%% 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('./subsystems/'); % Path for Subsystems Simulink files

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

% Simulink Model name
mdl = 'nano_hexapod_model';

%% Colors for the figures
colors = colororder;

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

% Control in Cartesian Space

% Alternatively, control can be implemented directly in Cartesian space, as shown in Figure ref:fig:nhexa_control_cartesian.
% Here, the controller processes Cartesian errors $\bm{\epsilon}_{\mathcal{X}}$ to generate forces and torques $\bm{\mathcal{F}}$, which are then mapped to actuator forces through the transpose of the inverse Jacobian matrix.

% The plant behavior in Cartesian space, illustrated in Figure ref:fig:nhexa_plant_frame_cartesian, reveals interesting characteristics.
% Some degrees of freedom, particularly the vertical translation and rotation about the vertical axis, exhibit simpler second-order dynamics.
% A key advantage of this approach is that control performance can be individually tuned for each direction.
% This is particularly valuable when performance requirements differ between degrees of freedom - for instance, when higher positioning accuracy is required vertically than horizontally, or when certain rotational degrees of freedom can tolerate larger errors than others.

% However, significant coupling exists between certain degrees of freedom, particularly between rotations and translations (e.g., $\epsilon_{R_x}/\mathcal{F}_y$ or $\epsilon_{D_y}/\bm\mathcal{M}_x$).

% For the conceptual validation of the nano-hexapod, control in the strut space has been selected due to its simpler implementation and the beneficial decoupling properties observed at low frequencies.
% More sophisticated control strategies will be explored during the detailed design phase.


%% Identify plant from actuator forces to external metrology
stewart = initializeSimplifiedNanoHexapod();
initializeSample('type', 'cylindrical', 'm', 10, 'H', 300e-3);
initializeLoggingConfiguration('log', 'none');
initializeController('type', 'open-loop');

% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput');   io_i = io_i + 1; % Actuator Inputs [N]
io(io_i) = linio([mdl, '/plant'],      1, 'openoutput');  io_i = io_i + 1; % External Metrology [m, rad]

% With no payload
G = linearize(mdl, io);
G.InputName  = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
G.OutputName = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'};

%% Plant in the Cartesian Frame
G_cart = G*inv(stewart.geometry.J');
G_cart.InputName  = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};

%% Plant in the frame of the struts
G_struts = stewart.geometry.J*G;
G_struts.OutputName  = {'D1', 'D2', 'D3', 'D4', 'D5', 'D6'};

%% Bode plot of the plant projected in the frame of the struts
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
for i = 1:5
    for j = i+1:6
        plot(freqs, abs(squeeze(freqresp(G_struts(i,j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
             'HandleVisibility', 'off');
    end
end
plot(freqs, abs(squeeze(freqresp(G_struts(1,1), freqs, 'Hz'))), 'color', colors(1,:), ...
     'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_i$')
for i = 2:6
    plot(freqs, abs(squeeze(freqresp(G_struts(i,i), freqs, 'Hz'))), 'color', colors(1,:), ...
         'HandleVisibility', 'off');
end
plot(freqs, abs(squeeze(freqresp(G_struts(1,2), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
     'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_j$')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
ylim([1e-9, 1e-4]);
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;

ax2 = nexttile;
hold on;
for i = 1:6
    plot(freqs, 180/pi*angle(squeeze(freqresp(G_struts(i,i), freqs, 'Hz'))), 'color', [colors(1,:),0.5]);
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);

