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A Space Manipulator with Its Base Attitude Controller

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A Space Manipulator with Its Base Attitude Controller DYNAMIC INTERACTION OF A SPACE MANIPULATOR WITH ITS BASE ATTITUDE CONTROLLER Eric Martin B. Eng. (University of Sherbrooke), 1992 M. Eng. (McGill University), 1995 Department of Mechanical Engineering McGill University Montreal, Quebec, Canada A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfilment of the requirements of the degree of Doctor of Phiiosophy February 1999 @ Eric Martin National Library Bibliothèque nationale du Canada Acquisitions and Acquisitions et Bibliographie Services services bibliographiques 395 Wellington Street 395, nie Wellington OnawaON K1AW ûttawaON KIAON4 Canada Canada The author has granted a non- L'auteur a accordé une Licence non exclusive licence allowing the exclusive permettant à la National Library of Canada to Bibliothèque nationale du Canada de reproduce, loan, distribute or seil reproduire, prêter, distribuer ou copies of this tbesis in microform, vendre des copies de cette thèse sous paper or electronic formats. la fome de microfichelfilm, de reproduction sur papier ou sur format électronique. The author retains ownership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'auteur qui protège cette thèse. thesis nor substantial extracts fiom it Ni la thèse ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent être imprimés reproduced without the author' s ou autrement reproduits sans son permission. autorisation. To Dominique, Charles, Philippe and Jérémie for their patience and understanding during the drajting of this manuscript. Abstract Space manipulators mounted on a free-floating base are structurally flexible mechan- ical systems. For some applications, it is necessary to control the attitude of the base by the use of on-off thrusters. However, thruster operation produces a rather broad frequency spectrum that can excite sensitive modes of the flexible system. This sit- uation is likely to occur especially when the rnanipulator is moving a big payload. The excitation of these modes can introduce further disturbances to the attitude control system; therefore, undesirable fuel replenisliing limit cycles may develop. To investigate these dynamic interactions, the dynamics mode1 of an N-flexible-joint space manipulator is developed and used to describe a three-flexible-joint manipu- lator mounted on a six-degree-of freedom spacecraft dubbed in t his thesis "spatial systern". Since the attitude controller assumes the use of on-off thrusters, which are nonlinear devices, the describing-function technique, an approximate method for the analysis of nonlinear systems, is used to analyze four different control systems using an approximate two-mas8 system. This technique is adapted to be used in conjunction with the root-locus concept, thus providing a different picture of the problem and helping in the control system design. A pararnetric study is performed to compare the control schemes using those analytical tools, which is validated with simulations using the spatial system. It is shown that the three proposed variations of a classical control schemc are very effective to minimize such undesirable dynaniic interactions. Finally, Mecano, a commercial mechanical-system modelling and anal- ysis software tool, is adapted for the study of control systems and used to study the effect of link elasticity on the robustness of the proposed control schemes. Résumé Les robots manipulateurs montés sur une base flottante et opérant dans l'espace sont des systèmes mécaniques flexibles. Pour certaines opérations, il est nécessaire de commander la position de la base en utilisant des fusées de type tout-ou-rien. Cependant, l'opération de ces fusées produit un large spectre de fréquences qui peu- vent exciter les modes vibratoires du système, cet te situation devenant plus probable lorsque le manipulateur transporte de grosses charges. L'excitation de ces niodes peut introduire davantage de perturbations au système de commande, continuant alors le cycle et augmentant du même coup la consommation de combustible, sans stabiliser la base. Afin d'étudier ce problème, le modéle dynamique d'un manipulateur à N articulations élastiques est développi! et utilisé pour décrire un robot spatial à trois articulations élastiques. Puisque la commande présume l'utilisation de fusées tout- ou-rien, qui sont des mécanismes non-linéaires, la technique des fonctions descriptives a été utilisée pour étudier quatre modèles différents à l'aide d'un système simplifié à deux masses. Cette technique a été utilisée conjointement avec la méthode du lieu g/'eométrique des racines pour ainsi analyser le problème d'un point de vue différent. Une étude paramétrique a été effectuée à l'aide de