Correcly export code blocks
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matlab/index.html
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@ -101,7 +101,7 @@ The Campbell Diagram displays the evolution of the real and imaginary parts of t
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It is shown in Figure [[fig:campbell_diagram]], and one can see that the system becomes unstable for $\Omega > \omega_0$ (the real part of one of the poles becomes positive).
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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Ws = linspace(0, 2, 51); % Vector of considered rotation speed [rad/s]
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p_ws = zeros(4, length(Ws));
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@ -117,7 +117,7 @@ It is shown in Figure [[fig:campbell_diagram]], and one can see that the system
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clear pole_G;
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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figure;
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ax1 = subplot(1,2,1);
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@ -185,7 +185,7 @@ Define the rotating speed for the Simscape Model.
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W = 0.1; % Rotation Speed [rad/s]
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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Kiff = tf(zeros(2));
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Kdvf = tf(zeros(2));
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@ -223,7 +223,7 @@ The same transfer function from $[F_u, F_v]$ to $[d_u, d_v]$ is written down fro
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Both transfer functions are compared in Figure [[fig:plant_simscape_analytical]] and are found to perfectly match.
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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freqs = logspace(-1, 1, 1000);
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figure;
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@ -302,7 +302,7 @@ The transfer functions from $[F_u, F_v]$ to $[d_u, d_v]$ are identified for the
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They are compared in Figure [[fig:plant_compare_rotating_speed]].
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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freqs = logspace(-2, 1, 1000);
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figure;
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@ -402,7 +402,7 @@ Let's define initial values for the model.
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w0 = sqrt(k/m); % [rad/s]
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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kp = 0; % [N/m]
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cp = 0; % [N/(m/s)]
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#+end_src
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@ -438,7 +438,7 @@ The rotation speed is set to $\Omega = 0.1 \omega_0$.
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W = 0.1*w0; % [rad/s]
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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Kiff = tf(zeros(2));
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Kdvf = tf(zeros(2));
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#+end_src
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@ -472,7 +472,7 @@ The same transfer function from $[F_u, F_v]$ to $[f_u, f_v]$ is written down fro
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The two are compared in Figure [[fig:plant_iff_comp_simscape_analytical]] and found to perfectly match.
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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freqs = logspace(-1, 1, 1000);
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figure;
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@ -550,7 +550,7 @@ The transfer functions from $[F_u, F_v]$ to $[f_u, f_v]$ are identified for the
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#+end_src
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The obtained transfer functions are shown in Figure [[fig:plant_iff_compare_rotating_speed]].
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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freqs = logspace(-2, 1, 1000);
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figure;
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@ -649,7 +649,7 @@ It is shown that for non-null rotating speed, one pole is bound to the right-hal
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xlim([freqs(1), freqs(end)]);
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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figure;
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gains = logspace(-2, 4, 100);
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@ -722,7 +722,7 @@ Let's define initial values for the model.
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w0 = sqrt(k/m); % [rad/s]
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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kp = 0; % [N/m]
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cp = 0; % [N/(m/s)]
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#+end_src
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@ -743,12 +743,12 @@ Let's arbitrary choose the following control parameters:
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wi = 0.1*w0;
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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Kiff = (g/(wi+s))*eye(2);
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#+end_src
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And the following rotating speed.
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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W = 0.1*w0;
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#+end_src
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@ -759,7 +759,7 @@ And the following rotating speed.
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#+end_src
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The obtained Loop Gain is shown in Figure [[fig:loop_gain_modified_iff]].
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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freqs = logspace(-2, 1, 1000);
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figure;
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@ -801,7 +801,7 @@ The obtained Loop Gain is shown in Figure [[fig:loop_gain_modified_iff]].
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** Root Locus
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As shown in the Root Locus plot (Figure [[fig:root_locus_modified_iff]]), for some value of the gain, the system remains stable.
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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figure;
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gains = logspace(-2, 4, 100);
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@ -877,7 +877,7 @@ In order to visualize the effect of $\omega_i$ on the attainable damping, the Ro
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wis = [0.01, 0.1, 0.5, 1]*w0; % [rad/s]
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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figure;
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gains = logspace(-2, 4, 100);
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@ -975,7 +975,7 @@ To find the optimum, the gain that maximize the simultaneous damping of the mode
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end
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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figure;
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yyaxis left
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plot(wis, opt_zeta, '-o', 'DisplayName', '$\xi_{cl}$');
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@ -1040,7 +1040,7 @@ Let's define initial values for the model.
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w0 = sqrt(k/m); % [rad/s]
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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kp = 0; % [N/m]
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cp = 0; % [N/(m/s)]
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#+end_src
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@ -1080,7 +1080,7 @@ The rotation speed is set to $\Omega = 0.1 \omega_0$.
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W = 0.1*w0; % [rad/s]
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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Kiff = tf(zeros(2));
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Kdvf = tf(zeros(2));
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#+end_src
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@ -1094,7 +1094,7 @@ The results are shown in Figure [[fig:plant_iff_kp]].
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One can see that for $k_p > m \Omega^2$, the systems shows alternating complex conjugate poles and zeros.
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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%% Name of the Simulink File
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mdl = 'rotating_frame';
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@ -1137,7 +1137,7 @@ One can see that for $k_p > m \Omega^2$, the systems shows alternating complex c
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Giff_l.OutputName = {'fu', 'fv'};
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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freqs = logspace(-2, 1, 1000);
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figure;
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@ -1194,7 +1194,7 @@ Thus, decentralized IFF controller with pure integrators can be used if:
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k_{p} > m \Omega^2
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\end{equation}
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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figure;
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gains = logspace(-2, 2, 100);
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@ -1306,7 +1306,7 @@ To study the second point, Root Locus plots for the following values of $k_p$ ar
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It is shown that large values of $k_p$ decreases the attainable damping.
