*5.1. Model–in–the–Loop Validation*

Pilot commands, here named *δ* (*pilot*) *<sup>a</sup>* , *<sup>δ</sup>* (*pilot*) *<sup>e</sup>* , *<sup>δ</sup>* (*pilot*) *<sup>c</sup>* , and *<sup>δ</sup>* (*pilot*) *p* are an input to the control system and follow the same convention described in Section 3.3.1. According to the given requirements, no closed-loop control is designed for MR collective pitch, such that *δ<sup>c</sup>* ≡ *δ* (*pilot*) *<sup>c</sup>* .

In the framework of control system design, simulation models for selected AHRS and actuators are also developed. Modeling parameters in terms of accuracy and performance are obtained from both datasheets and dedicate experiments performed in laboratory facilities.

The first controller is designed to stabilize yaw motion by the actuation of TR collective pitch angle *θ*0*TR* through the closed-loop feedback of yaw rate *r*. Let *er* = *ξ<sup>r</sup> δ* (*pilot*) *<sup>p</sup>* <sup>−</sup> *<sup>r</sup>* be the error between the desired and the measured angular rate, provided that *ξr* > 0 is a prescribed constant that transforms the non-dimensional command provided by the remote pilot into the desired yaw rate. The control scheme is described by the equation:

$$\delta\_p = k\_p^{(r)} e\_r + k\_i^{(r)} \int\_0^t e\_r(s) \, ds \tag{27}$$

where *k* (*r*) *<sup>p</sup>* > 0 and *k* (*r*) *<sup>i</sup>* > 0 are control gains, respectively, providing proportional and integral contributions related to the error signal *er*(*t*).

The second controller is used to stabilize the fuselage's attitude in terms of roll and pitch angles by the actuation of MR lateral and longitudinal cyclic control angles, respectively. With respect to roll angle stabilization, it is:

$$\delta\_a = k\_p^{(\phi)} e\_\Phi + k\_i^{(\phi)} \int\_0^t e\_\Phi(s) \, ds + k\_d^{(\phi)} p \tag{28}$$

where *k* (*φ*) *<sup>p</sup>* > 0 and *k* (*φ*) *<sup>i</sup>* > 0. A derivative–like contribution is also provided by the direct feedback of roll rate *p* through the gain *k* (*φ*) *<sup>d</sup>* < 0. The error between desired and measured roll angle is calculated as *e<sup>φ</sup>* = *ξφ δ* (*pilot*) *<sup>a</sup>* <sup>−</sup> *<sup>φ</sup>*, where *ξφ* <sup>&</sup>gt; 0 is a prescribed constant. Controller structure for the stabilization of pitch angle follows the same approach, namely:

$$\delta\_{\varepsilon} = k\_p^{(\theta)} \, e\_{\theta} + k\_i^{(\theta)} \int\_0^t e\_{\theta}(s) \, ds + k\_d^{(\theta)} \, q \tag{29}$$

where *k* (*θ*) *<sup>p</sup>* > 0, *k* (*θ*) *<sup>i</sup>* > 0, and *k* (*θ*) *<sup>d</sup>* < 0. The error between desired and measured pitch angle is *e<sup>θ</sup>* = *ξθ δ* (*pilot*) *<sup>e</sup>* <sup>−</sup> *<sup>θ</sup>*, where *ξθ* <sup>&</sup>gt; 0.

In Figures 7 and 8 the results of a sample maneuver are reported. Simulation is started at *h* = 50 m with null attitude of the helicopter (*φ*<sup>0</sup> = *θ*<sup>0</sup> = *ψ*<sup>0</sup> = 0 deg) and an initial angular rate about the yaw axis, such that *<sup>p</sup>*<sup>0</sup> <sup>=</sup> *<sup>q</sup>*<sup>0</sup> <sup>=</sup> 0 deg/s and *<sup>r</sup>*<sup>0</sup> <sup>=</sup> <sup>−</sup>5 deg/s. MR collective pitch angle is kept constant and equal to the value obtained in Table 3 for the hovering condition, namely *θ*<sup>0</sup> = 12.62 deg, corresponding to *δ* (*pilot*) *<sup>c</sup>* <sup>=</sup> 0.495. Let *ξ<sup>r</sup>* = 40 · *π*/180 rad/s, *ξφ* = 25 · *π*/180 rad, and *ξθ* = 12 · *π*/180 rad. Input values to the controllers are *δ* (*pilot*) *p* = 0, *δ* (*pilot*) *<sup>a</sup>* <sup>=</sup> <sup>−</sup>0.08, and *<sup>δ</sup>* (*pilot*) *<sup>e</sup>* <sup>=</sup> <sup>−</sup>0.163, which respectively provide the desired values *<sup>φ</sup>* <sup>=</sup> <sup>−</sup>2 deg, *<sup>θ</sup>* <sup>=</sup> <sup>−</sup>1.96, and *<sup>r</sup>* <sup>=</sup> 0 deg/s necessary to hover. In Figure 7, state variables describing fuselage attitude are plotted as a function of time, showing the stabilizing effect of implemented controllers. The corresponding control pitch angles are depicted in Figure 8, where the hover trim variables reported in Table 3 are

retrieved. Given the highly-classified nature of the data involved during the dronization process, the adopted first-guess controller gains are omitted.

**Figure 7.** MIL stabilization of attitude variables.

**Figure 8.** MIL stabilization of control pitch angles to the hovering condition.
