Asymptotic stabilization of the hanging equilibrium manifold of the 3D pendulum

The 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom; it is acted on by gravity and it is fully actuated by control forces. The 3D pendulum has two disjoint equilibrium manifolds, namely a hanging equilibrium manifold and an inverted equilibrium manifold. This paper shows that a controller based on angular velocity feedback can be used to asymptotically stabilize the hanging equilibrium manifold of the 3D pendulum. Lyapunov analysis and nonlinear geometric methods are used to assess the global closed-loop properties. We explicitly construct compact sets that lie in the domain of attraction of the hanging equilibrium of the closed-loop. Finally, this controller is shown to achieve almost global asymptotic stability of the hanging equilibrium manifold. An invariant manifold of the closed-loop that converges to the inverted equilibrium manifold is identified. Copyright © 2007 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/56146/1/1178_ftp.pd

Globally Convergent Adaptive Tracking of Angular Velocity and Inertia Identification for a 3-DOF Rigid Body

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57820/1/AdaptiveTrackingTCST2006.pd

Adaptive Tracking of Angular Velocity for a Planar Rigid Body With Unknown Models for Inertia and Input Nonlinearity

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57795/1/AdaptiveTrackingTACTTCST1D.pd

Inertia-Free Spacecraft Attitude Tracking with Disturbance Rejection and Almost Global Stabilization

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76737/1/AIAA-41565-705.pd

Dynamics and control of a 3D pendulum

Abstract — New pendulum models are introduced and stud-ied. The pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force and control forces and moments. Several different pendulum models are developed to analyze properties of the uncontrolled pendulum. Symmetry assumptions are shown to lead to the planar 1D pendulum and to the spherical 2D pendulum models as special cases. The case where the rigid body is asymmetric and the center of mass is distinct from the pivot location leads to the 3D pendulum. Rigid pendulum and multi-body pendulum control problems are proposed. The 3D pendulum models provide a rich source of examples for nonlinear dynamics and control, some of which are similar to simpler pendulum models and some of which are completely new. I

Stabilization of a 3D rigid pendulum

Abstract-We introduced models for a 3D pendulum, consisting of a rigid body that is supported at a frictionless pivot, in a 2004 CDC paper [1]. In that paper, several different classifications were given and models were developed for each classification. Control problems were posed based on these various models. This paper continues that line of research by studying stabilization problems for a reduced model of the 3D pendulum. Two different stabilization strategies are proposed. The first controller, based on angular velocity feedback only, asymptotically stabilizes the hanging equilibrium. The domain of attraction is shown to be almost global. The second controller, based on angular velocity and reduced attitude feedback, asymptotically stabilizes the inverted equilibrium, providing an almost global domain of attraction. Simulation results are provided to illustrate closed loop properties

