%% 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;

%% Simscape model name
mdl = 'rotating_model';

%% Nano-Hexapod
mn = 15; % Nano-Hexapod mass [kg]

%% Light Sample
ms = 1; % Sample Mass [kg]

%% General Configuration
model_config = struct();
model_config.controller = "open_loop"; % Default: Open-Loop
model_config.Tuv_type   = "normal";    % Default: 2DoF stage

%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/controller'],        1, 'openinput');  io_i = io_i + 1; % [Fu, Fv]
io(io_i) = linio([mdl, '/fd'],                1, 'openinput');  io_i = io_i + 1; % [Fdx, Fdy]
io(io_i) = linio([mdl, '/xf'],                1, 'openinput');  io_i = io_i + 1; % [Dfx, Dfy]
io(io_i) = linio([mdl, '/translation_stage'], 1, 'openoutput'); io_i = io_i + 1; % [Fmu, Fmv]
io(io_i) = linio([mdl, '/translation_stage'], 2, 'openoutput'); io_i = io_i + 1; % [Du, Dv]
io(io_i) = linio([mdl, '/ext_metrology'],     1, 'openoutput'); io_i = io_i + 1; % [Dx, Dy]

%% Voice Coil (i.e. soft) Nano-Hexapod
kn = 1e4; % Nano-Hexapod Stiffness [N/m]
cn = 2*0.005*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]

Wz = 0; % Rotating Velocity [rad/s]
G_vc_norot = linearize(mdl, io, 0.0);
G_vc_norot.InputName = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy'};
G_vc_norot.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};

Wz = 2*pi; % Rotating Velocity [rad/s]
G_vc_fast = linearize(mdl, io, 0.0);
G_vc_fast.InputName = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy'};
G_vc_fast.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};

%% APA (i.e. relatively stiff) Nano-Hexapod
kn = 1e6; % Nano-Hexapod Stiffness [N/m]
cn = 2*0.005*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]

Wz = 0; % Rotating Velocity [rad/s]
G_md_norot = linearize(mdl, io, 0.0);
G_md_norot.InputName = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy'};
G_md_norot.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};

Wz = 2*pi; % Rotating Velocity [rad/s]
G_md_fast = linearize(mdl, io, 0.0);
G_md_fast.InputName = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy'};
G_md_fast.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};

%% Piezoelectric (i.e. stiff) Nano-Hexapod
kn = 1e8; % Nano-Hexapod Stiffness [N/m]
cn = 2*0.005*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]

Wz = 0; % Rotating Velocity [rad/s]
G_pz_norot = linearize(mdl, io, 0.0);
G_pz_norot.InputName = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy'};
G_pz_norot.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};

Wz = 2*pi; % Rotating Velocity [rad/s]
G_pz_fast = linearize(mdl, io, 0.0);
G_pz_fast.InputName = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy'};
G_pz_fast.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};

%% Compute negative spring in [N/m]
Kneg_light = (15+1)*(2*pi)^2;

%% Effect of rotation on the nano-hexapod dynamics
freqs = logspace(0, 1, 1000);

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

ax1 = nexttile([2,1]);
hold on;
plot(freqs, abs(squeeze(freqresp(G_vc_norot('Du', 'Fu'), freqs, 'Hz'))), '--',  'color', colors(1,:), ...
    'DisplayName', '$\Omega = 0\,$rpm, $D_u/F_u$');
plot(freqs, abs(squeeze(freqresp(G_vc_fast( 'Du', 'Fu'), freqs, 'Hz'))), '-' ,  'color', colors(1,:), ...
    'DisplayName', '$\Omega = 60\,$rpm, $D_u/F_u$');
plot(freqs, abs(squeeze(freqresp(G_vc_fast( 'Dv', 'Fu'), freqs, 'Hz'))), '-' , 'color', [colors(1,:), 0.5], ...
    'DisplayName', '$\Omega = 60\,$rpm, $D_v/F_u$');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Magnitude [m/N]'); set(gca, 'XTickLabel',[]);
ylim([1e-6, 1e-2])

ax2 = nexttile;
hold on;
plot(freqs, 180/pi*angle(squeeze(freqresp(G_vc_norot('Du', 'Fu'), freqs, 'Hz'))), '--', 'color', colors(1,:));
plot(freqs, 180/pi*angle(squeeze(freqresp(G_vc_fast( 'Du', 'Fu'), freqs, 'Hz'))), '-' , 'color', colors(1,:));
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([1, 1e3]);

