%% 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

%% Colors for the figures
colors = colororder;

% FRF Identification - Setup
% Similarly to what was done for the identification of the APA, the identification is performed in three steps:
% 1. White noise excitation with small amplitude.
%    This is used to determine the main resonance of the system.
% 2. Sweep sine excitation with the amplitude lowered around the resonance.
%    The sweep sine is from 10Hz to 400Hz.
% 3. High frequency noise.
%    The noise is band-passed between 300Hz and 2kHz.

% Then, the result of the second identification is used between 10Hz and 350Hz and the result of the third identification if used between 350Hz and 2kHz.


%% Sampling frequency/time
Ts = 1e-4; % Sampling Time [s]
Nfft = floor(1/Ts);
win = hanning(Nfft);
Noverlap = floor(Nfft/2);

%% Load Data
leg_sweep    = load('frf_data_leg_1_sweep.mat', 'u', 'Vs', 'de', 'da');
leg_noise_hf = load('frf_data_leg_1_noise_hf.mat', 'u', 'Vs', 'de', 'da');

%% We get the frequency vector that will be the same for all the frequency domain analysis.
[~, f] = tfestimate(leg_sweep.u, leg_sweep.de, win, Noverlap, Nfft, 1/Ts);
i_lf = f <= 350; % Indices used for the low frequency
i_hf = f >  350; % Indices used for the low frequency

% FRF Identification - Interferometer
% In this section, the dynamics from the excitation voltage $u$ to the interferometer $d_a$ is identified.
% The transfer function from $u$ to the interferometer measured displacement $d_a$ is estimated and shown in Figure ref:fig:strut_1_frf_dvf_plant_tf.

%% Compute FRF function from u to da
[frf_sweep, ~]    = tfestimate(leg_sweep.u,    leg_sweep.da,    win, Noverlap, Nfft, 1/Ts);
[frf_noise_hf, ~] = tfestimate(leg_noise_hf.u, leg_noise_hf.da, win, Noverlap, Nfft, 1/Ts);

%% Combine the FRF
int_frf = [frf_sweep(i_lf); frf_noise_hf(i_hf)];

%% Plot the measured FRF
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(f, abs(int_frf), 'k-');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $d_e/u$ [m/V]'); set(gca, 'XTickLabel',[]);
hold off;
ylim([1e-9, 1e-3]);

ax2 = nexttile;
hold on;
plot(f, 180/pi*angle(int_frf), 'k-');
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([10, 2e3]);

% FRF Identification - IFF
% In this section, the dynamics from $u$ to $V_s$ is identified.
% Then the FRF are estimated and shown in Figure ref:fig:strut_1_frf_iff_plant_tf

%% Compute the FRF
[frf_sweep,    ~] = tfestimate(leg_sweep.u,    leg_sweep.Vs,    win, Noverlap, Nfft, 1/Ts);
[frf_noise_hf, ~] = tfestimate(leg_noise_hf.u, leg_noise_hf.Vs, win, Noverlap, Nfft, 1/Ts);

%% Combine the FRF
iff_frf = [frf_sweep(i_lf); frf_noise_hf(i_hf)];

%% Plot the measured FRF
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(f, abs(iff_frf), 'k-');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $V_s/u$ [V/V]'); set(gca, 'XTickLabel',[]);
hold off;
ylim([1e-2, 1e2]);

ax2 = nexttile;
hold on;
plot(f, 180/pi*angle(iff_frf), 'k-');
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([10, 2e3]);

% Measurement Data
% The measurements are loaded.

%% Load data
leg_enc_sweep    = load('frf_data_leg_coder_1_noise.mat',    'u', 'Vs', 'de', 'da');
leg_enc_noise_hf = load('frf_data_leg_coder_1_noise_hf.mat', 'u', 'Vs', 'de', 'da');

% FRF Identification - Interferometer
% In this section, the dynamics from $u$ to $d_a$ is identified.

