From 6e9f050efe20fe0b2b3903841aade4ddb4462a12 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Tue, 15 Apr 2025 11:49:09 +0200 Subject: [PATCH] Remove use of tikz in the text --- nass-rotating-3dof-model.org | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/nass-rotating-3dof-model.org b/nass-rotating-3dof-model.org index 5d6dc3f..0f452e6 100644 --- a/nass-rotating-3dof-model.org +++ b/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.