# Stabilization of an Unconventional Large Airship When Hovering
###### Abstract  
In this paper, we present the stabilization of an unconventional unmanned airship above a loading and unloading area. The study concerns a quad-rotor flying wing airship. This airship is devoted to freight transport. However, during the loading and unloading phases, the airship is very sensitive to squalls. In this context, we present in this paper the dynamic model of the airship, and we propose a strategy for controlling it under the effects of a gust of wind. A feedforward/feedback control law is proposed to stabilize the airship when hovering. As part of the control allocation, the non-linear equations between the control vectors and the response of the airship actuators are highlighted and solved analytically through energy optimization constraints. A comparison with classical numerical algorithms was performed and demonstrated the power and interest of our analytic algorithm. unconventional large airship; modelling; stabilization; feedforward/feedback technique; control allocation +
Footnote †: journal:  
However, in order to achieve this potential, several problems must be resolved, in particular, the stabilization of these machines in the presence of gusts of wind, mainly when hovering during the critical phases of loading and unloading. Several research laboratories are also seized with this interesting subject. Among the airships developed by laboratories, we note the MC500 (Figure 1) with a capacity of 500 m\({}^{3}\) developed by the interuniversity group DIRISOFT in France and which will serve as a support for our developments. The MC500 is original by the unconventional shape of its hull and the plethora of novelties that characterize it. The advancement of digital aerodynamics, control techniques, and on-board electronics have made it possible to design airships of unconventional shapes, see, for example, [5; 6]. The use of an unconventional shape was guided by the search for an optimal way to capture sunlight using photovoltaic films. This requires having large \"flat surfaces\", hence the choice of a flying wing. For the MC500, the choice of the quadcopter configuration with steerable rotors is dictated by a concern for the redundancy of the actuators in order to better control the machine with unusual dimensions and so that they can stabilize quickly and resist a gust of wind detected. It should be emphasized that this tends to complicate the task of developing stabilization control laws that would be compatible with the capacities of the actuators. Among the new features of the airship, the designers planned to equip it with a LIDAR. This device represents a step forward in carrying out adequate checks to minimize the drift of these bulky objects under the effects of gusts of wind. LIDAR is an optical measurement technique based on the analysis of the properties of a light beam returned to its emitter [7]. LIDAR measures the wind speed upstream of the flying object in order to provide an alert in the event of dangerous turbulence being detected. This technology offers the possibility of using new control concepts for airships, such as feedforward control algorithms. In this sense, in this article, we present a feedforward control; the objective being to minimize the drift of the airship during these atmospheric turbulences. Several control approaches have been proposed for these aerial objects, such as linear control [8; 9], feedback linearization [9; 10], adaptive control [11], IQR based controllers [12], or backstepping control [13]. In reference to [11], two control approaches to analyzing the stability and robustness of the AURORA self-propelled airship are presented. The first is based on linearized models of the airship, and the second is based on nonlinear control techniques such as dynamic inversion and backstepping. The established nonlinear control laws were tested against a simulated wind disturbance. The backstepping approach is extended in [14] to include input saturation and wind effect compensation. A wind estimator was presented.