Research Papers

Dynamics and Control of Spacecraft With a Generalized Model of Variable Speed Control Moment Gyroscopes

[+] Author and Article Information
Sasi P. Viswanathan

Mechanical and Aerospace Engineering,
New Mexico State University,
Las Cruces, NM 88003
e-mail: sashi@nmsu.edu

Amit K. Sanyal

Assistant Professor
Mechanical and Aerospace Engineering,
New Mexico State University,
Las Cruces, NM 88003
e-mail: asanyal@nmsu.edu

Frederick Leve

Air Force Research Laboratory,
Space Vehicles Directorate,
Kirtland Air Force Base,
Albuquerque, NM 87117
e-mail: afrl.rvsv@kirtland.af.mil

N. Harris McClamroch

Professor Emeritus
Aerospace Engineering,
University of Michigan,
Ann Arbor, MI 48109-2140
e-mail: nhm@engin.umich.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received February 6, 2014; final manuscript received November 19, 2014; published online March 4, 2015. Assoc. Editor: May-Win L. Thein.

J. Dyn. Sys., Meas., Control 137(7), 071003 (Jul 01, 2015) (12 pages) Paper No: DS-14-1063; doi: 10.1115/1.4029626 History: Received February 06, 2014; Revised November 19, 2014; Online March 04, 2015

The attitude dynamics model for a spacecraft with a variable speed control moment gyroscope (VSCMG) is derived using the principles of variational mechanics. The resulting dynamics model is obtained in the framework of geometric mechanics, relaxing some of the assumptions made in prior literature on control moment gyroscopes (CMGs). These assumptions include symmetry of the rotor and gimbal structure, and no offset between the centers of mass of the gimbal and the rotor. The dynamics equations show the complex nonlinear coupling between the internal degrees-of-freedom associated with the VSCMG and the spacecraft base body's rotational degrees-of-freedom. This dynamics model is then further generalized to include the effects of multiple VSCMGs placed in the spacecraft base body, and sufficient conditions for nonsingular VSCMG configurations are obtained. General ideas on control of the angular momentum of the spacecraft using changes in the momentum variables of a finite number of VSCMGs are provided. A control scheme using a finite number of VSCMGs for attitude stabilization maneuvers in the absence of external torques and when the total angular momentum of the spacecraft is zero is presented. The dynamics model of the spacecraft with a finite number of VSCMGs is then simplified under the assumptions that there is no offset between the centers of mass of the rotor and gimbal, and the rotor is axisymmetric. As an example, the case of three VSCMGs with axisymmetric rotors, placed in a tetrahedron configuration inside the spacecraft, is considered. The control scheme is then numerically implemented using a geometric variational integrator (GVI). Numerical simulation results with zero and nonzero rotor offset between centers of mass of gimbal and rotor are presented.

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Grahic Jump Location
Fig. 1

(a) CAD Rendering of a VSCMG design with an axisymmetric rotor and (b) vector representation of VSCMG axes, with rotor offset in the axial direction η(t) from the center of mass of the gimbal about its axis g

Grahic Jump Location
Fig. 2

(a) CAD Rendering of the three VSCMGs in tetrahedron configuration; (b) satellite with three VSCMGs actuators; and (c) vector representation of three VSCMGs, in tetrahedron formation with respect to the base body coordinate frame [X Y Z]

Grahic Jump Location
Fig. 3

Plots of: (a) norm of angular velocity of the spacecraft base body, (b) norm of control torque, (c) attitude stabilization error, and (d) norm of VSCMG angular momentum

Grahic Jump Location
Fig. 4

(a) VSCMG gimbal rates for σ = 0 and (b) VSCMG gimbal rates for σ = 0.005 m

Grahic Jump Location
Fig. 5

(a) VSCMG rotor rates for σ = 0 and (b) VSCMG rotor rates for σ = 0.005 m

Grahic Jump Location
Fig. 6

(a) Difference in gimbal rates, α˙ei=α˙σ=0i−α˙σ≠0i and (b) error in rotor rate, θ˙ei=θ˙σ=0i−θ˙σ≠0i



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