This paper presents a modelling of an unmanned airship. We are studying a quadrotor flying wing. The modelling of this airship includes an aerodynamic study. A special focus is done on the computation of the added masses. Considering that the velocity potential of the air surrounding the airship obeys the Laplace's equation, the added masses matrix will be determined by means of the velocity potential flow theory. Typically, when the shape of the careen is quite different from that of an ellipsoid, designers in preprocessing prefer to avoid complications arising from mathematical analysis of the velocity potential. They use either complete numerical studies, or geometric approximation methods, although these methods can give relatively large differences compared to experimental measurements performed on the airship at the time of its completion. We tried to develop here as far as possible the mathematical analysis of the velocity potential flow of this unconventional shape using certain assumptions. The shape of the careen is assumed to be an elliptic cone. To retrieve the velocity potential shapes, we use the spheroconal coordinates. This leads to the Lamé's equations. The whole system of equations governing the interaction air-structure, including the boundary conditions, is solved in an analytical setting.

This paper presents preliminary results of the modelling of an unconventional unmanned airship moving in an ideal fluid. We are studying here a quad-rotor flying wing. The airships are also governed by the aerodynamic forces that have to be modelled. An evaluation of the added masses of the airship’s components is presented. A first dynamic modelling including the effect of the added masses is proposed. A control law based on the elaborated dynamic model was applied to this large flying object to evaluate its sensitivity when manoeuvring over an uploading area.

Purpose This paper presents preliminary results of the modeling of a large autonomous quad-rotor airship, with flying wing shape. This airship is supposed to be a flexible body. This study promotes an entirely analytical methodology with some assumptions. In this study and as first assumption, the shape of the careen is supposed to be an elliptic cone. To retrieve the velocity potential shapes, this paper solved the Laplace’s equation by using the sphero-conal coordinates. This leads to the Lamé’s equations. The whole system equations governing the interaction of air–structure, including the boundary conditions, is solved in an analytical setting. Design/methodology/approach This paper opted for a modeling and determination of the added masses of a flexible airship by an analytical method illustrated by a comparison with a geometric method. This analytical method includes the study of complex functions which are the Lamé functions. Findings This paper provides an analytical way to estimate an aerodynamic phenomenon which acts on the airship and in particular on its envelope and known as the phenomenon of added masses or virtual masses, as well as the means of defining it and the calculation analytically for the case of the flexible airship. Research limitations/implications Considering that the calculation of the added masses is very difficult and the numerical methods increase the number of degrees of freedom, the analytical method established in this paper has become a solution of calculations of these virtual masses. Practical implications This paper includes an application for determining the added masses of a new generation MC500 airship. Originality/value This paper allows defining an analytical method which determines the added masses of an airship, which helps the automation engineer to develop a control strategy to stabilize this airship.

The paper presents the modelling and stabilisation of an unconventional airship. The complexity of such a new design requires both proper dynamic modelling and control. A complete dynamic model is built here. Based on the developed dynamic model, a nonlinear control law is proposed for this airship to evaluate its sensitivity during manoeuvres above a loading area. The proposed stabilisation controller derives its source from a polytopic quasi-Linear Parameter varying (qLPV) model of the nonlinear system. A controller, which takes into account certain modelling uncertainties and the stability of the system, is analysed using Lyapunov’s theory. Finally, to facilitate the design of the controller, we express the stability conditions using Linear Matrix Inequalities (LMIs). Numerical simulations are presented to highlight the power of the proposed controller.