Modelling and Control of Airship with Slung Payload

Abstract

This study explores the modelling and control of a multibody system comprising an airship, gondola, and a slung payload. Lighter-than-air vehicles undergo inertial forces that are often neglected in heavier-than-air vehicles. These inertial forces are modelled using added mass and added inertia and there can be significant discrepancies between the values obtained empirically and those of the actual vehicle. The dynamics of the multibody system were first modelled using the Udwadia-Kalaba method. The resulting equation of motion was used to identify the added mass, added inertia, and inertia of the airship through system identification procedure. The proposed system identification method utilizes semidefinite programming with equality and inequality constraints to find any unknown parameters in the mass matrix of the multibody system. Three experiments were carried out to perform the system identification and validate the dynamic model. A comparison of reconstructed trajectories before and after applying system identification shows that the identified mass matrix produces more accurate results with 35% lower root mean squared error of position when compared with the trajectories simulated before carrying out system identification. Aerodynamic coefficients, including lift and drag coefficients, were calculated for a full-scale airship prototype using the Reynold's averaged Navier-Stokes with Spalart-Allmaras turbulence model.

Using the nonlinear dynamic model of the multibody system, two fuzzy logic controllers were developed to attenuate the payload's oscillations and maintain the payload at a desired position. Two more fuzzy logic controllers were designed to navigate the airship-gondola-slung-payload system in the longitudinal plane to a target location. An additional fuzzy logic controller was developed to deliver the payload by means of controlling the altitude. The proposed control method addresses a gap in the literature, which lacks experimental studies on airships with slung payloads using fuzzy logic control. The controller was evaluated under wind disturbance through simulations and in outdoor experiments. Despite the adverse weather conditions, the navigation fuzzy logic controller operated as intended, effectively responding to inputs and attempting to correct errors while adhering to the upper and lower bounds of the thrusters.