Modeling and Control of a Rotating Flexible Spacecraft: A Port-Hamiltonian Approach

Abstract

In this brief, we develop a mathematical model of a flexible spacecraft system composed of a hub and two symmetrical beams using the port-Hamiltonian framework. This class of system has favorable properties, such as passivity for controller synthesis and stability analysis, where the global Hamiltonian plays the role of a Lyapunov function candidate. The spacecraft model is viewed as a power-conserving interconnection between an infinite (beam) and finite (hub) dimensional system. We show that the interconnection result has a port-Hamiltonian structure and is passive. The introduction of a nonlinear feedback term, which takes into account the beam's flexibility, is developed using the control by an interconnection approach. The closedloop stability is proven; then, through explicitly solving the partial differential equations of the system, asymptotic stability is obtained. Finally, the experimental results are carried out to assess the validity of the proposed design methodology.

Twenty years of distributed port-Hamiltonian systems: a literature review

“…An example of such systems is a robot manipulator with flexible links. Along the same line, a simplified model for a rotating flexible spacecraft was presented in Aoues et al (2017), where the model consists of a center rigid hub, two flexible (Euler-Bernoulli) beams each connected to a tip mass. Finally, in Ramirez et al (2013), an underactuated simplified model for a flexible nano-gripper for DNA manipulation was presented.…”

Port-Hamiltonian formulation and symplectic discretization of plate models Part II: Kirchhoff model for thin plates

“…For what concerns the use of this model for control and simulation purposes, the reader can refer to [19] for a stability and stabilization proof of the Euler-Bernoulli beam or to [20] for an illustration of a rotating spacecraft with flexible appendages model as PH Bernoulli beams.…”

“…Starting from the results stated in [5], this system may be interconnected over its boundary to other finite or infinite dimensional PH systems, such as rigid bodies or other flexible appendages. This may find useful applications in simulating a multi-body environment for spatial applications, like the attitude motion of a satellite with flexible solar panels [20]. Since no causality is imposed on the boundary ports, the discretization method herein proposed allows the construction of arbitrarily complex connections among different modules.…”

Exponential stabilization of a clamped Timoshenko beam with actuation on a tip mass

“…Systems modelled by a mixed set of Partial Differential Equations (PDE) and Ordinary Differential Equations (ODE) have a wide range of applications, ranging from spatial manipulators [1] to micro-grippers [2]. This is because distributed parameters systems modelled by a set of PDE are frequently controlled by actuators that have lumped dynamics, which are modelled by a set of ODE.…”