%% Compute FRF function from u to da
[frf_sweep, ~]    = tfestimate(leg_enc_sweep.u,    leg_enc_sweep.da,    win, Noverlap, Nfft, 1/Ts);
[frf_noise_hf, ~] = tfestimate(leg_enc_noise_hf.u, leg_enc_noise_hf.da, win, Noverlap, Nfft, 1/Ts);

%% Combine the FRF
int_with_enc_frf = [frf_sweep(i_lf); frf_noise_hf(i_hf)];



% The obtained FRF is very close to the one that was obtained when no encoder was fixed to the struts as shown in Figure ref:fig:strut_leg_compare_int_frf.

%% Plot the FRF from u to da with and without the encoder
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(f, abs(int_with_enc_frf), '-', 'DisplayName', 'With encoder');
plot(f, abs(int_frf),          '-', 'DisplayName', 'Without encoder');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $d_a/u$ [m/V]'); set(gca, 'XTickLabel',[]);
hold off;
ylim([1e-7, 1e-3]);
legend('location', 'northeast')

ax2 = nexttile;
hold on;
plot(f, 180/pi*angle(int_with_enc_frf), '-');
plot(f, 180/pi*angle(int_frf), '-');
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([10, 2e3]);

% FRF Identification - Encoder
% In this section, the dynamics from $u$ to $d_e$ (encoder) is identified.

% The FRF from $u$ to the encoder measured displacement $d_e$ is computed and shown in Figure ref:fig:strut_1_enc_frf_dvf_plant_tf.

%% Compute FRF function from u to da
[frf_sweep, ~]    = tfestimate(leg_enc_sweep.u,    leg_enc_sweep.de,    win, Noverlap, Nfft, 1/Ts);
[frf_noise_hf, ~] = tfestimate(leg_enc_noise_hf.u, leg_enc_noise_hf.de, win, Noverlap, Nfft, 1/Ts);

%% Combine the FRF
enc_frf = [frf_sweep(i_lf); frf_noise_hf(i_hf)];

%% Plot the FRF from u to de
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(f, abs(enc_frf), 'k-');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $d_e/u$ [m/V]'); set(gca, 'XTickLabel',[]);
hold off;
ylim([1e-7, 1e-3]);

ax2 = nexttile;
hold on;
plot(f, 180/pi*angle(enc_frf), 'k-');
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([10, 2e3]);



% #+name: fig:strut_1_enc_frf_dvf_plant_tf
% #+caption: Estimated FRF for the DVF plant (transfer function from $u$ to the encoder $d_e$)
% #+RESULTS:
% [[file:figs/strut_1_enc_frf_dvf_plant_tf.png]]

% The transfer functions from $u$ to $d_e$ (encoder) and to $d_a$ (interferometer) are compared in Figure ref:fig:strut_1_comp_enc_int.


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

ax1 = nexttile([2,1]);
hold on;
plot(f, abs(enc_frf),          'DisplayName', 'Encoder');
plot(f, abs(int_with_enc_frf), 'DisplayName', 'Interferometer');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $d/u$ [m/V]'); set(gca, 'XTickLabel',[]);
hold off;
legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 2);
ylim([1e-8, 1e-3]);

ax2 = nexttile;
hold on;
plot(f, 180/pi*angle(enc_frf));
plot(f, 180/pi*angle(int_with_enc_frf));
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([10, 2e3]);

% APA Resonances Frequency
% As shown in Figure ref:fig:strut_1_spurious_resonances, we can clearly see three spurious resonances at 197Hz, 290Hz and 376Hz.


%% Transfer function from Vs to de with indicated resonances
figure;
hold on;
plot(f, abs(enc_frf), 'k-');
text(93,  4e-4,  {'93Hz'}, 'VerticalAlignment','bottom','HorizontalAlignment','center')
text(200, 1.3e-4,{'197Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
text(300, 4e-6,  {'290Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
text(400, 1.4e-6,{'376Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $d_e/u$ [m/V]'); xlabel('Frequency [Hz]');
hold off;
ylim([1e-7, 1e-3]); xlim([10, 2e3]);

% FRF Identification - Force Sensor
% In this section, the dynamics from $u$ to $V_s$ is identified.


