Nonlinear Controller Design for a Flexible Spacecraft
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Nonlinear Controller Design for a Flexible Spacecraft 1 ´ Jose Luis Redondo Gutierrez
· Ansgar Heidecker1
Accepted: 8 September 2020 © The Author(s) 2020
Abstract This paper combines the nonlinear Udwadia-Kalaba control approach with the Assumed Mode Method to model flexible structures and derives an attitude controller for a spacecraft. The study case of this paper is a satellite with four flexible cantilever beams attached to a rigid central hub. Two main topics are covered in this paper. The first one is the formulation of the equation of motion and the second one is the nonlinear controller design. The combination of these two techniques is able to provide a controller that damps the vibration of a flexible structure while achieving the desired rigid-motion state. Keywords Attitude control · Non-linear control · Flexible satellites · Active damping · Udwadia-Kalaba
Introduction Historically the flexibility of most satellites has not posed a major difficulty. This is because most of the flexible structures deployed so far have natural frequencies considerably higher than external disturbances and control actuation. Examples of cases where large structures have been modeled as rigid bodies can be found in [16] and [23]. In [15] and [3], even though rigid dynamics are used, the potential influence of the coupling between natural frequencies and external or internal disturbances is pointed out. This coupling is studied for two particular controllers over a large solar sail in [18]. Studies on how to model the deformation of large structures in space are also conducted in [4, 7, 22, 25].
Jose Luis Redondo Guti´errez
[email protected] Ansgar Heidecker [email protected] 1
German Aerospace Center (DLR), Institute of Space Systems, Bremen, Germany
The Journal of the Astronautical Sciences
In contrast to the historic perspective the interest of space industry in flexible structures has considerably increased during the last decades. See e.g. recent planetary society mission LightSail-2 [13] or DLR mission Tandem-L [11]. The current development in this area is driven by two main factors [24]: the miniaturization of satellites [1, 12, 14] and technological advances in related key areas, such as ultralight deployable booms or sail films [2]. The main advantages of these structures are their low launching volume, as they are deployed once in orbit, and the low mass in relation to the final size of the structure. Examples of applications of this kind of technology are solar sailing [19], active deorbiting of debris [17] and solar power generation [9]. Such lightweight structures triggered the development of controllers with specific performance bounds [26] and fixed maneuver times [5]. Additionally, flexibility in combination with liquid propellant is becoming more and more relevant [6, 8]. This paper demonstrates a controller design methodology which takes into account the complex nonlinear motion of a flexible satellite. The chosen study case consists of a rigid body with four flexible cantileve
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