**2. The ADMIRE aircraft model**

The Aeronautical Research Institute of Sweden developed the ADMIRE model using the generic aero-data model with dynamic models of an engine, actuators, atmosphere, and sensors. The ADMIRE model has 12 states but generally, these states were reduced to simply nonlinear dynamics of the system. The short-period longitudinal flight dynamics governing the ADMIRE benchmark model are given as follows [18–20]:

$$
\begin{bmatrix}
\dot{\boldsymbol{a}} \\
\dot{\boldsymbol{q}}
\end{bmatrix} = \begin{bmatrix}
\mathbf{Z}\_{a} & \mathbf{Z}\_{q} \\
\mathbf{M}\_{a} & \mathbf{M}\_{q}
\end{bmatrix} \begin{bmatrix}
\boldsymbol{\alpha} \\
\boldsymbol{q}
\end{bmatrix} + \begin{bmatrix}
\mathbf{Z}\_{\delta\_{\varepsilon}} & \mathbf{Z}\_{\boldsymbol{l}\_{\mathrm{u}}} \\
\mathbf{M}\_{\delta\_{\varepsilon}} & \mathbf{M}\_{\boldsymbol{l}\_{\mathrm{u}}}
\end{bmatrix} \begin{bmatrix}
\delta\_{\varepsilon} \\
\mathbf{t}\_{\mathrm{st}}
\end{bmatrix}
$$

$$
\mathbf{n}\_{\mathrm{z}} = \begin{bmatrix}
\mathbf{n}\_{\mathrm{z}\mathrm{z}} & \mathbf{n}\_{\mathrm{z}\mathrm{q}}
\end{bmatrix} \begin{bmatrix}
\boldsymbol{\alpha} \\
\boldsymbol{\alpha}
\end{bmatrix} + \begin{bmatrix}
\mathbf{n}\_{\mathrm{z}\mathrm{z}} & \mathbf{n}\_{\mathrm{z}\mathrm{q}}
\end{bmatrix} \begin{bmatrix}
\delta\_{\mathrm{e}} \\
\mathbf{t}\_{\mathrm{ss}}
\end{bmatrix} \tag{1}
$$

where state variables *α* and *q* are the angles of attack and the Euler pitch rate, respectively. The control inputs are the elevator angle, *δ<sup>e</sup>* and throttle setting, *tss*, respectively, and the output variable is load-factor, *nz* (**Figure 1**).

*Performance Improvement for Fighter Aircraft Using Fuzzy Switching LQI Controller DOI: http://dx.doi.org/10.5772/intechopen.107032*

**Figure 1.** *ADMIRE aircraft model and control surfaces.*