%% Compute FRF function from u to da
[frf_sweep, ~]    = tfestimate(leg_enc_sweep.u,    leg_enc_sweep.Vs,    win, Noverlap, Nfft, 1/Ts);
[frf_noise_hf, ~] = tfestimate(leg_enc_noise_hf.u, leg_enc_noise_hf.Vs, win, Noverlap, Nfft, 1/Ts);

%% Combine the FRF
iff_with_enc_frf = [frf_sweep(i_lf); frf_noise_hf(i_hf)];



% Let's now compare the IFF plants whether the encoders are fixed to the APA or not (Figure ref:fig:strut_1_frf_iff_comp_enc).

%% Compare the IFF plant with and without the encoders
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(f, abs(iff_with_enc_frf), 'DisplayName', 'With Encoder');
plot(f, abs(iff_frf), 'DisplayName', 'Without Encoder');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $V_s/u$ [V/V]'); set(gca, 'XTickLabel',[]);
hold off;
legend('location', 'northeast', 'FontSize', 8);
ylim([1e-2, 1e2]);

ax2 = nexttile;
hold on;
plot(f, 180/pi*angle(iff_with_enc_frf));
plot(f, 180/pi*angle(iff_frf));
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([10, 2e3]);

% Non-Minimum phase zero?

% In order to determine if the complex conjugate zero of Figure ref:fig:strut_1_enc_frf_iff_plant_tf is minimum phase or non-minimum phase, longer measurements are performed.


long_noise = load('frf_struts_align_3_noise_long.mat', 't', 'u', 'Vs');

Ts = 1e-4; % Sampling Time [s]
Nfft = floor(10/Ts);
win = hanning(Nfft);
Noverlap = floor(Nfft/2);

%% Transfer function estimation
[frf_noise, f] = tfestimate(long_noise.u, long_noise.Vs, win, Noverlap, Nfft, 1/Ts);

%% Bode plot of the FRF from u to de
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(f, abs(frf_noise), '.-');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $d_e/u$ [m/V]'); set(gca, 'XTickLabel',[]);
hold off;

ax2 = nexttile;
hold on;
plot(f, 180/pi*angle(frf_noise), '.-');
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([38, 45]);

% FRF Identification - Setup
% The identification of the struts dynamics is performed in two steps:
% 1. The excitation signal is a white noise with small amplitude.
%    This is used to estimate the low frequency dynamics.
% 2. Then a high frequency noise band-passed between 300Hz and 2kHz is used to estimate the high frequency dynamics.

% Then, the result of the first identification is used between 10Hz and 350Hz and the result of the second identification if used between 350Hz and 2kHz.

% Here are the leg numbers that have been measured.

%% Numnbers of the measured legs
strut_nums = [1 2 3 4 5];



% The data are loaded for both the first and second identification:

%% First identification (low frequency noise)
leg_noise = {};
for i = 1:length(strut_nums)
    leg_noise(i) = {load(sprintf('frf_data_leg_coder_%i_noise.mat', strut_nums(i)), 'u', 'Vs', 'de', 'da')};
end

%% Second identification (high frequency noise)
leg_noise_hf = {};
for i = 1:length(strut_nums)
    leg_noise_hf(i) = {load(sprintf('frf_data_leg_coder_%i_noise_hf.mat', strut_nums(i)), 'u', 'Vs', 'de', 'da')};
end

Ts = 1e-4; % Sampling Time [s]
Nfft = floor(1/Ts);
win = hanning(Nfft);
Noverlap = floor(Nfft/2);



% We get the frequency vector that will be the same for all the frequency domain analysis.