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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figure;
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gains = logspace(-2, 4, 100);
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@ -1375,7 +1375,7 @@ Let's take $k_p = 5 m \Omega^2$ and find the optimal IFF control gain $g$ such t
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end
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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figure;
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gains = logspace(-2, 4, 100);
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@ -1458,7 +1458,7 @@ Let's define initial values for the model.
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w0 = sqrt(k/m); % [rad/s]
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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kp = 0; % [N/m]
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cp = 0; % [N/(m/s)]
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#+end_src
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@ -1469,7 +1469,7 @@ The rotating speed is set to $\Omega = 0.1 \omega_0$.
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W = 0.1*w0;
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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Kiff = tf(zeros(2));
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Kdvf = tf(zeros(2));
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#+end_src
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@ -1506,7 +1506,7 @@ The same transfer function from $[F_u, F_v]$ to $[v_u, v_v]$ is written down fro
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The two are compared in Figure [[fig:plant_iff_comp_simscape_analytical]] and found to perfectly match.
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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freqs = logspace(-1, 1, 1000);
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figure;
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@ -1579,7 +1579,7 @@ The corresponding Root Locus plots for the following rotating speeds are shown i
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It is shown that for rotating speed $\Omega < \omega_0$, the closed loop system is unconditionally stable and arbitrary damping can be added to the poles.
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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gains = logspace(-2, 1, 100);
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figure;
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@ -1659,12 +1659,12 @@ Let's define initial values for the model.
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w0 = sqrt(k/m); % [rad/s]
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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kp = 0; % [N/m]
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cp = 0; % [N/(m/s)]
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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Kiff = tf(zeros(2));
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Kdvf = tf(zeros(2));
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#+end_src
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@ -1676,7 +1676,7 @@ The rotating speed is set to $\Omega = 0.1 \omega_0$.
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** Root Locus
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*** Pseudo Integrator IFF :ignore:
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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kp = 0;
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cp = 0;
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#+end_src
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@ -1728,7 +1728,7 @@ The rotating speed is set to $\Omega = 0.1 \omega_0$.
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#+end_src
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*** DVF :ignore:
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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kp = 0;
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cp = 0;
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#+end_src
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@ -1752,7 +1752,7 @@ The rotating speed is set to $\Omega = 0.1 \omega_0$.
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#+end_src
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*** Root Locus :ignore:
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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figure;
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gains = logspace(-2, 2, 100);
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@ -1819,7 +1819,7 @@ The rotating speed is set to $\Omega = 0.1 \omega_0$.
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** Controllers - Optimal Gains
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In order to compare to three considered Active Damping techniques, gains that yield maximum damping of all the modes are computed for each case.
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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%% IFF with pseudo integrators
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gains = linspace(0, (w0^2/W^2 - 1)*wi, 100);
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opt_zeta_iff = 0;
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@ -1837,7 +1837,7 @@ In order to compare to three considered Active Damping techniques, gains that yi
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end
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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%% IFF with Parallel Stiffness
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gains = logspace(-2, 4, 100);
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opt_zeta_kp = 0;
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@ -1855,7 +1855,7 @@ In order to compare to three considered Active Damping techniques, gains that yi
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end
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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%% Direct Velocity Feedback
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gains = logspace(0, 2, 100);
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opt_zeta_dvf = 0;
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@ -1889,7 +1889,7 @@ The obtained damping ratio and control are shown below.
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** Transmissibility
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<<sec:comp_transmissibilty>>
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*** Open Loop :ignore:
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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Kdvf = tf(zeros(2));
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Kiff = tf(zeros(2));
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@ -1916,7 +1916,7 @@ The obtained damping ratio and control are shown below.
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#+end_src
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*** Pseudo Integrator IFF :ignore:
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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kp = 0;
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cp = 0;
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@ -1955,7 +1955,7 @@ The obtained damping ratio and control are shown below.
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Kiff = opt_gain_kp/s*tf(eye(2));
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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Kdvf = tf(zeros(2));
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#+end_src
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@ -1978,7 +1978,7 @@ The obtained damping ratio and control are shown below.
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#+end_src
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*** DVF :ignore:
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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kp = 0;
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cp = 0;
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@ -2008,7 +2008,7 @@ The obtained damping ratio and control are shown below.
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#+end_src
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*** Transmissibility :ignore:
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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freqs = logspace(-2, 1, 1000);
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figure;
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@ -2039,7 +2039,7 @@ The obtained damping ratio and control are shown below.
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** Compliance
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<<sec:comp_compliance>>
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*** Open Loop :ignore:
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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Kdvf = tf(zeros(2));
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Kiff = tf(zeros(2));
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@ -2066,7 +2066,7 @@ The obtained damping ratio and control are shown below.
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#+end_src
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*** Pseudo Integrator IFF :ignore:
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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kp = 0;
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cp = 0;
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@ -2095,7 +2095,7 @@ The obtained damping ratio and control are shown below.
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Kiff = opt_gain_kp/s*tf(eye(2));
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#+end_src
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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Kdvf = tf(zeros(2));
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#+end_src
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@ -2108,7 +2108,7 @@ The obtained damping ratio and control are shown below.
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#+end_src
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*** DVF :ignore:
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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kp = 0;
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cp = 0;
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@ -2128,7 +2128,7 @@ The obtained damping ratio and control are shown below.
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#+end_src
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*** Compliance :ignore:
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#+begin_src matlab :exports code
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#+begin_src matlab :exports none
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freqs = logspace(-2, 1, 1000);
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figure;
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