%% Clear Workspace and Close figures
clear; close all; clc;

%% Intialize Laplace variable
s = zpk('s');

%% Add useful folders to the path
addpath('test_bench_apa300ml/');
addpath('png/');
addpath('mat/');
addpath('src/');

%% Frequency vector used for many plots
freqs = 2*logspace(0, 3, 1000);

%% Open Simscape Model
options = linearizeOptions;
options.SampleTime = 0;

% Name of the Simulink File
mdl = 'test_bench_apa300ml';

open(mdl)

%% Initialize the structure with default values
n_hexapod = struct();
n_hexapod.actuator = initializeAPA(...
    'type', '2dof', ...
    'Ga', 1, ... % Actuator constant [N/V]
    'Gs', 1);    % Sensor constant [V/m]

%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Va'],  1, 'openinput');  io_i = io_i + 1; % DAC Voltage
io(io_i) = linio([mdl, '/Vs'],  1, 'openoutput'); io_i = io_i + 1; % Sensor Voltage
io(io_i) = linio([mdl, '/de'],  1, 'openoutput'); io_i = io_i + 1; % Encoder
io(io_i) = linio([mdl, '/da'],  1, 'openoutput'); io_i = io_i + 1; % Interferometer

%% Run the linearization
Ga = linearize(mdl, io, 0.0, options);
Ga.InputName  = {'Va'};
Ga.OutputName = {'Vs', 'de', 'da'};

%% Bode plot of the transfer function from u to taum
freqs = logspace(1, 3, 1000);

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

ax1 = nexttile([2,1]);
hold on;
plot(freqs, abs(squeeze(freqresp(Ga('Vs', 'Va'), freqs, 'Hz'))), 'k-')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]);
hold off;

ax2 = nexttile;
hold on;
plot(freqs, 180/pi*angle(squeeze(freqresp(Ga('Vs', 'Va'), freqs, 'Hz'))), 'k-')
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
yticks(-360:45:360);
ylim([-180, 0])

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

%% Bode plot of the transfer function from Va to de and da
freqs = logspace(1, 3, 1000);

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

ax1 = nexttile([2,1]);
hold on;
plot(freqs, abs(squeeze(freqresp(Ga('de', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Encoder')
plot(freqs, abs(squeeze(freqresp(Ga('da', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Interferometer')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $d/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
hold off;
legend('location', 'southwest');

ax2 = nexttile;
hold on;
plot(freqs, 180/pi*angle(squeeze(freqresp(Ga('de', 'Va'), freqs, 'Hz'))))
plot(freqs, 180/pi*angle(squeeze(freqresp(Ga('da', 'Va'), freqs, 'Hz'))))
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
yticks(-360:45:360);
ylim([-180, 0])

linkaxes([ax1,ax2],'x');

%% Load Data
load('meas_apa_frf.mat', 'f', 'Ts', 'enc_frf', 'iff_frf', 'apa_nums');

%% Initialize a 2DoF APA with Ga=Gs=1
n_hexapod.actuator = initializeAPA(...
    'type', '2dof', ...
    'ga', 1, ...
    'gs', 1);

%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Va'], 1, 'openinput');  io_i = io_i + 1; % Actuator Voltage
io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; % Sensor Voltage
io(io_i) = linio([mdl, '/de'], 1, 'openoutput'); io_i = io_i + 1; % Encoder
io(io_i) = linio([mdl, '/da'], 1, 'openoutput'); io_i = io_i + 1; % Attocube

%% Identification
Gs = linearize(mdl, io, 0.0, options);
Gs.InputName  = {'Va'};
Gs.OutputName = {'Vs', 'de', 'da'};

%% Estimated Actuator Constant
ga = -mean(abs(enc_frf(f>10 & f<20)))./dcgain(Gs('de', 'Va')); % [N/V]

%% Estimated Sensor Constant
gs = -mean(abs(iff_frf(f>400 & f<500)))./(ga*abs(squeeze(freqresp(Gs('Vs', 'Va'), 1e3, 'Hz')))); % [V/m]

