Modelling and control of an buoyancy driven airship Xiaotao Wu To cite this version: Xiaotao Wu. Modelling and control of an buoyancy driven airship. Automatic Control Engineering. Ecole Centrale de Nantes (ECN); South China University of Technology, 2011. English. tel-01146532 HAL Id: tel-01146532 https://hal.archives-ouvertes.fr/tel-01146532 Submitted on 28 Apr 2015 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Ecole Centrale de Nantes ÉCOLE DOCTORALE Sciences et Technologies de l’Information et Mathématiques Année 2011 N° B.U. : THESE DE DOCTORAT EN COTUTELLE Diplôme délivré d'une part, par l'Ecole Centrale de Nantes et par l'Université de Technology de Chine du Sud (Chine) d'autre part Spécialité : AUTOMATIQUE ET INFORMATIQUE APPLIQUEE Présentée et soutenue publiquement par : Xiaotao WU le : 30 Mai 2011 à l’Université de Technology de Chine du Sud, Guangzhou, Chine TITRE Modélisation et Commande d’un Dirigeable Propulsé par la Force de Flottabilité JURY Président : Weizhou SU Professeur, Université de Technology de Chine du Sud, Chine Rapporteurs : Rogelio LOZANO Directeur de Recherche, CNRS Chun-Yi SU Professeur, Université Concordia, Canada Examinateurs : Claude MOOG Directeur de Recherche, CNRS Yueming HU Professeur, Université de Technology de Chine du Sud, Chine Invité : Hailong PEI Professeur, Université de Technology de Chine du Sud, Chine Directeur de thèse : Claude MOOG Laboratoire : IRCCyN Co- Directeur de thèse : Yueming HU Laboratoire : Faculté d’Automatique, Université de Technology de Chine du Sud, Chine N° ED : 503-127 Abstract A new concept of airship without thrust, elevator or rudder is considered in this thesis. It is ac- tuated by a moving mass and a mass-adjustable internal air bladder. This results into the motion of the center of gravity and the change of the net lift. The development of this concept of airship is motivated by energy saving. An eight degrees-of-freedom complete nonlinear mathematical model of this airship is derived through the Newton-Euler approach. The interconnection between the airship’s rigid body and the moveable mass is clearly presented. The dynamics in the longitudinal plane is ana- lyzed and controlled through a LQR method, an input-output feedback linearization, and the maximal feedback linearization with internal stability. Thanks to maximal feedback linearization, an efficient nonlinear control is derived. In this process, modelling, analysis, and control are solved for special cases of the airship, which become gradually closer to the most general model. The most constrained special case reduces to a two degree-of-freedom system. It is shown that the basic properties of this two DOF mechanical system remain instrumental for the analysis and synthesis of advanced airship models. These properties are far from being obvious from the most complex model. Through a sin- gular perturbation approach, the superposition of the two control actions in the longitudinal plane and in the lateral plane is shown to achieve the control of the dynamics in three dimension. i Resum´ e´ Un nouveau concept de dirigeable sans propulseur, ni gouvernail de direction, ni gouvernail de profondeur est consider´ e´ dans cette these.` Il est actionne´ par une masse mobile et une vessie d’air en interne dont la masse est reglable.´ Cela resulte´ en un deplacement´ du centre de gravite´ et un changement de la force de flottabilite´ nette. Le developpement´ de ce concept de dirigeable est motive´ par les economies´ d’energie.´ Un modele` complet a` huit degres´ de liberte´ de ce dirigeable est obtenu par l’approche de Newton-Euler. L’interconnection entre le corps rigide du dirigeable et de la masse mobile est clairement present´ ee.´ La dynamique dans le plan longitudinal est analysee´ et commandee´ par la methode´ LQR, une linearisation´ entree-sortie,´ et la linearisation´ maximale par bouclage, avec stabilite´ interne. Graceˆ a` la linearisation´ maximale par bouclage, une commande non lineaire´ efficace est deduite.´ Dans ce processus, la modelisation,´ l’analyse et la commande sont resolues´ pour les cas particuliers du dirigeable qui deviennent peu a` peu moins contraints et se rapprochent du cas le plus gen´ eral.´ Le cas le plus contraint se reduit´ a` un systeme` qui a deux degres´ de liberte.´ Il est montre´ que les propriet´ es´ de base de certains systemes` mecaniques´ simples restent determinantes´ pour l’analyse et la synthese` des dirigeables avances.