%% Effect of rotation on the nano-hexapod dynamics
freqs = logspace(1, 2, 1000);

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

ax1 = nexttile([2,1]);
hold on;
plot(freqs, abs(squeeze(freqresp(G_md_norot('Du', 'Fu'), freqs, 'Hz'))), '--',  'color', colors(2,:), ...
    'DisplayName', '$\Omega = 0\,$rpm, $D_u/F_u$');
plot(freqs, abs(squeeze(freqresp(G_md_fast( 'Du', 'Fu'), freqs, 'Hz'))), '-' ,  'color', colors(2,:), ...
    'DisplayName', '$\Omega = 60\,$rpm, $D_u/F_u$');
plot(freqs, abs(squeeze(freqresp(G_md_fast( 'Dv', 'Fu'), freqs, 'Hz'))), '-' , 'color', [colors(2,:), 0.5], ...
    'DisplayName', '$\Omega = 60\,$rpm, $D_v/F_u$');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Magnitude [m/N]'); set(gca, 'XTickLabel',[]);
ylim([1e-8, 1e-4])

ax2 = nexttile;
hold on;
plot(freqs, 180/pi*angle(squeeze(freqresp(G_md_norot('Du', 'Fu'), freqs, 'Hz'))), '--', 'color', colors(2,:));
plot(freqs, 180/pi*angle(squeeze(freqresp(G_md_fast( 'Du', 'Fu'), freqs, 'Hz'))), '-' , 'color', colors(2,:));
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');

%% Effect of rotation on the nano-hexapod dynamics
freqs = logspace(2, 3, 1000);

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

ax1 = nexttile([2,1]);
hold on;
plot(freqs, abs(squeeze(freqresp(G_pz_norot('Du', 'Fu'), freqs, 'Hz'))), '--',  'color', colors(3,:), ...
    'DisplayName', '$\Omega = 0\,$rpm, $D_u/F_u$');
plot(freqs, abs(squeeze(freqresp(G_pz_fast( 'Du', 'Fu'), freqs, 'Hz'))), '-' ,  'color', colors(3,:), ...
    'DisplayName', '$\Omega = 60\,$rpm, $D_u/F_u$');
plot(freqs, abs(squeeze(freqresp(G_pz_fast( 'Dv', 'Fu'), freqs, 'Hz'))), '-' , 'color', [colors(3,:), 0.5], ...
    'DisplayName', '$\Omega = 60\,$rpm, $D_v/F_u$');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Magnitude [m/N]'); set(gca, 'XTickLabel',[]);
ylim([1e-10, 1e-6])

ax2 = nexttile;
hold on;
plot(freqs, 180/pi*angle(squeeze(freqresp(G_pz_norot('Du', 'Fu'), freqs, 'Hz'))), '--', 'color', colors(3,:));
plot(freqs, 180/pi*angle(squeeze(freqresp(G_pz_fast( 'Du', 'Fu'), freqs, 'Hz'))), '-' , 'color', colors(3,:));
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');

%% Compute the optimal control gain
wis = logspace(-2, 3, 200); % [rad/s]

opt_iff_hpf_xi_vc = zeros(1, length(wis)); % Optimal simultaneous damping
opt_iff_hpf_gain_vc = zeros(1, length(wis)); % Corresponding optimal gain

opt_iff_hpf_xi_md = zeros(1, length(wis)); % Optimal simultaneous damping
opt_iff_hpf_gain_md = zeros(1, length(wis)); % Corresponding optimal gain

opt_iff_hpf_xi_pz = zeros(1, length(wis)); % Optimal simultaneous damping
opt_iff_hpf_gain_pz = zeros(1, length(wis)); % Corresponding optimal gain

for wi_i = 1:length(wis)
    wi = wis(wi_i);
    Kiff = 1/(s + wi)*eye(2);

    fun = @(g)computeSimultaneousDamping(g, G_vc_fast({'fu', 'fv'}, {'Fu', 'Fv'}), Kiff);

    [g_opt, xi_opt] = fminsearch(fun, 0.1);
    opt_iff_hpf_xi_vc(wi_i) = 1/xi_opt;
    opt_iff_hpf_gain_vc(wi_i) = g_opt;

    fun = @(g)computeSimultaneousDamping(g, G_md_fast({'fu', 'fv'}, {'Fu', 'Fv'}), Kiff);

    [g_opt, xi_opt] = fminsearch(fun, 0.1);
    opt_iff_hpf_xi_md(wi_i) = 1/xi_opt;
    opt_iff_hpf_gain_md(wi_i) = g_opt;

    fun = @(g)computeSimultaneousDamping(g, G_pz_fast({'fu', 'fv'}, {'Fu', 'Fv'}), Kiff);