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

%% Bode plot of the plant projected in the Cartesian frame
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
for i = 1:5
    for j = i+1:6
        plot(freqs, abs(squeeze(freqresp(G_cart(i,j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
             'HandleVisibility', 'off');
    end
end
plot(freqs, abs(squeeze(freqresp(G_cart(1,1), freqs, 'Hz'))), 'color', colors(1,:), ...
    'DisplayName', '$\epsilon_{D_x}/\mathcal{F}_x$ [m/N]')
plot(freqs, abs(squeeze(freqresp(G_cart(2,2), freqs, 'Hz'))), 'color', colors(2,:), ...
    'DisplayName', '$\epsilon_{D_y}/\mathcal{F}_y$ [m/N]')
plot(freqs, abs(squeeze(freqresp(G_cart(3,3), freqs, 'Hz'))), 'color', colors(3,:), ...
    'DisplayName', '$\epsilon_{D_z}/\mathcal{F}_z$ [m/N]')
plot(freqs, abs(squeeze(freqresp(G_cart(4,4), freqs, 'Hz'))), 'color', colors(4,:), ...
    'DisplayName', '$\epsilon_{R_x}/\mathcal{M}_x$ [rad/Nm]')
plot(freqs, abs(squeeze(freqresp(G_cart(5,5), freqs, 'Hz'))), 'color', colors(5,:), ...
    'DisplayName', '$\epsilon_{R_y}/\mathcal{M}_y$ [rad/Nm]')
plot(freqs, abs(squeeze(freqresp(G_cart(6,6), freqs, 'Hz'))), 'color', colors(6,:), ...
    'DisplayName', '$\epsilon_{R_z}/\mathcal{M}_z$ [rad/Nm]')
plot(freqs, abs(squeeze(freqresp(G_cart(1,5), freqs, 'Hz'))), 'color', [0, 0, 0, 0.5], ...
     'DisplayName', 'Coupling')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude'); set(gca, 'XTickLabel',[]);
ylim([1e-9, 4e-3]);
leg = legend('location', 'southwest', 'FontSize', 7, 'NumColumns', 3);
leg.ItemTokenSize(1) = 15;

ax2 = nexttile;
hold on;
for i = 1:6
    plot(freqs, 180/pi*angle(squeeze(freqresp(G_cart(i,i), freqs, 'Hz'))), 'color', colors(i,:));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);

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



% #+name: fig:nhexa_decentralized_iff_schematic
% #+caption: Schematic of the implemented decentralized IFF controller. The damped plant has a new inputs $\bm{f}^{\prime}$
% #+RESULTS:
% [[file:figs/nhexa_decentralized_iff_schematic.png]]


% \begin{equation}\label{eq:nhexa_kiff}
%     \bm{K}_{\text{IFF}}(s) = g \cdot \begin{bmatrix}
%         K_{\text{IFF}}(s) & & 0 \\
%         & \ddots & \\
%         0 & & K_{\text{IFF}}(s)
%     \end{bmatrix}, \quad K_{\text{IFF}}(s) = \frac{1}{s}
% \end{equation}


% In this section, the stiffness in parallel with the force sensor has been omitted since the Stewart platform is not subjected to rotation.
% The effect of this parallel stiffness will be examined in the next section when the platform is integrated into the complete NASS system.

% The Root Locus analysis, shown in Figure ref:fig:nhexa_decentralized_iff_root_locus, reveals the evolution of the closed-loop poles as the controller gain $g$ varies from $0$ to $\infty$.
% A key characteristic of force feedback control with collocated sensor-actuator pairs is observed: all closed-loop poles are bounded to the left-half plane, indicating guaranteed stability [[cite:&preumont08_trans_zeros_struc_contr_with]].
% This property is particularly valuable as the coupling is very large around resonance frequencies, enabling control of modes that would be difficult to include within the bandwidth using position feedback alone.

% The bode plot of an individual loop gain (i.e. the loop gain of $K_{\text{IFF}}(s) \cdot \frac{f_{ni}}{f_i}(s)$), presented in Figure ref:fig:nhexa_decentralized_iff_loop_gain, exhibits the typical characteristics of integral force feedback of having a phase bounded between $-90^o$ and $+90^o$.
% The loop-gain is high around the resonance frequencies, indicating that the decentralized IFF provides significant control authority over these modes.
% This high gain, combined with the bounded phase, enables effective damping of the resonant modes while maintaining stability.


