Dynamics and Control of Rigid-flexible Coupling Microsatellite

Abstract

El proyecto APSCO-SSS fue iniciado por la Asia-Pacific Space Cooperation Organization (APSCO). Este consta de 3 satélites siendo uno de ellos el microsatélite SSS-1 que a diferencia de otros satélites está conformado por partes rígidas y flexibles como lo son el mástil entendible. La vibración generada por este apéndice flexible representa un reto al momento de orientar la nave espacial en la dirección deseada. El primer objetivo de este trabajo es modelar la dinámica del sistema por medio del método de Lagrange, para esto el cuerpo principal del satélite y el subsatélite en la punta del mástil extensible son asumidos como cuerpos rígidos, el mástil es tomado como una Euler-Bernoulli beam donde solo se considera la deformación lateral, mas no la torsional o la axial. Una vez obtenida las ecuaciones del movimiento se buscará la síntesis de un controlador robusto que sea capaz de contrarrestar la vibración del sistema debido al mástil flexible, para esto se usaran las técnicas de síntesis de control H infinito y Mu. Variación paramétrica es añadida para poner a prueba los controladores obtenidos analizando su respuesta y proceder con la comparación de su efectividad.

The APSCO-SSS project is initiated by the Asia-Pacific Space Cooperation Organization (APSCO). This project consists of 1 micro-satellite (SSS-1) and 2 cube-satellites (SSS-2A and SSS- 2B) implemented for different objectives such as: demonstration of coilable mast deployment, ADSB technology and remote sensing. In this project, the micro-satellite SSS-1 is formed by a mainsatellite and a sub-satellite joined by a coilable mast obtaining as a result a rigid-flexible multi body system. Flexible vibration of the coilable mast will bring great difficulty and challenge to the control of the micro-satellite. The first step of this thesis research is to obtain the mathematical model of the rigid-flexible coupling micro-satellite, for this the Lagrange method is used. In terms of dynamics, the coilable mast is normally viewed as a flexible appendage and simplified as an Euler-Bernoulli beam, but the SSS-1 is equipped with a large mass element (sub-satellite) at the tip of the flexible structure, as a consequence and in contrast to previous work, the new mathematical model must include this rigid sub-satellite when deriving the equations of motion. The satellite is modeled as a body that can rotate in the three axis, the flexible appendage can be affected by lateral deflection while axial and torsional deformation are not considered in this study. Kinetic energy is firstly derived as a natural step in the Lagrange procedure, this consist of the kinetic energy obtained from the three satellite elements (rigid main satellite, flexible coilable mast and rigid sub-satellite). Some matrix notations are used in order to simplified the large total kinetic energy expression and using the assumed modes method the mass matrix of the entire system can be obtained. The stiffness and damping matrices of the model are obtained by defining the potential energy of the system and then applying the assumed modes method for discretization. In this project large and fast rotations are not considered, therefore lateral deformation of the flexible appendage is not too large. This assumption permits to linearize the obtained dynamic plant to further synthesize a linear controller for direct attitude control and vibration suppression. Two controllers are proposed to work with the dynamic plant in close loop configuration, the first is the H infinity controller which main purpose is to minimize the impact of the exogenous inputs (w) into the regulated outputs (z). For this the norm of the transfer function known as LFT from w to z must be minimized. The second controller is obtained by using the μ synthesis, in contrast to the first proposed controller this procedure is capable of considering the parametric uncertainty of the system while deriving a robust controller. Regarding the control strategy, the dynamic plant is interconnected with different weighting functions that can prioritize some task over others. In this project the control system priority is to set the entire structure in the desire orientation, after this the system focuses on suppress the vibration of the flexible appendage. As sensor data the system will the three Euler angles and the lateral acceleration of the displacement of the flexible appendage. Results obtained from the two synthesized controllers are compared when working with the nominal and uncertain dynamic plant.