    [g_opt, xi_opt] = fminsearch(fun, 0.1);
    opt_iff_hpf_xi_pz(wi_i) = 1/xi_opt;
    opt_iff_hpf_gain_pz(wi_i) = g_opt;
end

%% Find optimal parameters with at least a gain margin of 2
i_iff_hpf_vc = find(opt_iff_hpf_gain_vc < 0.5*(wis*((sqrt(1e4/16)/(2*pi))^2 - 1)));
i_iff_hpf_vc = i_iff_hpf_vc(1);

i_iff_hpf_md = find(opt_iff_hpf_xi_md > 0.95*max(opt_iff_hpf_xi_md));
i_iff_hpf_md = i_iff_hpf_md(end)+1;

i_iff_hpf_pz = find(opt_iff_hpf_xi_pz > 0.95*max(opt_iff_hpf_xi_pz));
i_iff_hpf_pz = i_iff_hpf_pz(end)+1;

%% Optimal modified IFF parameters that yields maximum simultaneous damping
figure;
yyaxis left
hold on;
plot(wis, opt_iff_hpf_xi_vc, '-', 'DisplayName', '$\xi_{cl}$');
plot(wis(i_iff_hpf_vc), opt_iff_hpf_xi_vc(i_iff_hpf_vc), '.', 'MarkerSize', 15, 'HandleVisibility', 'off');
hold off;
set(gca, 'YScale', 'lin');
ylim([0,1]);
ylabel('Damping Ratio $\xi$');

yyaxis right
hold on;
plot(wis, opt_iff_hpf_gain_vc, '-', 'DisplayName', '$g_{opt}$');
plot(wis, wis*((sqrt(1e4/16)/(2*pi))^2 - 1), '--', 'DisplayName', '$g_{max}$');
plot(wis(i_iff_hpf_vc), opt_iff_hpf_gain_vc(i_iff_hpf_vc), '.', 'MarkerSize', 15, 'HandleVisibility', 'off');
set(gca, 'YScale', 'lin');
ylim([0,200]);
xlabel('$\omega_i$ [rad/s]');
set(gca, 'YTickLabel',[]);
ylabel('Controller gain $g$');
set(gca, 'XScale', 'log');
xticks([1e-2,1,1e2])
legend('location', 'northwest', 'FontSize', 8);

figure;
yyaxis left
hold on;
plot(wis, opt_iff_hpf_xi_md, '-');
plot(wis(i_iff_hpf_md), opt_iff_hpf_xi_md(i_iff_hpf_md), '.', 'MarkerSize', 15, 'HandleVisibility', 'off');
hold off;
set(gca, 'YScale', 'lin');
ylim([0,1]);
ylabel('Damping Ratio $\xi$');

yyaxis right
hold on;
plot(wis, opt_iff_hpf_gain_md, '-');
plot(wis(i_iff_hpf_md), opt_iff_hpf_gain_md(i_iff_hpf_md), '.', 'MarkerSize', 15, 'HandleVisibility', 'off');
plot(wis, wis*((sqrt(1e6/16)/(2*pi))^2 - 1), '--');
set(gca, 'YScale', 'lin');
ylim([0,1000]);
xlabel('$\omega_i$ [rad/s]');
ylabel('Controller gain $g$');
set(gca, 'YTickLabel',[]);
set(gca, 'XScale', 'log');
xticks([1e-2,1,1e2])

figure;
yyaxis left
hold on;
plot(wis, opt_iff_hpf_xi_pz, '-');
plot(wis(i_iff_hpf_pz), opt_iff_hpf_xi_pz(i_iff_hpf_pz), '.', 'MarkerSize', 15, 'HandleVisibility', 'off');
hold off;
set(gca, 'YScale', 'lin');
ylim([0,1]);
ylabel('Damping Ratio $\xi$');

yyaxis right
hold on;
plot(wis, opt_iff_hpf_gain_pz, '-');
plot(wis(i_iff_hpf_pz), opt_iff_hpf_gain_pz(i_iff_hpf_pz), '.', 'MarkerSize', 15, 'HandleVisibility', 'off');
plot(wis, wis*((sqrt(1e8/16)/(2*pi))^2 - 1), '--');
set(gca, 'YScale', 'lin');
ylim([0,10000]);
xlabel('$\omega_i$ [rad/s]');
set(gca, 'YTickLabel',[]);
ylabel('Controller gain $g$');
set(gca, 'XScale', 'log');
xticks([1e-2,1,1e2])