%% Set the identified constants
n_hexapod.actuator = initializeAPA(...
    'type', '2dof', ...
    'ga', ga, ... % Actuator gain [N/V]
    'gs', gs);    % Sensor gain [V/m]

%% Identify again the dynamics with correct Ga,Gs
Gs = linearize(mdl, io, 0.0, options);
Gs = Gs*exp(-Ts*s);
Gs.InputName  = {'Va'};
Gs.OutputName = {'Vs', 'de', 'da'};

%% Bode plot of the transfer function from u to de
freqs = logspace(1,4,1000);

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

ax1 = nexttile([2,1]);
hold on;
for i = 1:length(apa_nums)
    plot(f, abs(enc_frf(:, i)), 'color', [0,0,0,0.2]);
end
set(gca,'ColorOrderIndex',1);
plot(freqs, abs(squeeze(freqresp(Gs('de', 'Va'), freqs, 'Hz'))))
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $d\mathcal{L}_m/u$ [m/V]'); set(gca, 'XTickLabel',[]);
hold off;
ylim([1e-8, 1e-3]);

ax2 = nexttile;
hold on;
for i = 1:length(apa_nums)
    plot(f, 180/pi*angle(enc_frf(:,1)), 'color', [0,0,0,0.2]);
end
set(gca,'ColorOrderIndex',1);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('de', 'Va'), 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, 180]);

linkaxes([ax1,ax2],'x');
xlim([10, 2e3]);

%% Bode plot of the transfer function from Va to Vs (both Simscape and measured FRF)
freqs = logspace(1,4,1000);

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

ax1 = nexttile([2,1]);
hold on;
for i = 1:length(apa_nums)
    plot(f, abs(iff_frf(:, i)), 'color', [0,0,0,0.2]);
end
set(gca,'ColorOrderIndex',1);
plot(freqs, abs(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz'))))
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $\tau_m/u$ [V/V]'); set(gca, 'XTickLabel',[]);
hold off;
ylim([1e-2, 1e2]);

ax2 = nexttile;
hold on;
for i = 1:length(apa_nums)
    plot(f, 180/pi*angle(iff_frf(:,1)), 'color', [0,0,0,0.2]);
end
set(gca,'ColorOrderIndex',1);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('Vs', 'Va'), 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, 180]);

linkaxes([ax1,ax2],'x');
xlim([10, 2e3]);

%% Initialize the APA as a flexible body
n_hexapod.actuator = initializeAPA(...
    'type', 'flexible', ...
    'ga', 1, ...
    'gs', 1);

%% Identify the dynamics
Gs = linearize(mdl, io, 0.0, options);
Gs.InputName  = {'Va'};
Gs.OutputName = {'Vs', 'de', 'da'};

%% Actuator Constant
ga = -mean(abs(enc_frf(f>10 & f<20)))./dcgain(Gs('de', 'Va')); % [N/V]

%% Sensor Constant
gs = -mean(abs(iff_frf(f>400 & f<500)))./(ga*abs(squeeze(freqresp(Gs('Vs', 'Va'), 1e3, 'Hz')))); % [V/m]

%% Set the identified constants
n_hexapod.actuator = initializeAPA(...
    'type', 'flexible', ...
    'ga', ga, ... % Actuator gain [N/V]
    'gs', gs);    % Sensor gain [V/m]

%% Identify with updated constants
Gs = linearize(mdl, io, 0.0, options);
Gs = Gs*exp(-Ts*s);
Gs.InputName  = {'Va'};
Gs.OutputName = {'Vs', 'de', 'da'};