´ Ces propriet´ es´ sont loin d’etreˆ evidentes´ sur le modele` complet. Graceˆ a` une approche de perturbations singulieres,` la superposition des deux actions de controleˆ dans le plan longitudinal et dans le plan lateral´ conduit a` une commande pertinente pour la dynamique en trois dimensions. ii Remerciements First of all, I would like to thank my two supervisors: Dr. Claude H. Moog and Prof. Yueming Hu. Dr. Moog, I appreciate for your enduring guidance, encouragement and support throughout my three-year PhD program in France. I am very fortunate and honored to be able to work with you, Dr. Moog. During the last three years, you always show your knowledgeability, responsibility, and patience to me. I look forward to learning more from you for much longer. Prof. Yueming Hu, I really appreciate for your involvement six year ago when I applied a master position. During these six years, you gave me lots of opportunities to cultivate my capacity. I espe- cially would like to thank your encourage in this period. Without your encourage, I can not have this achievement. This six-year period, I have been working with your, is the most important segment in my lift. I would like to thank the China Scholarship Council for its generous fund support for my study in France. With this fund support, I can focus on the research in the last three years. I also would like to thank the Education Department of the Chinese Embassy in France and the Guangzhou Service Center for Scholarly Exchange for lots of advantage they offered. I sincerely thank all my instructors at Institut de Recherche en Communications et Cybern´etique de Nantes (IRCCyN) for sharing their insights and enthusiasm, and being generous with their time. I Would like to particularly thank Dr. Aoustin Yannick, Dr. Chevallereau Christine, Dr. Chriette Abdelhamid, and Dr. Khalil Wisama, who have repeatedly helped me in complex situations. The director of IRCCyN Dr. Malabre Michel and the secretary of the control team Ms. Thureau Emily also helped me in numerous ways. Lots of my colleagues in IRCCyN, like Ezzat Marwa, Menard Tomas, and Henaff Sebastien, also offer lost of helps to me. Thanks to my teachers and colleagues in the Automation College and the Engineering Research Center of Precision Electronic Manufacturing Equipments MOE of South China University of Tech- nology. Particularly, I thank Dr. Liu Yu who gave me lots of supports during my PhD study. My sincere thanks to my family for their love, understanding, and persistent encouragement. My parents, Wu Jishu and Zhan Yuxiang, elder brother Wu Juntao, sister-in-law Li Ying, and my nephew Wu Zhuoyan, have always been a great source of inspiration. iii Dedication dedicated to my family iv Nomenclature α the angle of attack θ the pitch angle λ2,λ1,λ0 parameters of the feedback controller ξ the flight path angle ρa the density of the air the volume of the airship ∇ Ω the angular velocity of the airship in the body frame, Ω (Ω , Ω , Ω )T ≡ 1 2 3 Ωi the ith element of Ω b the position of the airship in the inertial frame B the momentum of the added mass P the momentum of the moveable mass, P (P , P , P )T p p ≡ p1 p2 p3 P the total momentum of the airship’s rigid body j Ci aerodynamic coefficients e1, e2, e3 the body frame unit vectors F the aerodynamic force, F diag X , Y , Z a a ≡ { a a a} Fat the aerodynamic force with respect to the body frame FI the added inertial force v vi Fs the total external force acting on the airship’s rigid body Fint the internal force acting on the moveable mass by the body the identity matrix of appropriate dimensions I FGB the resultant force of the gravity and the buoyancy in the inertial frame FGBt the resultant force of the gravity and the buoyancy in the body frame J the second diagonal element of Js Ji the ith diagonal element of J J the added inertial matrix, J diag m , m , m f f ≡ { 44 55 66} J the moment of inertia of m , J diag J , J , J s s s ≡ { x y z} J the moment of inertia of m and the added mass, J = diag J , J , J = J + J s { 1 2 3} f s k the parameter of the feedback controller i, j, k the inertial frame unit vectors K the angular momentum of the added mass Ks the total angular momentum of the airship’s rigid body mb the mass of the internal air bladder mh the uniformly distributed mass of the hull ms the stationary mass of the airship mv the total mass of airship, mv = ms + m¯ mw the center offset mass m¯ the mass of the moveable mass mi the ith element of M m0 the net buoyancy of the airship m the mass of the airship displaced air Ma the aerodynamic pitch moment vii M the aerodynamic moment, M diag L ,