%% Identify the IFF Plant
stewart = initializeSimplifiedNanoHexapod('actuator_kp', 0); % Ignoring parallel stiffness for now
initializeSample('type', 'cylindrical', 'm', 10, 'H', 300e-3);
initializeLoggingConfiguration('log', 'none');
initializeController('type', 'open-loop');

% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput');             io_i = io_i + 1; % Actuator Inputs [N]
io(io_i) = linio([mdl, '/plant'],      2, 'openoutput', [], 'fn');  io_i = io_i + 1; % Force Sensors [N]

% With no payload
G_iff = linearize(mdl, io);
G_iff.InputName  = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
G_iff.OutputName = {'fm1', 'fm2', 'fm3', 'fm4', 'fm5', 'fm6'};

%% IFF Controller Design
Kiff = -500/s * ... % Gain
        eye(6);     % Diagonal 6x6 controller (i.e. decentralized)

Kiff.InputName = {'fm1', 'fm2', 'fm3', 'fm4', 'fm5', 'fm6'};
Kiff.OutputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};

%% Root Locus plot of the Decentralized IFF Control
gains = logspace(-2, 1, 200);

figure;
tiledlayout(1, 1, 'TileSpacing', 'compact', 'Padding', 'None');
nexttile();
hold on;
plot(real(pole(G_iff)),  imag(pole(G_iff)),  'x', 'color', colors(1,:), ...
    'DisplayName', '$g = 0$');
plot(real(tzero(G_iff)), imag(tzero(G_iff)), 'o', 'color', colors(1,:), ...
    'HandleVisibility', 'off');

for g = gains
    clpoles = pole(feedback(G_iff, g*Kiff, +1));
    plot(real(clpoles), imag(clpoles), '.', 'color', colors(1,:), ...
        'HandleVisibility', 'off');
end

% Optimal gain
clpoles = pole(feedback(G_iff, Kiff, +1));
plot(real(clpoles), imag(clpoles), 'kx', ...
    'DisplayName', '$g_{opt}$');
hold off;
axis equal;
xlim([-600, 50]); ylim([-50, 600]);
xticks([-600:100:0]);
yticks([0:100:600]);
set(gca, 'XTickLabel',[]); set(gca, 'YTickLabel',[]);
xlabel('Real part'); ylabel('Imaginary part');

%% Loop gain for the Decentralized IFF
figure;
tiledlayout(3, 1, 'TileSpacing', 'compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(freqs, abs(squeeze(freqresp(-G_iff(1,1)*Kiff(1,1), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Loop Gain'); set(gca, 'XTickLabel',[]);
ylim([1e-2, 1e2]);
% leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
% leg.ItemTokenSize(1) = 15;

ax2 = nexttile;
hold on;
plot(freqs, 180/pi*angle(squeeze(freqresp(-G_iff(1,1)*Kiff(1,1), 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([1, 1e3]);



% #+name: fig:nhexa_hac_iff_schematic
% #+caption: HAC-IFF control architecture with the High Authority Controller being implemented in the frame of the struts
% #+RESULTS:
% [[file:figs/nhexa_hac_iff_schematic.png]]

% The effect of decentralized IFF on the plant dynamics can be observed by comparing two sets of transfer functions.
% Figure ref:fig:nhexa_decentralized_hac_iff_plant_undamped shows the original transfer functions from actuator forces $\bm{f}$ to strut errors $\bm{\epsilon}_{\mathcal{L}}$, characterized by pronounced resonant peaks.
% When decentralized IFF is implemented, the transfer functions from modified inputs $\bm{f}^{\prime}$ to strut errors $\bm{\epsilon}_{\mathcal{L}}$, shown in Figure ref:fig:nhexa_decentralized_hac_iff_plant_damped, exhibit significantly attenuated resonances.
% This damping of structural resonances serves two purposes: it reduces vibrations in the vicinity of resonances and simplifies the design of the high authority controller by providing a simpler plant dynamics.