ces méthodes pour comparer les différents modèles de commande. Cette étude a été confirmée par des simulations du robot spatial décrit précédemment. Cette étude démontre que les trois variations proposées aux méthodes de commande utilisées à l'heure actuelle dans l'espace sont de très bonnes solutions de rechange étant donné qu'elles peuvent à toute fin utile éliminer le problème d'interactions dynamiques. Acknowledgement s I would like to thank my research supervisors, Professors J. Angeles and E. Pa- padopoulos for their guidance, encouragement and support during the course of this research. Their help in reviewiiig the manuscript is also gratefully acknowledged. Working in conjunction with them was a very enriching experience and a great plea- sure. The support of this work by Quebec's Fonds pour la Formation de Chercheurs et l'Aide à la Recherche (FCXR) and by Canada's Natural Sciences and Engineering Research Council (NSERC) is gratefully acknowledged. Funding was also provided to the author through NSERC and FCAR graduate scholarships. The support of Quebec's Ministère des unaires internationales under the Quebec-Wallonia Scientific Collaboration Agreement is highly acknowledged. 1 also want to thank Dr. Dave Parry of Spar Aerospace Ltd. for providing us with detailed CANADARM data, and Mr. Yves Lombard of Samtech to let us use freely the finite-element software package Mecano. Many thanks are also due to the Centre for intelligent Machines (CIM) for al1 the computer facilities provided and for the pleasant research environment. Working at CIM was a wonderful experience; special thanks are due to CIM7s staff, secretaries, and dl fellow students. Finally, 1 am very grateful to my wife, Dominique Mathieu, for her love, support and understanding throughout rny thesis work. Thanks must also be given to my sons Charles, Philippe and Jérémie for allowing me to work on this research. Contents Abstract Résumé Acknowledgements List of Figures List of Tables Nomenclature xvi 1 Introduction 1 1.1 Robots in Space .............................. 1 1.2 Literature Survey ............................. 4 1.2.1 Dynamics and Controi of Space Robots ............. 4 1.2.2 Attitude Control of Spacecraft .................. 6 1.2.3 Control of Large Space Structures (LSS) ............ 11 1.2.4 Payload- Attitude Controller Interaction ............. 14 1.3 Objectives and Organization of this Thesis ............... 17 1.3.1 Problem Formulation and Objectives .............. 17 1.3.2 Research Tools .......................... 18 1.3.3 Thesis Organization ....................... 19 1.4 Contributions ............................... 20 2 Modelling. Control and Analysis of Rigid Spacecraft 21 2.1 Introduction ................................ 21 2.2 Modelling of Rigid Spacecraft ...................... 21 2.3 Classical Attitude Control Scheme .................... 2.3.1 On-Off Thrusters Command ................... 2.3.2 State Estimation ......................... 2.3.3 Model Integration ......................... 2.4 Methods of Analysis ........................... 2.4.1 Describing-Function Analysis .................. 2.4.2 Root-Locus Analysis ....................... 2.4.3 Simulation ............................. 2.5 Stability .................................. 2.5.1 Definitions ............................. 2.5.2 Application ............................ 2.6 Summary ................................. 3 Modelling of Flexible Space Manipulator Systems 3.1 Introduction ................................ 3.2 General Lagrangian Formulation ..................... 3.3 Linearization of the Equations of Motion ................ 3.4 Description and Validation of the Spatial System ........... 3.41 Model Description and Parameter Identification ........ 3.4.2 Model Validation ......................... 3.4.3 Determination of Frequencies and Damping Ratios ...... 3.5 Finite Element Formulation-Adaptation of a FEM Package for Con- trol Purposes ............................... 3.5.1 General Background on Control Systems ............ 3.5.2 Derivation of the State-Variable Equations ........... 3.5.3 Application: Attitude Control .................. 3.6 Summary ................................. 4 Control Synthesis Using an Asymptotic State Estimator 4.1 Introduction ................................ 4.2 Classical Rate Est imator-Pro blem Description ............ 4.2.1 The Interaction Problem with a Planar System ........ 4.2.2 The Interaction Problem with A Spatial System ........ 4.2.3 Problem Demonstration with Theoretical Analysis and Para- metric Study ........................... vii 4.3 Attitude Control using an Asymptotic State Estimator ........ 112 4.3.1 Asymptotic State Estimator Theory ............... 112 4.3.2 Asymptotic State Estimator for Space Robotic Systems .... 116 4.4 Demonstration of the
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