% Only used to have the frequency vector "f"
[~, f] = tfestimate(leg_noise{1}.u, leg_noise{1}.de, win, Noverlap, Nfft, 1/Ts);
i_lf = f <= 350;
i_hf = f >  350;

% FRF Identification - Encoder
% In this section, the dynamics from $u$ to $d_e$ (encoder) is identified.

% Then, the transfer function from the DAC output voltage $u$ to the measured displacement by the encoder $d_e$ is computed:

%% Transfer function estimation
enc_frf = zeros(length(f), length(strut_nums));

for i = 1:length(strut_nums)
    [frf_lf, ~] = tfestimate(leg_noise{i}.u,    detrend(leg_noise{i}.de, 0),    win, Noverlap, Nfft, 1/Ts);
    [frf_hf, ~] = tfestimate(leg_noise_hf{i}.u, detrend(leg_noise_hf{i}.de, 0), win, Noverlap, Nfft, 1/Ts);
    enc_frf(:, i) = [frf_lf(i_lf); frf_hf(i_hf)];
end



% The obtained transfer functions are shown in Figure ref:fig:struts_frf_dvf_plant_tf.

%% Bode plot of the FRF from u to de
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
for i = 1:length(strut_nums)
    plot(f, abs(enc_frf(:, i)), ...
         'DisplayName', sprintf('Leg %i', strut_nums(i)));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $d_e/u$ [m/V]'); set(gca, 'XTickLabel',[]);
hold off;
legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 2);
ylim([1e-8, 1e-3]);

ax2 = nexttile;
hold on;
for i = 1:length(strut_nums)
    plot(f, 180/pi*angle(enc_frf(:, i)));
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([10, 2e3]);

% FRF Identification - Interferometer
% In this section, the dynamics from $u$ to $d_a$ (interferometer) is identified.

% Then, the transfer function from the DAC output voltage $u$ to the measured displacement by the Attocube is computed for all the struts and shown in Figure ref:fig:struts_frf_int_plant_tf.
% All the struts are giving very similar FRF.

%% Transfer function estimation
int_frf = zeros(length(f), length(strut_nums));
for i = 1:length(strut_nums)
    [frf_lf, ~] = tfestimate(leg_noise{i}.u,    leg_noise{i}.da,    win, Noverlap, Nfft, 1/Ts);
    [frf_hf, ~] = tfestimate(leg_noise_hf{i}.u, leg_noise_hf{i}.da, win, Noverlap, Nfft, 1/Ts);
    int_frf(:, i) = [frf_lf(i_lf); frf_hf(i_hf)];
end

%% Plot the FRF from u to de (interferometer)
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
for i = 1:length(strut_nums)
    plot(f, abs(int_frf(:, i)), ...
         'DisplayName', sprintf('Leg %i', strut_nums(i)));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $d_a/u$ [m/V]'); set(gca, 'XTickLabel',[]);
hold off;
legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 2);
ylim([1e-9, 1e-3]);

ax2 = nexttile;
hold on;
for i = 1:length(strut_nums)
    plot(f, 180/pi*angle(int_frf(:, i)));
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([10, 2e3]);

% FRF Identification - Force Sensor
% In this section, the dynamics from $u$ to $V_s$ is identified.
% Then the FRF are estimated and shown in Figure ref:fig:struts_frf_iff_plant_tf.
% They are also shown all to be very similar.

%% FRF estimation of the transfer function from u to Vs
iff_frf = zeros(length(f), length(strut_nums));
for i = 1:length(strut_nums)
    [frf_lf, ~] = tfestimate(leg_noise{i}.u,    leg_noise{i}.Vs,    win, Noverlap, Nfft, 1/Ts);
    [frf_hf, ~] = tfestimate(leg_noise_hf{i}.u, leg_noise_hf{i}.Vs, win, Noverlap, Nfft, 1/Ts);
    iff_frf(:, i) = [frf_lf(i_lf); frf_hf(i_hf)];
end

