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RAGEON edited CRM MRAC of a First-Order Nonlinear System1.tex
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\chapter{CRM MRAC of a First-Order Nonlinear System}
% LABEL THE FOLLOWING EQUATION \label{eq:xmc}
The idea behind Closed-loop reference models is to force the
trajectories of the closed loop reference model to move towards the plant model. The differential equations are given as
\begin{align}\dot x_m^o &= a_m x_m^o + k_mr,& a_m <0 \\
\dot x_m^c &= a_m x_m^c +k_mr - le^c, \qquad&l, a_m < 0 \\
e^c&=x_p-x_m^c \end{align}