Fusarium: more than a node or a foot-shaped basal cell

Recent publications have argued that there are potentially serious consequences for researchers in recognising distinct genera in the terminal fusarioid clade of the family Nectriaceae. Thus, an alternate hypothesis, namely a very broad concept of the genus Fusarium was proposed. In doing so, however, a significant body of data that supports distinct genera in Nectriaceae based on morphology, biology, and phylogeny is disregarded. A DNA phylogeny based on 19 orthologous protein-coding genes was presented to support a very broad concept of Fusarium at the F1 node in Nectriaceae. Here, we demonstrate that re-analyses of this dataset show that all 19 genes support the F3 node that represents Fusarium sensu stricto as defined by F. sambucinum (sexual morph synonym Gibberella pulicaris). The backbone of the phylogeny is resolved by the concatenated alignment, but only six of the 19 genes fully support the F1 node, representing the broad circumscription of Fusarium. Furthermore, a re-analysis of the concatenated dataset revealed alternate topologies in different phylogenetic algorithms, highlighting the deep divergence and unresolved placement of various Nectriaceae lineages proposed as members of Fusarium. Species of Fusarium s. str. are characterised by Gibberella sexual morphs, asexual morphs with thin- or thick-walled macroconidia that have variously shaped apical and basal cells, and trichothecene mycotoxin production, which separates them from other fusarioid genera. Here we show that the Wollenweber concept of Fusarium presently accounts for 20 segregate genera with clear-cut synapomorphic traits, and that fusarioid macroconidia represent a character that has been gained or lost multiple times throughout Nectriaceae. Thus, the very broad circumscription of Fusarium is blurry and without apparent synapomorphies, and does not include all genera with fusarium-like macroconidia, which are spread throughout Nectriaceae (e.g., Cosmosporella, Macroconia, Microcera). In this study four new genera are introduced, along with 18 new species and 16 new combinations. These names convey information about relationships, morphology, and ecological preference that would otherwise be lost in a broader definition of Fusarium. To assist users to correctly identify fusarioid genera and species, we introduce a new online identification database, Fusarioid-ID, accessible at www.fusarium.org. The database comprises partial sequences from multiple genes commonly used to identify fusarioid taxa (act1, CaM, his3, rpb1, rpb2, tef1, tub2, ITS, and LSU). In this paper, we also present a nomenclator of names that have been introduced in Fusarium up to January 2021 as well as their current status, types, and diagnostic DNA barcode data. In this study, researchers from 46 countries, representing taxonomists, plant pathologists, medical mycologists, quarantine officials, regulatory agencies, and students, strongly support the application and use of a more precisely delimited Fusarium (= Gibberella) concept to accommodate taxa from the robust monophyletic node F3 on the basis of a well-defined and unique combination of morphological and biochemical features. This F3 node includes, among others, species of the F. fujikuroi, F. incarnatum-equiseti, F. oxysporum, and F. sambucinum species complexes, but not species of Bisifusarium [F. dimerum species complex (SC)], Cyanonectria (F. buxicola SC), Geejayessia (F. staphyleae SC), Neocosmospora (F. solani SC) or Rectifusarium (F. ventricosum SC). The present study represents the first step to generating a new online monograph of Fusarium and allied fusarioid genera (www.fusarium.org)

Global dynamics and stabilization of rigid body attitude systems.

Attitude control is fundamental to the design and operation of many large engineering systems that consist in whole or in part of rotational components, with system performance defined in terms of global attitude control objectives. The 3D pendulum is a rigid body, freely rotating about a pivot point that is not the center-of-mass. It is acted upon by gravitational and control moments. New results are obtained for the problem of feedback stabilization of a 3D pendulum; these results exemplify attitude stabilization for a 3-DOF rigid body with potential forces. New results are first obtained for the global dynamics of the 3D pendulum. We identify integrals of its motion, and it is shown that the 3D pendulum has two disjoint equilibrium manifolds, namely the hanging equilibrium manifold and the inverted equilibrium manifold. New nonlinear controllers are shown to provide almost global stabilization of these equilibrium manifolds or almost global stabilization of any desired equilibrium in these manifolds. We identify a performance constraint, namely that there are closed-loop trajectories that can take arbitrarily long to converge to the equilibrium. We then study the problem of stabilization under input saturation effects. We show that as long as the saturation limit is greater than a certain lower bound, the inverted equilibrium manifold or any desired equilibrium in these manifolds, can be almost globally asymptotically stabilized. A new non-smooth controller is proposed that stabilizes the inverted equilibrium manifold such that the domain of attraction is almost global and is geometrically simple, and the closed-loop does not exhibit a performance constraint. We then present experimental results on stabilization of the inverted equilibrium manifold illustrating the closed-loop performance. Next, new stabilization results for an axially symmetric 3D pendulum are presented that generalize stabilization results in the literature for the planar pendulum, the spherical pendulum and the spinning top. Finally, we show how results for the 3D pendulum provide a guide to obtaining almost globally stabilizing controllers for an orbiting spacecraft with gravity-gradient effects using low authority controllers such as pulsed plasma thrusters. All dynamics and stabilization results presented in this dissertation are based on new and novel problem formulations for attitude systems with a potential. They treat global issues in a geometric framework, and they provide substantial additions to the prior literature on stabilization of attitude systems.Ph.D.Aerospace engineeringApplied SciencesMechanical engineeringMechanicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/126641/2/3276110.pd