%% Plot the FRF from u to Vs
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
for i = 1:length(strut_nums)
    plot(f, abs(iff_frf(:, i)), ...
         'DisplayName', sprintf('Leg %i', strut_nums(i)));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $V_s/u$ [V/V]'); set(gca, 'XTickLabel',[]);
hold off;
ylim([1e-2, 1e2]);
legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);

ax2 = nexttile;
hold on;
for i = 1:length(strut_nums)
    plot(f, 180/pi*angle(iff_frf(:, i)));
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([10, 2e3]);

% Misalignment of the APA and flexible joints

% The misalignment between the two flexible joints and the APA has been measured for all the struts:
% - the strut is fixed to the mounting bench
% - using an indicator, the height difference from the flexible joints and the APA is measured both for the top and bottom joints and on both sides
% - then it is possible to obtain the misalignment for both flexible joints

% The raw measurements are shown in Table ref:tab:meas_misalignment_struts_raw.

% As the flexible joint's "thickness" is 1mm larger than the APA "thickness", ideally (i.e. if it were perfectly centered) we would measure =-0.50mm= each time.


strut_nums = [1, 2, 3, 4, 5];

%             R Top  B Top  R Bot  B Bot
strut_align = [[-0.40, -0.60, -0.16, -0.82]   % Strut 1
               [-0.67, -0.30, -0.34, -0.63]   % Strut 2
               [-0.07, -0.88, -0.16, -0.79]   % Strut 3
               [-0.48, -0.46,  0.07, -1.00]   % Strut 4
               [-0.33, -0.64, -0.48, -0.52]]; % Strut 5

%% Save the estimated FRF for further analysis
save('./mat/meas_struts_frf.mat', 'f', 'enc_frf', 'int_frf', 'iff_frf', 'strut_nums', 'strut_align');

% Measured misalignment of the APA and flexible joints
% The misalignment between the APA and the flexible joints are measured.

% The results are defined below and summarized in Table ref:tab:meas_misalignment_struts_new_raw.


%               R Top  B Top  R Bot  B Bot
strut_align = [[-0.54, -0.50, -0.50, -0.52]   % strut 1
               [-0.44, -0.55, -0.49, -0.49]   % strut 2
               [-0.48, -0.50, -0.50, -0.46]   % strut 3
               [-0.45, -0.51, -0.51, -0.45]   % strut 4
               [-0.50, -0.50, -0.50, -0.50]   % strut 5
               [-0.50, -0.49, -0.43, -0.54]]; % strut 6

% FRF Identification - Setup
% The excitation signal is a low pass filtered white noise.
% Both the encoder and the force sensor voltage are measured.

% Here are the leg numbers that have been measured.

%% Numnbers of the measured legs
strut_nums = [1 2 3 4 5 6];

%% First identification (low frequency noise)
leg_noise = {};
for i = 1:length(strut_nums)
    leg_noise(i) = {load(sprintf('frf_struts_align_%i_noise.mat', strut_nums(i)), 'u', 'Vs', 'de')};
end

Ts = 1e-4; % Sampling Time [s]
Nfft = floor(1/Ts);
win = hanning(Nfft);
Noverlap = floor(Nfft/2);



% We get the frequency vector that will be the same for all the frequency domain analysis.

% Only used to have the frequency vector "f"
[~, f] = tfestimate(leg_noise{1}.u, leg_noise{1}.de, win, Noverlap, Nfft, 1/Ts);

% FRF Identification - Encoder
% In this section, the dynamics from $u$ to $d_e$ (encoder) is identified.

% Then, the transfer function from the DAC output voltage $u$ to the measured displacement by the encoder $d_e$ is computed:

%% Transfer function estimation
enc_frf = zeros(length(f), length(strut_nums));

for i = 1:length(strut_nums)
    enc_frf(:, i) = tfestimate(leg_noise{i}.u,    leg_noise{i}.de,    win, Noverlap, Nfft, 1/Ts);
end

%% Transfer function estimation
iff_frf = zeros(length(f), length(strut_nums));

for i = 1:length(strut_nums)
    iff_frf(:, i) = tfestimate(leg_noise{i}.u,    leg_noise{i}.Vs,    win, Noverlap, Nfft, 1/Ts);
end



% The obtained transfer functions are shown in Figure ref:fig:struts_align_frf_dvf_plant_tf.

