Put two figures in minipage
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@ -494,19 +494,28 @@ Thus, if the added parallel stiffness $k_p$ is higher than the negative stiffnes
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This is confirmed by the Bode plot in Figure ref:fig:plant_iff_kp.
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# while recovering the alternating poles and zeros near the imaginary axis.
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#+name: fig:plant_iff_kp
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#+caption: Bode Plot of $f_u/F_u$ without parallel spring, with parallel springs with stiffness $k_p < m \Omega^2$ and $k_p > m \Omega^2$, $\Omega = 0.1 \omega_0$
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#+attr_latex: :scale 1
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[[file:figs/plant_iff_kp.pdf]]
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# Root Locus plot
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Figure ref:fig:root_locus_iff_kp shows Root Loci plots for $k_p = 0$, $k_p < m \Omega^2$ and $k_p > m \Omega^2$ when $K_F$ is a pure integrator eqref:eq:Kf_pure_int.
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It is shown that if the added stiffness is higher than the maximum negative stiffness, the poles of the closed-loop system stay in the (stable) right half-plane, and hence the unconditional stability of IFF is recovered.
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#+attr_latex: :options [b]{0.42\linewidth}
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#+begin_minipage
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#+name: fig:plant_iff_kp
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#+caption: Bode Plot of $f_u/F_u$ without parallel spring, with parallel springs with stiffness $k_p < m \Omega^2$ and $k_p > m \Omega^2$, $\Omega = 0.1 \omega_0$
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#+attr_latex: :scale 1 :float nil
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[[file:figs/plant_iff_kp.pdf]]
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#+end_minipage
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\hfill
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#+attr_latex: :options [b]{0.52\linewidth}
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#+begin_minipage
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#+name: fig:root_locus_iff_kp
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#+caption: Root Locus for IFF without parallel spring, with parallel springs with stiffness $k_p < m \Omega^2$ and $k_p > m \Omega^2$, $\Omega = 0.1 \omega_0$
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#+attr_latex: :scale 1
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#+attr_latex: :scale 1 :float nil
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[[file:figs/root_locus_iff_kp.pdf]]
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#+end_minipage
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** Optimal Parallel Stiffness
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# The zero is the poles of the system without the force sensors => w0 = sqrt(kp/m) +/- Omega ?? => seems not true
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