%% Maximum rotating velocity
Wz = 2*pi; % [rad/s]

%% Minimum parallel stiffness
kp_min = (mn + ms) * Wz^2; % [N/m]

%% Parameters for simulation
mn = 15; % Nano-Hexapod mass [kg]
ms = 1; % Sample Mass [kg]

%% IFF Controller
Kiff_vc = 1/(s + 0.1*sqrt(1e4/(mn+ms)))*eye(2); % IFF
Kiff_md = 1/(s + 0.1*sqrt(1e6/(mn+ms)))*eye(2); % IFF
Kiff_pz = 1/(s + 0.1*sqrt(1e8/(mn+ms)))*eye(2); % IFF

%% General Configuration
model_config = struct();
model_config.controller = "open_loop"; % Default: Open-Loop
model_config.Tuv_type   = "parallel_k";    % Default: 2DoF stage

%% Computes the optimal parameters and attainable simultaneous damping - Voice Coil nano-hexapod
kps_vc = logspace(log10(kp_min), log10(1e4), 100); % Tested parallel stiffnesses [N/m]
kps_vc(end) = [];

opt_iff_kp_xi_vc   = zeros(1, length(kps_vc)); % Optimal simultaneous damping
opt_iff_kp_gain_vc = zeros(1, length(kps_vc)); % Corresponding optimal gain

for kp_i = 1:length(kps_vc)
    % Voice Coil Nano-Hexapod
    kp = kps_vc(kp_i);
    cp = 2*0.001*sqrt((ms + mn)*kp);
    kn = 1e4 - kp; % Nano-Hexapod Stiffness [N/m]
    cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]

    % Identify dynamics
    Giff_vc = linearize(mdl, io, 0);
    Giff_vc.InputName  = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy'};
    Giff_vc.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};

    fun = @(g)computeSimultaneousDamping(g, Giff_vc({'fu', 'fv'}, {'Fu', 'Fv'}), Kiff_vc);

    [g_opt, xi_opt] = fminsearch(fun, 0.1);
    opt_iff_kp_xi_vc(kp_i) = 1/xi_opt;
    opt_iff_kp_gain_vc(kp_i) = g_opt;
end

%% Computes the optimal parameters and attainable simultaneous damping - APA nano-hexapod
kps_md = logspace(log10(kp_min), log10(1e6), 100); % Tested parallel stiffnesses [N/m]
kps_md(end) = [];

opt_iff_kp_xi_md   = zeros(1, length(kps_md)); % Optimal simultaneous damping
opt_iff_kp_gain_md = zeros(1, length(kps_md)); % Corresponding optimal gain


for kp_i = 1:length(kps_md)
    % Voice Coil Nano-Hexapod
    kp = kps_md(kp_i);
    cp = 2*0.001*sqrt((ms + mn)*kp);
    kn = 1e6 - kp; % Nano-Hexapod Stiffness [N/m]
    cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]

    % Identify dynamics
    Giff_md = linearize(mdl, io, 0);
    Giff_md.InputName  = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy'};
    Giff_md.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};

    fun = @(g)computeSimultaneousDamping(g, Giff_md({'fu', 'fv'}, {'Fu', 'Fv'}), Kiff_md);

    [g_opt, xi_opt] = fminsearch(fun, 0.1);
    opt_iff_kp_xi_md(kp_i) = 1/xi_opt;
    opt_iff_kp_gain_md(kp_i) = g_opt;
end

%% Computes the optimal parameters and attainable simultaneous damping - Piezo nano-hexapod
kps_pz = logspace(log10(kp_min), log10(1e8), 100); % Tested parallel stiffnesses [N/m]
kps_pz(end) = [];

opt_iff_kp_xi_pz   = zeros(1, length(kps_pz)); % Optimal simultaneous damping
opt_iff_kp_gain_pz = zeros(1, length(kps_pz)); % Corresponding optimal gain


for kp_i = 1:length(kps_pz)
    % Voice Coil Nano-Hexapod
    kp = kps_pz(kp_i);
    cp = 2*0.001*sqrt((ms + mn)*kp);
    kn = 1e8 - kp; % Nano-Hexapod Stiffness [N/m]
    cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]

    % Identify dynamics
    Giff_pz = linearize(mdl, io, 0);
    Giff_pz.InputName  = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy'};
    Giff_pz.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};

    fun = @(g)computeSimultaneousDamping(g, Giff_pz({'fu', 'fv'}, {'Fu', 'Fv'}), Kiff_pz);