%% Identify the IFF Plant
initializeController('type', 'iff');

% 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, '/plant'],      1, 'openoutput');  io_i = io_i + 1; % External Metrology [m,rad]

% With no payload
G_hac = linearize(mdl, io);
G_hac.InputName  = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
G_hac.OutputName = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'};

%% Plant in the frame of the struts
G_hac_struts = stewart.geometry.J*G_hac;
G_hac_struts.OutputName  = {'D1', 'D2', 'D3', 'D4', 'D5', 'D6'};

%% Bode plot of the plant projected in the frame of the struts
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
for i = 1:5
    for j = i+1:6
        plot(freqs, abs(squeeze(freqresp(G_struts(i,j), freqs, 'Hz'))), 'color', [0,0,0,0.1], ...
             'HandleVisibility', 'off');
    end
end
plot(freqs, abs(squeeze(freqresp(G_struts(1,1), freqs, 'Hz'))), 'color', colors(1,:), ...
     'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_i$')
for i = 2:6
    plot(freqs, abs(squeeze(freqresp(G_struts(i,i), freqs, 'Hz'))), 'color', colors(1,:), ...
         'HandleVisibility', 'off');
end
plot(freqs, abs(squeeze(freqresp(G_struts(1,2), freqs, 'Hz'))), 'color', [0,0,0,0.1], ...
     'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_j$')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
ylim([1e-9, 1e-4]);
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;

ax2 = nexttile;
hold on;
for i = 1:6
    plot(freqs, 180/pi*angle(squeeze(freqresp(G_struts(i,i), freqs, 'Hz'))), 'color', colors(1,:));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);

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

%% Bode plot of the plant projected in the frame of the struts
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
for i = 1:5
    for j = i+1:6
        plot(freqs, abs(squeeze(freqresp(G_hac_struts(i,j), freqs, 'Hz'))), 'color', [0,0,0,0.1], ...
             'HandleVisibility', 'off');
    end
end
plot(freqs, abs(squeeze(freqresp(G_struts(1,1), freqs, 'Hz'))), 'color', [colors(1,:), 0.2], ...
     'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_i$')
plot(freqs, abs(squeeze(freqresp(G_hac_struts(1,1), freqs, 'Hz'))), 'color', colors(2,:), ...
     'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_i^\prime$')
for i = 2:6
    plot(freqs, abs(squeeze(freqresp(G_struts(i,i), freqs, 'Hz'))), 'color', [colors(1,:), 0.2], ...
         'HandleVisibility', 'off');
    plot(freqs, abs(squeeze(freqresp(G_hac_struts(i,i), freqs, 'Hz'))), 'color', colors(2,:), ...
         'HandleVisibility', 'off');
end
plot(freqs, abs(squeeze(freqresp(G_hac_struts(1,2), freqs, 'Hz'))), 'color', [0,0,0,0.1], ...
     'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_j^\prime$')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
ylim([1e-9, 1e-4]);
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;

ax2 = nexttile;
hold on;
for i = 1:6
    plot(freqs, 180/pi*angle(squeeze(freqresp(G_struts(i,i), freqs, 'Hz'))), 'color', [colors(1,:), 0.2]);
    plot(freqs, 180/pi*angle(squeeze(freqresp(G_hac_struts(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([-180, 180]);
yticks([-180, -90, 0, 90, 180]);

