Correct Matlab script

figs/inkscape/convert_svg.sh

@@ -0,0 +1,18 @@
+#!/bin/bash
+
+# Directory containing SVG files
+INPUT_DIR="."
+
+# Loop through all SVG files in the directory
+for svg_file in "$INPUT_DIR"/*.svg; do
+    # Check if there are SVG files in the directory
+    if [ -f "$svg_file" ]; then
+        # Output PDF file name
+        pdf_file="../${svg_file%.svg}.pdf"
+        png_file="../${svg_file%.svg}"
+        
+        # Convert SVG to PDF using Inkscape
+        inkscape "$svg_file" --export-filename="$pdf_file" && \
+            pdftocairo -png -singlefile -cropbox "$pdf_file" "$png_file"
+    fi
+done

matlab/rotating_7_nano_hexapod.m

@@ -221,6 +221,19 @@ 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;
 
+%% Define the obtained controllers
+Kiff_hpf_vc = Kiff*opt_iff_hpf_gain_vc(i_iff_hpf_vc);
+Kiff_hpf_vc.InputName  = {'fu', 'fv'};
+Kiff_hpf_vc.OutputName = {'Fu', 'Fv'};
+
+Kiff_hpf_md = Kiff*opt_iff_hpf_gain_md(i_iff_hpf_md);
+Kiff_hpf_md.InputName  = {'fu', 'fv'};
+Kiff_hpf_md.OutputName = {'Fu', 'Fv'};
+
+Kiff_hpf_pz = Kiff*opt_iff_hpf_gain_pz(i_iff_hpf_pz);
+Kiff_hpf_pz.InputName  = {'fu', 'fv'};
+Kiff_hpf_pz.OutputName = {'Fu', 'Fv'};
+
 %% Optimal modified IFF parameters that yields maximum simultaneous damping
 figure;
 yyaxis left
@@ -303,9 +316,9 @@ 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
+Kiff_vc = 1/(s + 0.1*sqrt(1e4/(mn+ms)))*eye(2); % IFF - VC
+Kiff_md = 1/(s + 0.1*sqrt(1e6/(mn+ms)))*eye(2); % IFF - MD
+Kiff_pz = 1/(s + 0.1*sqrt(1e8/(mn+ms)))*eye(2); % IFF - PZ
 
 %% General Configuration
 model_config = struct();
@@ -397,6 +410,19 @@ end
 [~, i_kp_md] = min(abs(kps_md - 1e4));
 [~, i_kp_pz] = min(abs(kps_pz - 1e6));
 
+%% Define the obtained controllers
+Kiff_kp_vc = Kiff_vc*opt_iff_kp_gain_vc(i_kp_vc);
+Kiff_kp_vc.InputName  = {'fu', 'fv'};
+Kiff_kp_vc.OutputName = {'Fu', 'Fv'};
+
+Kiff_kp_md = Kiff_md*opt_iff_kp_gain_md(i_kp_md);
+Kiff_kp_md.InputName  = {'fu', 'fv'};
+Kiff_kp_md.OutputName = {'Fu', 'Fv'};
+
+Kiff_kp_pz = Kiff_pz*opt_iff_kp_gain_pz(i_kp_pz);
+Kiff_kp_pz.InputName  = {'fu', 'fv'};
+Kiff_kp_pz.OutputName = {'Fu', 'Fv'};
+
 %% Identify plants with choosen Parallel stiffnesses
 model_config.Tuv_type   = "parallel_k";    % Default: 2DoF stage
 

matlab/rotating_8_nass.m

@@ -209,7 +209,7 @@ hold off;
 yticks(-360:90:360);
 ylim([ -200, 20]);
 
-linkaxes([ax,ax2],'x');
+linkaxes([ax1,ax2],'x');
 xlim([freqs_vc(1), freqs_vc(end)]);
 xticks([1e-1, 1e0, 1e1]);
 
@@ -465,6 +465,4 @@ xticks([1e-1, 1e0, 1e1, 1e2, 1e3]);
 xtickangle(0)
 ldg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
 ldg.ItemTokenSize = [20, 1];
-
-linkaxes([ax1,ax2,ax3], 'y')
 ylim([1e-8, 1e-2])

nass-rotating-3dof-model.org

@@ -899,7 +899,7 @@ The decentralized acrshort:iff controller $\bm{K}_F$ corresponds to a diagonal c
 \end{equation}
 
 To determine how the acrshort:iff controller affects the poles of the closed-loop system, a Root Locus plot (Figure ref:fig:rotating_root_locus_iff_pure_int) is constructed as follows: the poles of the closed-loop system are drawn in the complex plane as the controller gain $g$ varies from $0$ to $\infty$ for the two controllers $K_{F}$ simultaneously.
-As explained in cite:preumont08_trans_zeros_struc_contr_with,skogestad07_multiv_feedb_contr, the closed-loop poles start at the open-loop poles (shown by $\tikz[baseline=-0.6ex] \node[cross out, draw=black, minimum size=1ex, line width=2pt, inner sep=0pt, outer sep=0pt] at (0, 0){};$) for $g = 0$ and coincide with the transmission zeros (shown by $\tikz[baseline=-0.6ex] \draw[line width=2pt, inner sep=0pt, outer sep=0pt] (0,0) circle[radius=3pt];$) as $g \to \infty$.
+As explained in cite:preumont08_trans_zeros_struc_contr_with,skogestad07_multiv_feedb_contr, the closed-loop poles start at the open-loop poles (shown by crosses) for $g = 0$ and coincide with the transmission zeros (shown by circles) as $g \to \infty$.
 
