Institute for Systems Research Technical Reports

Permanent URI for this collectionhttp://hdl.handle.net/1903/4376

This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.

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Author: search.filters.author.Wang, L.S.Subject: search.filters.subject.geometric control

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    Gyroscopic Control and Stabilization
    (1991) Wang, L.S.; Krishnaprasad, Perinkulam S.; ISR
    In this paper, we consider the geometry of gyroscopic systems with symmetry, starting from an intrinsic Lagrangian viewpoint. We note that natural mechanical systems with exogenous forces can be transformed into gyroscopic systems, when the forces are determined by a suitable class of feedback laws. To assess the stability of relative equilibria in the resultant feedback systems, we extend the energy-momentum block-diagonalization theorem of Simo, Lewis, Posbergh, and Marsden to gyroscopic systems with symmetry. We illustrate the main ideas by a key example of two coupled rigid bodies with internal rotors. The energy-momentum method yields computationally tractable stability criteria in this and other examples.
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    Steady Rigid-Body Motions in a Central Gravitational Field
    (1991) Wang, L.S.; Maddocks, J.H.; Krishnaprasad, Perinkulam S.; ISR
    In recent work, the exact dynamic equations for the motion of a finite rigid body in a central gravitational field were shown to be of Hamiltonian form with a noncanonical structure. In this paper, the notion of relative equilibrium is introduced based upon this exact model. In relative equilibrium, the orbit of the center of mass of the rigid body is a circle, but the center of attraction may or may not lie at the center of the orbit. This feature is used to classify great-circle and non-great-circle orbits. The existence of non-great-circle relative equilibria for the exact model is proved from various variational principles. While the orbital offset of the non-great-circle solutions is necessarily small, a numerical study reveals that there can be significant changes in orientation away from the classic Lagrange relative equilibria, which are solutions of an approximate model.
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    Mechanical Systems with Partial Damping: Two Examples
    (1991) Wang, L.S.; Krishnaprasad, Perinkulam S.; Dayawansa, Wijesuriya P.; ISR
    We discuss the problem of constructing steady state motions of mechanical systems with partial damping. A planar three bar linkage with viscous damping at one of the joints is considered as an example. We show that for a generic set of system parameters all steady state motions are confined to relative equilibria. We also consider the example of two rigid bodies with one-board rotors coupled via a ball-in-socket joint with viscous friction and show that in the steady state, the system is at a relative equilibrium.
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    Geometry, Dynamics and Control of Coupled Systems
    (1990) Wang, L.S.; Krishnaprasad, P.S.; ISR
    In this dissertation, we study the dynamics and control of coupled mechanical systems. A key feature of this work is the systematic use of modern geometric mechanics, including methods based on symplectic geometry, Lie symmetry groups, reductions, lagrangian mechanics and hamiltonian mechanics to investigate specific Eulerian manybody problems. A general framework for gyroscopic systems with symmetry is introduced and analyzed. The influence of the gyroscopic term (linear term in Lagrangian) on the dynamical behavior is exploited. The notion of gyroscopic control is proposed to emphasize the role of the gyroscopic term in designing control algorithms. The block-diagonalization techniques associated to the energy-momentum method which proved to be very useful in determining stability for simple mechanical systems with symmetry are successfully extended to gyroscopic systems with symmetry. The techniques developed here are applied to several interesting mechanical systems. These examples include the dual-spin method of attitude control for artificial satellites, a multi-body analog of the dual-spin problem a rigid body with momentum wheels in a central gravitational force field, and a rigid body with momentum wheels and a flexible attachment.