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



% #+name: fig:nhexa_decentralized_hac_iff_plant
% #+caption: Plant in the frame of the strut for the High Authority Controller.
% #+attr_latex: :options [htbp]
% #+begin_figure
% #+attr_latex: :caption \subcaption{\label{fig:nhexa_decentralized_hac_iff_plant_undamped}Undamped plant in the frame of the struts}
% #+attr_latex: :options {0.48\textwidth}
% #+begin_subfigure
% #+attr_latex: :width 0.95\linewidth
% [[file:figs/nhexa_decentralized_hac_iff_plant_undamped.png]]
% #+end_subfigure
% #+attr_latex: :caption \subcaption{\label{fig:nhexa_decentralized_hac_iff_plant_damped}Damped plant with Decentralized IFF}
% #+attr_latex: :options {0.48\textwidth}
% #+begin_subfigure
% #+attr_latex: :width 0.95\linewidth
% [[file:figs/nhexa_decentralized_hac_iff_plant_damped.png]]
% #+end_subfigure
% #+end_figure

% Building upon the damped plant dynamics shown in Figure ref:fig:nhexa_decentralized_hac_iff_plant_damped, a high authority controller is designed with the structure given in eqref:eq:nhexa_khac.
% The controller combines three elements: an integrator providing high gain at low frequencies, a lead compensator improving stability margins, and a low-pass filter for robustness to unmodeled high-frequency dynamics.
% The loop gain of an individual control channel is shown in Figure ref:fig:nhexa_decentralized_hac_iff_loop_gain.

% \begin{equation}\label{eq:nhexa_khac}
%     \bm{K}_{\text{HAC}}(s) = \begin{bmatrix}
%         K_{\text{HAC}}(s) & & 0 \\
%         & \ddots & \\
%         0 & & K_{\text{HAC}}(s)
%     \end{bmatrix}, \quad 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}}
% \end{equation}

% The stability of the MIMO feedback loop is analyzed through the /characteristic loci/ method.
% Such characteristic loci, shown in Figure ref:fig:nhexa_decentralized_hac_iff_root_locus, represent the eigenvalues of the loop gain matrix $\bm{G}(j\omega)\bm{K}(j\omega)$ plotted in the complex plane as frequency varies from $0$ to $\infty$.
% For MIMO systems, this method generalizes the classical Nyquist stability criterion: with the open-loop system being stable, the closed-loop system is stable if none of the characteristic loci encircle the -1 point [[cite:&skogestad07_multiv_feedb_contr]].
% As seen in Figure ref:fig:nhexa_decentralized_hac_iff_root_locus, all loci remain to the right of the -1 point, confirming the stability of the closed-loop system. Additionally, the distance of the loci from the -1 point provides information about stability margins for the coupled system.


%% High Authority Controller - Mid Stiffness Nano-Hexapod
% Wanted crossover
wc = 2*pi*20; % [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/200);

% Gain to have unitary crossover at 5Hz
H_gain = 1./abs(evalfr(G_hac_struts(1, 1), 1j*wc));

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

%% Plot of the eigenvalues of L in the complex plane
Ldet = zeros(6, length(freqs));
Lmimo = squeeze(freqresp(G_hac_struts*Khac, freqs, 'Hz'));
for i_f = 2:length(freqs)
    Ldet(:, i_f) = eig(squeeze(Lmimo(:,:,i_f)));
end

figure;
hold on;
for i = 1:6
plot(real(squeeze(Ldet(i,:))), imag(squeeze(Ldet(i,:))), ...
        '.', 'color', colors(1, :), ...
        'HandleVisibility', 'off');
plot(real(squeeze(Ldet(i,:))), -imag(squeeze(Ldet(i,:))), ...
        '.', 'color', colors(1, :), ...
        '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]);

%% Loop gain for the Decentralized HAC_IFF
figure;
tiledlayout(3, 1, 'TileSpacing', 'compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(freqs, abs(squeeze(freqresp(G_hac_struts(1,1)*Khac(1,1), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Loop Gain'); set(gca, 'XTickLabel',[]);
ylim([1e-2, 1e2]);

ax2 = nexttile;
hold on;
plot(freqs, 180/pi*angle(squeeze(freqresp(G_hac_struts(1,1)*Khac(1,1), 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([1, 1e3]);