y.Data, 'DisplayName', 'OL')
plot(1e6*exp_tomo_cl_m1.y.x.Data(1e3:end), 1e6*exp_tomo_cl_m1.y.y.Data(1e3:end), 'color', colors(2,:), 'DisplayName', 'CL')
hold off;
xlabel('$D_x$ [$\mu$m]'); ylabel('$D_y$ [$\mu$m]');
axis equal
xlim([-2, 2]); ylim([-2, 2]);
xticks([-2:1:2]);
yticks([-2:1:2]);
leg = legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;

%% Simulation of tomography experiment - no payload, 30rpm - YZ errors
figure;
tiledlayout(2, 1, 'TileSpacing', 'compact', 'Padding', 'None');

ax1 = nexttile();
hold on;
plot(1e6*exp_tomo_ol_m1.y.y.Data,          1e6*exp_tomo_ol_m1.y.z.Data, 'DisplayName', 'OL')
plot(1e6*exp_tomo_cl_m1.y.y.Data(1e3:end), 1e6*exp_tomo_cl_m1.y.z.Data(1e3:end), 'color', colors(2,:), 'DisplayName', 'CL')
hold off;
xlabel('$D_y$ [$\mu$m]'); ylabel('$D_z$ [$\mu$m]');
axis equal
xlim([-2, 2]); ylim([-0.4, 0.4]);
xticks([-2:1:2]);
yticks([-2:0.2:2]);
leg = legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;

ax2 = nexttile();
hold on;
plot(1e9*exp_tomo_cl_m1.y.y.Data(1e3:end), 1e9*exp_tomo_cl_m1.y.z.Data(1e3:end), 'color', colors(2,:), 'DisplayName', 'CL')
theta = linspace(0, 2*pi, 500); % Angle to plot the circle [rad]
plot(100*cos(theta), 50*sin(theta), 'k--', 'DisplayName', 'Beam size')
hold off;
xlabel('$D_y$ [nm]'); ylabel('$D_z$ [nm]');
axis equal
xlim([-500, 500]); ylim([-100, 100]);
xticks([-500:100:500]);
yticks([-100:50:100]);
leg = legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;



% #+name: fig:nass_tomo_1kg_60rpm
% #+caption: Position error of the sample in the XY (\subref{fig:nass_tomo_1kg_60rpm_xy}) and YZ (\subref{fig:nass_tomo_1kg_60rpm_yz}) planes during a simulation of a tomography experiment at $360\,\text{deg/s}$. 1kg payload is placed on top of the nano-hexapod.
% #+attr_latex: :options [htbp]
% #+begin_figure
% #+attr_latex: :caption \subcaption{\label{fig:nass_tomo_1kg_60rpm_xy}XY plane}
% #+attr_latex: :options {0.48\textwidth}
% #+begin_subfigure
% #+attr_latex: :scale 0.9
% [[file:figs/nass_tomo_1kg_60rpm_xy.png]]
% #+end_subfigure
% #+attr_latex: :caption \subcaption{\label{fig:nass_tomo_1kg_60rpm_yz}YZ plane}
% #+attr_latex: :options {0.48\textwidth}
% #+begin_subfigure
% #+attr_latex: :scale 0.9
% [[file:figs/nass_tomo_1kg_60rpm_yz.png]]
% #+end_subfigure
% #+end_figure

% - Effect of payload mass (Figure ref:fig:nass_tomography_hac_iff):
%   Worse performance for high masses, as expected from the control analysis, but still acceptable considering that the rotational velocity of 360deg/s is only used for light payloads.


%% Simulation of tomography experiment - no payload, 30rpm - YZ errors
figure;
tiledlayout(1, 1, 'TileSpacing', 'compact', 'Padding', 'None');

ax1 = nexttile();
hold on;
plot(1e9*exp_tomo_cl_m1.y.y.Data(1e3:end), 1e9*exp_tomo_cl_m1.y.z.Data(1e3:end), 'color', colors(1,:), 'DisplayName', '$m = 1$ kg')
theta = linspace(0, 2*pi, 500); % Angle to plot the circle [rad]
plot(100*cos(theta), 50*sin(theta), 'k--', 'DisplayName', 'Beam size')
hold off;
xlabel('$D_y$ [$\mu$m]'); ylabel('$D_z$ [$\mu$m]');
axis equal
xlim([-200, 200]); ylim([-100, 100]);
xticks([-200:50:200]); yticks([-100:50:100]);

%% Simulation of tomography experiment - no payload, 30rpm - YZ errors
figure;
tiledlayout(1, 1, 'TileSpacing', 'compact', 'Padding', 'None');

ax1 = nexttile();
hold on;
plot(1e9*exp_tomo_cl_m25.y.y.Data(1e3:end), 1e9*exp_tomo_cl_m25.y.z.Data(1e3:end), 'color', colors(2,:), 'DisplayName', '$m = 25$ kg')
theta = linspace(0, 2*pi, 500); % Angle to plot the circle [rad]
plot(100*cos(theta), 50*sin(theta), 'k--', 'DisplayName', 'Beam size')
hold off;
xlabel('$D_y$ [$\mu$m]'); ylabel('$D_z$ [$\mu$m]');
axis equal
xlim([-200, 200]); ylim([-100, 100]);
xticks([-200:50:200]); yticks([-100:50:100]);

%% Simulation of tomography experiment - no payload, 30rpm - YZ errors
figure;
tiledlayout(1, 1, 'TileSpacing', 'compact', 'Padding', 'None');

ax1 = nexttile();
hold on;
plot(1e9*exp_tomo_cl_m50.y.y.Data(1e3:end), 1e9*exp_tomo_cl_m50.y.z.Data(1e3:end), 'color', colors(3,:), 'DisplayName', '$m = 50$ kg')
theta = linspace(0, 2*pi, 500); % Angle to plot the circle [rad]
plot(100*cos(theta), 50*sin(theta), 'k--', 'DisplayName', 'Beam size')
hold off;
xlabel('$D_y$ [$\mu$m]'); ylabel('$D_z$ [$\mu$m]');
axis equal
xlim([-200, 200]); ylim([-100, 100]);
xticks([-200:50:200]); yticks([-100:50:100]);