    [g_opt, xi_opt] = fminsearch(fun, 0.1);
    opt_iff_kp_xi_pz(kp_i) = 1/xi_opt;
    opt_iff_kp_gain_pz(kp_i) = g_opt;
end

%% Find result with wanted parallel stiffness
[~, i_kp_vc] = min(abs(kps_vc - 1e3));
[~, i_kp_md] = min(abs(kps_md - 1e4));
[~, i_kp_pz] = min(abs(kps_pz - 1e6));

%% Identify plants with choosen Parallel stiffnesses
model_config.Tuv_type   = "parallel_k";    % Default: 2DoF stage

% Voice Coil
kp = 1e3;
cp = 2*0.001*sqrt((ms + mn)*kp);
kn = 1e4-kp; % Nano-Hexapod Stiffness [N/m]
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]

% Identify dynamics
Wz = 2*pi; % [rad/s]
G_vc_kp_fast = linearize(mdl, io, 0);
G_vc_kp_fast.InputName  = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy'};
G_vc_kp_fast.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};

Wz = 0; % [rad/s]
G_vc_kp_norot = linearize(mdl, io, 0);
G_vc_kp_norot.InputName  = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy'};
G_vc_kp_norot.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};

% APA
kp = 1e4;
cp = 2*0.001*sqrt((ms + mn)*kp);
kn = 1e6 - kp; % Nano-Hexapod Stiffness [N/m]
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]

% Identify dynamics
Wz = 2*pi; % [rad/s]
G_md_kp_fast = linearize(mdl, io, 0);
G_md_kp_fast.InputName  = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy'};
G_md_kp_fast.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};

Wz = 0; % [rad/s]
G_md_kp_norot = linearize(mdl, io, 0);
G_md_kp_norot.InputName  = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy'};
G_md_kp_norot.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};

% Piezo
kp = 1e6;
cp = 2*0.001*sqrt((ms + mn)*kp);
kn = 1e8 - kp; % Nano-Hexapod Stiffness [N/m]
cn = 2*0.01*sqrt((ms + mn)*kn); % Nano-Hexapod Damping [N/(m/s)]

% Identify dynamics
Wz = 2*pi; % [rad/s]
G_pz_kp_fast = linearize(mdl, io, 0);
G_pz_kp_fast.InputName  = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy'};
G_pz_kp_fast.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};

Wz = 0; % [rad/s]
G_pz_kp_norot = linearize(mdl, io, 0);
G_pz_kp_norot.InputName  = {'Fu', 'Fv', 'Fdx', 'Fdy', 'Dfx', 'Dfy'};
G_pz_kp_norot.OutputName = {'fu', 'fv', 'Du', 'Dv', 'Dx', 'Dy'};

%% Optimal IFF gain and associated simultaneous damping as a function of the parallel stiffness
figure;
hold on;
plot(kps_vc, opt_iff_kp_xi_vc, '-', ...
     'color', colors(1,:), 'DisplayName', '$k_n = 0.01\,N/\mu m$');
plot(kps_vc(i_kp_vc), opt_iff_kp_xi_vc(i_kp_vc), '.', ...
     'color', colors(1,:), 'MarkerSize', 15, 'HandleVisibility', 'off');
plot(kps_md, opt_iff_kp_xi_md, '-', ...
     'color', colors(2,:), 'DisplayName', '$k_n = 1\,N/\mu m$');
plot(kps_md(i_kp_md), opt_iff_kp_xi_md(i_kp_md), '.', ...
     'color', colors(2,:), 'MarkerSize', 15, 'HandleVisibility', 'off');
plot(kps_pz, opt_iff_kp_xi_pz, '-', ...
     'color', colors(3,:), 'DisplayName', '$k_n = 100\,N/\mu m$');
plot(kps_pz(i_kp_pz), opt_iff_kp_xi_pz(i_kp_pz), '.', ...
     'color', colors(3,:), 'MarkerSize', 15, 'HandleVisibility', 'off');
hold off;
xlabel('$k_p [N/m]$');
ylabel('Damping Ratio $\xi$');
set(gca, 'XScale', 'log');
set(gca, 'YScale', 'lin');
ylim([0,1]);
yticks([0:0.2:1])
legend('location', 'southeast', 'FontSize', 8);
xlim([kps_pz(1), kps_pz(end)])

