Yue Baozeng

Hybrid Control of Liquid-Filled Spacecraft Maneuvers by Dynamic Inversion and Input Shaping

In this paper, a hybrid control method for partially liquid-filled spacecraft maneuvers is proposed. This control scheme integrates the command input shaping technique and the feedback linearization method to guarantee the implementation of the maneuver task for spacecraft to yield the desirable suppression of liquid fuel slosh. The coupled slosh spacecraft in attitude maneuver carrying a sloshing liquid is considered as a multibody system with the sloshing motion modeled as a spherical pendulum. Nonlinearly coupled equations of attitude and orbital motion are presented for the partially liquid-filled spacecraft undergoing fuel slosh. A feedback linearization approach is applied to transform the nonlinear system dynamics into a linear system (inverse dynamics of the original system or so-called dynamics inversion) to compute the input corresponding to the reference output. Dynamic inversion and input shaping techniques are used to design a controller for the reference tacking maneuver of spacecraft with f...

Nonlinear phenomena of three-dimensional liquid sloshing in microgravity environment

The dynamic problem of three-dimensional liquid sloshing is numerically studied in this paper. The arbitrary Lagrange-Euler (ALE) kinematic description is introduced into the control equations system. The discrete numerical equations of finite element method are developed by Galerkin weighted residual method. The boundary condition about free-surface tension is represented in the form of weak integration that can be computed by our differential geometry method derived. The normal vector on free surface is calculated by using accurate formula presented in this paper. The numerical computations are performed and the comparison not only between numerical results and analytical results but also between numerical results and experimental results validated the effectiveness of the method. Finally, large amplitude sloshing of three-dimensional liquid in low-gravity environment is simulated and some important nonlinear characteristics are obtained. From the numerical results, it is concluded that the character of nonlinear sloshing of the liquid under low-gravity environment is much different from that of the liquid sloshing under normal gravity environment.

Modeling and Coupling Dynamics of the Spacecraft with Multiple Propellant Tanks

This paper is mainly focused on the modeling and coupling dynamics of the spacecraft with multiple propellant tanks. The dynamic boundary conditions on a curved, liquid, free surface under a low-gravity environment are transformed to general simple differential equations by using a Fourier–Bessel series expansion method, and the state vectors of coupled liquid-sloshing equations are composed by the modal coordinates of a relative potential function and the modal coordinates of the wave height. The overall coupled dynamic equations for the rigid platform motion and liquid fuel sloshing are subsequently obtained by means of Lagrange’s equations in terms of general quasi coordinates. The orbit thruster firing and attitude momentum wheel controller are applied to the coupled system to testify to the mathematical model and analyze the coupling dynamics of a coupled fluid–spacecraft system. MATLAB software is used for symbolic manipulation, coupling dynamics, and control simulations. Numerical simulations via c...

Bifurcation and Stability Analysis of the Hamiltonian—Casimir Model of Liquid Sloshing

Motion stability of a spacecraft is discussed. A canonical Hamiltonian model for liquid sloshing is presented for a moving rigid body. An equivalent mechanical pendulum model is used to represent the fuel slosh inside the container. In this model sloshing is represented by the moving mass, the rest of the mass of the spacecraft is assumed to be stationary. The spacecraft structure is considered to be an elliptical rigid shape and the steady rotation along the x-axis is taken as the major-axis rotation. Motion stability for the present model is analyzed using the Lyapunov theory with Casimir energy functions. Conditions for stability and instability are derived for a steady principal axis rotation of the rigid body. Simulation results are presented to distribute the region into stable and unstable regions. Besides this, the nonlinear behavior of the system is analyzed under the influence of an external force acting periodically. Chaos is observed through a bifurcation diagram. The time history map and phase portrait are also presented to analyze the nonlinear behavior of the system.

Simulation of Large-Amplitude Three-Dimensional Liquid Sloshing in Spherical Tanks

The propellant sloshing problem is of increasing concern in aerospace engineering. Computational-fluid-dynamics simulations have been carried out to predict three-dimensional large-amplitude liquid sloshing in spherical tanks. Basically an arbitrary Lagrangian–Eulerian method is followed. The main challenges are tracking the motion of the contact line and free surface, defining the nodal velocities on the space curved wall boundary, and maintaining rational computational mesh at the same time. A novel mesh moving strategy is presented to update the mesh and meanwhile to suppress the mesh distortion. The mesh nodes on the free surface and contact line are restricted to move along prescribed orbits, and the nodes on the container wall are moved by an algebraic mesh moving algorithm. The finite element method combined with the characteristic-based split algorithm is adopted. The numerical results are compared to analytical and published experimental results for validation, and good agreement is observed.

Heteroclinic bifurcations in attitude maneuver of coupled slosh-spacecraft with flexible appendage

In this paper, the chaotic dynamics in an attitude transition maneuver of a slosh-spacecraft coupled with flexible appendage in going from minor axis to major axis spin under the influence of dissipative effects due to fuel slosh and a small flexible appendage constrained to only torsional vibration is investigated. The slosh-spacecraft coupled with flexible appendage in attitude maneuver carrying a sloshing liquid is considered as multi-body system with the sloshing motion modeled as a spherical pendulum. The focus in this paper is that the dynamics of the liquid and flexible appendage vibration are coupled. The equations of motion are derived and transformed into a form suitable for the application of Melnikov’s method. Melnikov’s integral is used to predict the transversal intersections of the stable and unstable manifolds for the perturbed system. An analytical criterion for chaotic motion is derived in terms of system parameters. This criterion is evaluated for its significance to the design of spacecraft. The dependence of the onset of chaos on quantities such as body shape and magnitude of damping values, fuel fraction and torsional vibration frequency of flexible appendage are investigated. In addition, we show that a spacecraft carrying a sloshing liquid, after passive reorientation maneuver, will end up with periodic limit motion other than a final major axis spin because of the intrinsic non-linearity of fuel slosh. Furthermore, an extensive numerical simulation is carried out to validate the Melnikov’s analytical result.

Dynamic Analysis of the Flexible Spacecraft with Liquid Sloshing in Axisymmetrical Container

In this paper, the modeling and dynamic analysis of the spacecraft carrying a flexible appendage and a partially fuel-filled arbitrary axisymmetrical tank with curved wall are investigated. Governing equations of the liquid sloshing in the container are derived from the variational principle. The dynamic equations of modal coordinates of the liquid sloshing are established by the Galerkin method. The coupling vibration equations of the flexible appendage are drawn from the theory of the Euler–Bernoulli beam. The state equations of coupled motion of the main rigid platform are deduced by using Lagrange’s equations in term of general quasi coordinates. Numerical results are presented to verify the efficiency and validity of the method developed in this paper. Related results suggest that there are complex dynamical behaviors in the flex–rigid–liquid coupling spacecraft dynamical systems, which have a reference value to the overall design of the spacecraft system.

On Chaotification of Discrete Lagrange Systems

This paper is concerned with chaotification of discrete Lagrange systems in one dimension, via feedback control techniques. A chaotification theorem for discrete Lagrange systems is established. The controlled systems are proved to be chaotic in the sense of Devaney. In particular, the systems corresponding to the original systems and designed controllers are only required to satisfy some mild assumptions.