%% Bode plot of the transfer function from V_a to d_e (both Simscape and measured FRF)
figure;
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
for i = 1:length(apa_nums)
    plot(f, abs(enc_frf(:, i)), 'color', [0,0,0,0.2]);
end
set(gca,'ColorOrderIndex',1);
plot(freqs, abs(squeeze(freqresp(Gs('de', 'Va'), freqs, 'Hz'))))
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $d\mathcal{L}_m/u$ [m/V]'); set(gca, 'XTickLabel',[]);
hold off;
ylim([1e-9, 1e-3]);

ax2 = nexttile;
hold on;
for i = 1:length(apa_nums)
    plot(f, 180/pi*angle(enc_frf(:,1)), 'color', [0,0,0,0.2]);
end
set(gca,'ColorOrderIndex',1);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('de', 'Va'), 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, 180]);

linkaxes([ax1,ax2],'x');
xlim([10, 2e3]);

%% Bode plot of the transfer function from Va to Vs (both Simscape and measured FRF)
figure;
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
for i = 1:length(apa_nums)
    plot(f, abs(iff_frf(:, i)), 'color', [0,0,0,0.2]);
end
set(gca,'ColorOrderIndex',1);
plot(freqs, abs(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz'))))
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $\tau_m/u$ [V/V]'); set(gca, 'XTickLabel',[]);
hold off;
ylim([1e-2, 1e2]);

ax2 = nexttile;
hold on;
for i = 1:length(apa_nums)
    plot(f, 180/pi*angle(iff_frf(:,1)), 'color', [0,0,0,0.2]);
end
set(gca,'ColorOrderIndex',1);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('Vs', 'Va'), 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, 180]);

linkaxes([ax1,ax2],'x');
xlim([10, 2e3]);

%% Optimized parameters
n_hexapod.actuator = initializeAPA('type', '2dof', ...
                                   'Ga', -32.2, ...
                                   'Gs', 0.088, ...
                                   'k',  ones(6,1)*0.38e6, ...
                                   'ke', ones(6,1)*1.75e6, ...
                                   'ka', ones(6,1)*3e7, ...
                                   'c',  ones(6,1)*1.3e2, ...
                                   'ce', ones(6,1)*1e1, ...
                                   'ca', ones(6,1)*1e1 ...
                                   );

%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Va'],  1, 'openinput');  io_i = io_i + 1; % Actuator Voltage
io(io_i) = linio([mdl, '/Vs'],  1, 'openoutput'); io_i = io_i + 1; % Sensor Voltage
io(io_i) = linio([mdl, '/de'],  1, 'openoutput'); io_i = io_i + 1; % Encoder

%% Identification with optimized parameters
Gs = exp(-s*Ts)*linearize(mdl, io, 0.0, options);
Gs.InputName  = {'Va'};
Gs.OutputName = {'Vs', 'de'};

%% Comparison of the experimental data and Simscape Model
freqs = 5*logspace(0, 3, 1000);
figure;
tiledlayout(3, 2, 'TileSpacing', 'None', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
for i = 1:length(apa_nums)
    plot(f, abs(enc_frf(:, i)), 'color', [0,0,0,0.2]);
end
set(gca,'ColorOrderIndex',1);
plot(freqs, abs(squeeze(freqresp(Gs('de', 'Va'), freqs, 'Hz'))))
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $d_e/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
hold off;
ylim([1e-8, 1e-3]);

ax1b = nexttile([2,1]);
hold on;
for i = 1:length(apa_nums)
    plot(f, abs(iff_frf(:, i)), 'color', [0,0,0,0.2]);
end
set(gca,'ColorOrderIndex',1);
plot(freqs, abs(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz'))))
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]);
hold off;
ylim([1e-2, 1e2]);

ax2 = nexttile;
hold on;
for i = 1:length(apa_nums)
    plot(f, 180/pi*angle(enc_frf(:, i)), 'color', [0,0,0,0.2]);
end
set(gca,'ColorOrderIndex',1);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('de', 'Va'), 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, 180]);

ax2b = nexttile;
hold on;
for i = 1:length(apa_nums)
    plot(f, 180/pi*angle(iff_frf(:, i)), 'color', [0,0,0,0.2]);
end
set(gca,'ColorOrderIndex',1);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('Vs', 'Va'), 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, 180]);

linkaxes([ax1,ax2,ax1b,ax2b],'x');
xlim([10, 2e3]);