%% Computes the optimal parameters and attainable simultaneous damping - Piezo nano-hexapod
rdc_gains = 2*logspace(1, 5, 200);
% Obtained simultaneous damping
rdc_xi_vc = zeros(1, length(rdc_gains));
rdc_xi_md = zeros(1, length(rdc_gains));
rdc_xi_pz = zeros(1, length(rdc_gains));

Krdc = s*eye(2);
Krdc.InputName  = {'Du', 'Dv'};
Krdc.OutputName = {'Fu', 'Fv'};

for g_i = 1:length(rdc_gains)
    [~, xi] = damp(feedback(G_vc_fast({'Du', 'Dv'}, {'Fu', 'Fv'}), rdc_gains(g_i)*Krdc));
    rdc_xi_vc(g_i) = min(xi);

    [~, xi] = damp(feedback(G_md_fast({'Du', 'Dv'}, {'Fu', 'Fv'}), rdc_gains(g_i)*Krdc));
    rdc_xi_md(g_i) = min(xi);

    [~, xi] = damp(feedback(G_pz_fast({'Du', 'Dv'}, {'Fu', 'Fv'}), rdc_gains(g_i)*Krdc));
    rdc_xi_pz(g_i) = min(xi);
end

%% Optimal RDC
[~, i_rdc_vc] = min(abs(rdc_xi_vc - 0.99));
[~, i_rdc_md] = min(abs(rdc_xi_md - 0.99));
[~, i_rdc_pz] = min(abs(rdc_xi_pz - 0.99));

Krdc_vc = rdc_gains(i_rdc_vc)*Krdc;
Krdc_md = rdc_gains(i_rdc_md)*Krdc;
Krdc_pz = rdc_gains(i_rdc_pz)*Krdc;

%% Optimal IFF gain and associated simultaneous damping as a function of the parallel stiffness
figure;
hold on;
plot(rdc_gains, rdc_xi_vc, '-', ...
     'color', colors(1,:), 'DisplayName', '$k_n = 0.01\,N/\mu m$');
plot(rdc_gains(i_rdc_vc), rdc_xi_vc(i_rdc_vc), '.', ...
     'color', colors(1,:), 'MarkerSize', 15, 'HandleVisibility', 'off');
plot(rdc_gains, rdc_xi_md, '-', ...
     'color', colors(2,:), 'DisplayName', '$k_n = 1\,N/\mu m$');
plot(rdc_gains(i_rdc_md), rdc_xi_md(i_rdc_md), '.', ...
     'color', colors(2,:), 'MarkerSize', 15, 'HandleVisibility', 'off');
plot(rdc_gains, rdc_xi_pz, '-', ...
     'color', colors(3,:), 'DisplayName', '$k_n = 100\,N/\mu m$');
plot(rdc_gains(i_rdc_pz), rdc_xi_pz(i_rdc_pz), '.', ...
     'color', colors(3,:), 'MarkerSize', 15, 'HandleVisibility', 'off');
hold off;
xlabel('Relative Damping Controller gain $g$');
ylabel('Damping Ratio $\xi$');
set(gca, 'XScale', 'log');
set(gca, 'YScale', 'lin');
ylim([0,1]);
yticks([0:0.2:1])
xlim([rdc_gains(1), rdc_gains(end)])
legend('location', 'southeast', 'FontSize', 8);

%% Closed-Loop Plants - IFF with HPF
G_vc_norot_iff_hpf = feedback(G_vc_norot, Kiff_hpf_vc, 'name');
G_vc_fast_iff_hpf  = feedback(G_vc_fast,  Kiff_hpf_vc, 'name');

G_md_norot_iff_hpf = feedback(G_md_norot, Kiff_hpf_md, 'name');
G_md_fast_iff_hpf  = feedback(G_md_fast,  Kiff_hpf_md, 'name');

G_pz_norot_iff_hpf = feedback(G_pz_norot, Kiff_hpf_pz, 'name');
G_pz_fast_iff_hpf  = feedback(G_pz_fast,  Kiff_hpf_pz, 'name');

%% Closed-Loop Plants - IFF with Parallel Stiffness
G_vc_norot_iff_kp = feedback(G_vc_kp_norot, Kiff_kp_vc, 'name');
G_vc_fast_iff_kp  = feedback(G_vc_kp_fast,  Kiff_kp_vc, 'name');

G_md_norot_iff_kp = feedback(G_md_kp_norot, Kiff_kp_md, 'name');
G_md_fast_iff_kp  = feedback(G_md_kp_fast,  Kiff_kp_md, 'name');