 Whereas collocated IFF is usually associated with unconditional stability cite:preumont91_activ, this property is lost due to gyroscopic effects as soon as the rotation velocity becomes non-null.
 This can be seen in the Root Locus plot (Figure ref:fig:rotating_root_locus_iff_pure_int) where poles corresponding to the controller are bound to the right half plane implying closed-loop system instability.
@@ -2853,7 +2853,7 @@ exportFig('figs/rotating_nano_hexapod_dynamics_pz.pdf', 'width', 'third', 'heigh
 #+end_subfigure
 #+end_figure
 
-** Optimal IFF with a  High-Pass Filter
+** Optimal IFF with a High-Pass Filter
 Integral Force Feedback with an added high-pass filter is applied to the three nano-hexapods.
 First, the parameters ($\omega_i$ and $g$) of the IFF controller that yield the best simultaneous damping are determined from Figure ref:fig:rotating_iff_hpf_nass_optimal_gain.
 The IFF parameters are chosen as follows:
@@ -2912,6 +2912,21 @@ 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;
 #+end_src
 
+#+begin_src matlab
+%% Define the obtained controllers
+Kiff_hpf_vc = Kiff*opt_iff_hpf_gain_vc(i_iff_hpf_vc);
+Kiff_hpf_vc.InputName  = {'fu', 'fv'};
+Kiff_hpf_vc.OutputName = {'Fu', 'Fv'};
+
+Kiff_hpf_md = Kiff*opt_iff_hpf_gain_md(i_iff_hpf_md);
+Kiff_hpf_md.InputName  = {'fu', 'fv'};
+Kiff_hpf_md.OutputName = {'Fu', 'Fv'};
+
+Kiff_hpf_pz = Kiff*opt_iff_hpf_gain_pz(i_iff_hpf_pz);
+Kiff_hpf_pz.InputName  = {'fu', 'fv'};
+Kiff_hpf_pz.OutputName = {'Fu', 'Fv'};
+#+end_src
+
 #+begin_src matlab :results none
 %% Optimal modified IFF parameters that yields maximum simultaneous damping
 figure;
@@ -3066,9 +3081,9 @@ 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
+Kiff_vc = 1/(s + 0.1*sqrt(1e4/(mn+ms)))*eye(2); % IFF - VC
+Kiff_md = 1/(s + 0.1*sqrt(1e6/(mn+ms)))*eye(2); % IFF - MD
+Kiff_pz = 1/(s + 0.1*sqrt(1e8/(mn+ms)))*eye(2); % IFF - PZ
 
 %% General Configuration
 model_config = struct();
@@ -3162,6 +3177,19 @@ end
 [~, i_kp_md] = min(abs(kps_md - 1e4));
 [~, i_kp_pz] = min(abs(kps_pz - 1e6));
 
+%% Define the obtained controllers
+Kiff_kp_vc = Kiff_vc*opt_iff_kp_gain_vc(i_kp_vc);
+Kiff_kp_vc.InputName  = {'fu', 'fv'};
+Kiff_kp_vc.OutputName = {'Fu', 'Fv'};
+
+Kiff_kp_md = Kiff_md*opt_iff_kp_gain_md(i_kp_md);
+Kiff_kp_md.InputName  = {'fu', 'fv'};
+Kiff_kp_md.OutputName = {'Fu', 'Fv'};
+
+Kiff_kp_pz = Kiff_pz*opt_iff_kp_gain_pz(i_kp_pz);
+Kiff_kp_pz.InputName  = {'fu', 'fv'};
+Kiff_kp_pz.OutputName = {'Fu', 'Fv'};
+
 %% Identify plants with choosen Parallel stiffnesses
 model_config.Tuv_type   = "parallel_k";    % Default: 2DoF stage
 
@@ -3839,7 +3867,7 @@ hold off;
 yticks(-360:90:360);
 ylim([ -200, 20]);
 
-linkaxes([ax,ax2],'x');
+linkaxes([ax1,ax2],'x');
 xlim([freqs_vc(1), freqs_vc(end)]);
 xticks([1e-1, 1e0, 1e1]);
 #+end_src
@@ -4246,8 +4274,6 @@ xticks([1e-1, 1e0, 1e1, 1e2, 1e3]);
 xtickangle(0)
 ldg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
 ldg.ItemTokenSize = [20, 1];
-
-linkaxes([ax1,ax2,ax3], 'y')
 ylim([1e-8, 1e-2])
 #+end_src