%% Bode plot of the FRF from u to de
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
for i = 1:length(strut_nums)
    plot(f, abs(enc_frf(:, i)), ...
         'DisplayName', sprintf('Leg %i', strut_nums(i)));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $d_e/u$ [m/V]'); set(gca, 'XTickLabel',[]);
hold off;
legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 2);
ylim([1e-8, 1e-3]);

ax2 = nexttile;
hold on;
for i = 1:length(strut_nums)
    plot(f, 180/pi*angle(enc_frf(:, i)));
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([10, 2e3]);

% TODO Noise measurement                                          :noexport:

%% Nothing connected to the actuator stacks
open_circuit  = load('frf_struts_align_3_huddle_open_circuit.mat',      't', 'Vs', 'de');

%% PD200 connected but its input short-circuited
mid_voltage   = load('frf_struts_align_3_huddle_mid_voltage_dac.mat',   't', 'Vs', 'de');

%% PD200 connected to the DAC that outputs 0V
zero_voltage  = load('frf_struts_align_3_huddle_dac_zero.mat',          't', 'Vs', 'de');

%% PD200 connected to the DAC that outputs 3.25V
short_circuit = load('frf_struts_align_3_huddle_amp_short_circuit.mat', 't', 'Vs', 'de');

Ts = 1e-4; % Sampling Time [s]
Nfft = floor(2/Ts);
win = hanning(Nfft);
Noverlap = floor(Nfft/2);

[pxx_oc, f] = pwelch(detrend(open_circuit.Vs, 0),  win, Noverlap, Nfft, 1/Ts);
[pxx_mv, ~] = pwelch(detrend(mid_voltage.Vs, 0),   win, Noverlap, Nfft, 1/Ts);
[pxx_zv, ~] = pwelch(detrend(zero_voltage.Vs, 0),  win, Noverlap, Nfft, 1/Ts);
[pxx_sc, ~] = pwelch(detrend(short_circuit.Vs, 0), win, Noverlap, Nfft, 1/Ts);

figure;
hold on;
plot(f, sqrt(pxx_oc), 'DisplayName', 'Open Circuit')
plot(f, sqrt(pxx_sc), 'DisplayName', 'Amp Short-Circuited')
plot(f, sqrt(pxx_zv), 'DisplayName', 'Zero Voltage (DAC)')
plot(f, sqrt(pxx_mv), 'DisplayName', 'Mid Voltage (DAC)')
hold off;
xlabel('Frequency [Hz]'); ylabel('ASD [$V/\sqrt{Hz}$]');
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
legend('location', 'northeast');
xlim([1, 5e3]);

[pxx_oc, f] = pwelch(detrend(open_circuit.de, 0),  win, Noverlap, Nfft, 1/Ts);
[pxx_mv, ~] = pwelch(detrend(mid_voltage.de, 0),   win, Noverlap, Nfft, 1/Ts);
[pxx_zv, ~] = pwelch(detrend(zero_voltage.de, 0),  win, Noverlap, Nfft, 1/Ts);
[pxx_sc, ~] = pwelch(detrend(short_circuit.de, 0), win, Noverlap, Nfft, 1/Ts);

figure;
hold on;
plot(f, sqrt(pxx_oc), 'DisplayName', 'Open Circuit')
plot(f, sqrt(pxx_sc), 'DisplayName', 'Amp Short-Circuited')
plot(f, sqrt(pxx_zv), 'DisplayName', 'Zero Voltage (DAC)')
plot(f, sqrt(pxx_mv), 'DisplayName', 'Mid Voltage (DAC)')
hold off;
xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
legend('location', 'northeast');
xlim([1, 5e3])