G_pz_norot_iff_kp = feedback(G_pz_kp_norot, Kiff_kp_pz, 'name');
G_pz_fast_iff_kp  = feedback(G_pz_kp_fast,  Kiff_kp_pz, 'name');

%% Closed-Loop Plants - RDC
G_vc_norot_rdc = feedback(G_vc_norot, Krdc_vc, 'name');
G_vc_fast_rdc  = feedback(G_vc_fast,  Krdc_vc, 'name');

G_md_norot_rdc = feedback(G_md_norot, Krdc_md, 'name');
G_md_fast_rdc  = feedback(G_md_fast,  Krdc_md, 'name');

G_pz_norot_rdc = feedback(G_pz_norot, Krdc_pz, 'name');
G_pz_fast_rdc  = feedback(G_pz_fast,  Krdc_pz, 'name');

%% Comparison of the damped plants (direct and coupling terms) for the three proposed active damping techniques (IFF with HPF, IFF with $k_p$ and RDC) applied on the three nano-hexapod stiffnesses
freqs_vc = logspace(-1, 2, 1000);

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

ax1 = nexttile([2,1]);
hold on;
plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast( 'Du', 'Fu'), freqs_vc, 'Hz'))), '-' , 'color', [zeros(1,3)]);
plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast( 'Dv', 'Fu'), freqs_vc, 'Hz'))), '-' , 'color', [zeros(1,3), 0.5]);
plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast_iff_hpf( 'Du', 'Fu'), freqs_vc, 'Hz'))), '-' , 'color', [colors(1,:)]);
plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast_iff_hpf( 'Dv', 'Fu'), freqs_vc, 'Hz'))), '-' , 'color', [colors(1,:), 0.5]);
plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast_iff_kp( 'Du', 'Fu'), freqs_vc, 'Hz'))), '-' , 'color', [colors(2,:)]);
plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast_iff_kp( 'Dv', 'Fu'), freqs_vc, 'Hz'))), '-' , 'color', [colors(2,:), 0.5]);
plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast_rdc( 'Du', 'Fu'), freqs_vc, 'Hz'))), '-' , 'color', [colors(3,:)]);
plot(freqs_vc, abs(squeeze(freqresp(G_vc_fast_rdc( 'Dv', 'Fu'), freqs_vc, 'Hz'))), '-' , 'color', [colors(3,:), 0.5]);
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Magnitude [m/N]'); set(gca, 'XTickLabel',[]);
ylim([1e-8, 1e-2])

ax2 = nexttile;
hold on;
plot(freqs_vc, 180/pi*angle(squeeze(freqresp(G_vc_fast( 'Du', 'Fu'), freqs_vc, 'Hz'))), '-' , 'color', [zeros(1,3)]);
plot(freqs_vc, 180/pi*angle(squeeze(freqresp(G_vc_fast_iff_hpf( 'Du', 'Fu'), freqs_vc, 'Hz'))), '-' , 'color', [colors(1,:)]);
plot(freqs_vc, 180/pi*angle(squeeze(freqresp(G_vc_fast_iff_kp( 'Du', 'Fu'), freqs_vc, 'Hz'))), '-' , 'color', [colors(2,:)]);
plot(freqs_vc, 180/pi*angle(squeeze(freqresp(G_vc_fast_rdc( 'Du', 'Fu'), freqs_vc, 'Hz'))), '-' , 'color', [colors(3,:)]);
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([freqs_vc(1), freqs_vc(end)]);

freqs_md = logspace(0, 3, 1000);

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

ax1 = nexttile([2,1]);
hold on;
plot(freqs_md, abs(squeeze(freqresp(G_md_fast( 'Du', 'Fu'), freqs_md, 'Hz'))), '-' , 'color', [zeros(1,3)]);
plot(freqs_md, abs(squeeze(freqresp(G_md_fast( 'Dv', 'Fu'), freqs_md, 'Hz'))), '-' , 'color', [zeros(1,3), 0.5]);
plot(freqs_md, abs(squeeze(freqresp(G_md_fast_iff_hpf( 'Du', 'Fu'), freqs_md, 'Hz'))), '-' , 'color', [colors(1,:)]);
plot(freqs_md, abs(squeeze(freqresp(G_md_fast_iff_hpf( 'Dv', 'Fu'), freqs_md, 'Hz'))), '-' , 'color', [colors(1,:), 0.5]);
plot(freqs_md, abs(squeeze(freqresp(G_md_fast_iff_kp( 'Du', 'Fu'), freqs_md, 'Hz'))), '-' , 'color', [colors(2,:)]);
plot(freqs_md, abs(squeeze(freqresp(G_md_fast_iff_kp( 'Dv', 'Fu'), freqs_md, 'Hz'))), '-' , 'color', [colors(2,:), 0.5]);
plot(freqs_md, abs(squeeze(freqresp(G_md_fast_rdc( 'Du', 'Fu'), freqs_md, 'Hz'))), '-' , 'color', [colors(3,:)]);
plot(freqs_md, abs(squeeze(freqresp(G_md_fast_rdc( 'Dv', 'Fu'), freqs_md, 'Hz'))), '-' , 'color', [colors(3,:), 0.5]);
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Magnitude [m/N]'); set(gca, 'XTickLabel',[]);
ylim([1e-10, 1e-4])

ax2 = nexttile;
hold on;
plot(freqs_md, 180/pi*angle(squeeze(freqresp(G_md_fast( 'Du', 'Fu'), freqs_md, 'Hz'))), '-' , 'color', [zeros(1,3)]);
plot(freqs_md, 180/pi*angle(squeeze(freqresp(G_md_fast_iff_hpf( 'Du', 'Fu'), freqs_md, 'Hz'))), '-' , 'color', [colors(1,:)]);
plot(freqs_md, 180/pi*angle(squeeze(freqresp(G_md_fast_iff_kp( 'Du', 'Fu'), freqs_md, 'Hz'))), '-' , 'color', [colors(2,:)]);
plot(freqs_md, 180/pi*angle(squeeze(freqresp(G_md_fast_rdc( 'Du', 'Fu'), freqs_md, 'Hz'))), '-' , 'color', [colors(3,:)]);
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([freqs_md(1), freqs_md(end)]);

freqs_pz = logspace(0, 3, 1000);

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

ax1 = nexttile([2,1]);
hold on;
plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast( 'Du', 'Fu'), freqs_pz, 'Hz'))), '-' , 'color', [zeros(1,3)], ...
    'DisplayName', 'OL');
plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast( 'Dv', 'Fu'), freqs_pz, 'Hz'))), '-' , 'color', [zeros(1,3), 0.5], ...
    'DisplayName', 'Coupling');
plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast_iff_hpf( 'Du', 'Fu'), freqs_pz, 'Hz'))), '-' , 'color', [colors(1,:)], ...
    'DisplayName', 'IFF + HPF');
plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast_iff_hpf( 'Dv', 'Fu'), freqs_pz, 'Hz'))), '-' , 'color', [colors(1,:), 0.5], ...
    'HandleVisibility', 'off');
plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast_iff_kp( 'Du', 'Fu'), freqs_pz, 'Hz'))), '-' , 'color', [colors(2,:)], ...
    'DisplayName', 'IFF + $k_p$');
plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast_iff_kp( 'Dv', 'Fu'), freqs_pz, 'Hz'))), '-' , 'color', [colors(2,:), 0.5], ...
    'HandleVisibility', 'off');
plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast_rdc( 'Du', 'Fu'), freqs_pz, 'Hz'))), '-' , 'color', [colors(3,:)], ...
    'DisplayName', 'RDC');
plot(freqs_pz, abs(squeeze(freqresp(G_pz_fast_rdc( 'Dv', 'Fu'), freqs_pz, 'Hz'))), '-' , 'color', [colors(3,:), 0.5], ...
    'HandleVisibility', 'off');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Magnitude [m/N]'); set(gca, 'XTickLabel',[]);
ylim([1e-12, 1e-6])
ldg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
ldg.ItemTokenSize = [20, 1];

ax2 = nexttile;
hold on;
plot(freqs_pz, 180/pi*angle(squeeze(freqresp(G_pz_fast( 'Du', 'Fu'), freqs_pz, 'Hz'))), '-' , 'color', [zeros(1,3)]);
plot(freqs_pz, 180/pi*angle(squeeze(freqresp(G_pz_fast_iff_hpf( 'Du', 'Fu'), freqs_pz, 'Hz'))), '-' , 'color', [colors(1,:)]);
plot(freqs_pz, 180/pi*angle(squeeze(freqresp(G_pz_fast_iff_kp( 'Du', 'Fu'), freqs_pz, 'Hz'))), '-' , 'color', [colors(2,:)]);
plot(freqs_pz, 180/pi*angle(squeeze(freqresp(G_pz_fast_rdc( 'Du', 'Fu'), freqs_pz, 'Hz'))), '-' , 'color', [colors(3,:)]);
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([freqs_pz(1), freqs_pz(end)]);