Attitude stabilization of a rigid body under the action of a vanishing control torque

Research outputpeer-review

Abstract

The problem of attitude stabilization of a rigid body with the use of restoring and dissipative torques is studied. The possibility of implementing a control system in which the restoring torque tends to zero as time increases, and the only remaining control torque is a linear time-invariant dissipative one, is investigated. Both cases of linear and essentially nonlinear restoring torques are considered. With the aid of the Lyapunov direct method and the comparison method, conditions are derived under which we can guarantee stability or asymptotic stability of an equilibrium position of the body despite the vanishing of the restoring torque. A numerical simulation is provided to demonstrate the effectiveness of analytical results.

Original languageEnglish
Pages (from-to)285-293
Number of pages9
JournalNonlinear Dynamics
Volume93
Issue number2
DOIs
Publication statusPublished - 2018

Fingerprint

Torque control
Rigid Body
Torque
Stabilization
Lyapunov Direct Method
Asymptotic stability
Comparison Method
Asymptotic Stability
Linear Time
Control systems
Control System
Tend
Computer simulation
Numerical Simulation
Invariant
Zero
Demonstrate

Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

@article{a4503bae9be14230b168022b493783a1,
title = "Attitude stabilization of a rigid body under the action of a vanishing control torque",
abstract = "The problem of attitude stabilization of a rigid body with the use of restoring and dissipative torques is studied. The possibility of implementing a control system in which the restoring torque tends to zero as time increases, and the only remaining control torque is a linear time-invariant dissipative one, is investigated. Both cases of linear and essentially nonlinear restoring torques are considered. With the aid of the Lyapunov direct method and the comparison method, conditions are derived under which we can guarantee stability or asymptotic stability of an equilibrium position of the body despite the vanishing of the restoring torque. A numerical simulation is provided to demonstrate the effectiveness of analytical results.",
keywords = "Asymptotic stability, Attitude stabilization, Decomposition, Lyapunov function, Rigid body, Time-varying control",
author = "Aleksandrov, {A. Y.} and Tikhonov, {A. A.}",
year = "2018",
doi = "10.1007/s11071-018-4191-4",
language = "English",
volume = "93",
pages = "285--293",
journal = "Nonlinear Dynamics",
issn = "0924-090X",
publisher = "Springer",
number = "2",

}

TY - JOUR

T1 - Attitude stabilization of a rigid body under the action of a vanishing control torque

AU - Aleksandrov, A. Y.

AU - Tikhonov, A. A.

PY - 2018

Y1 - 2018

N2 - The problem of attitude stabilization of a rigid body with the use of restoring and dissipative torques is studied. The possibility of implementing a control system in which the restoring torque tends to zero as time increases, and the only remaining control torque is a linear time-invariant dissipative one, is investigated. Both cases of linear and essentially nonlinear restoring torques are considered. With the aid of the Lyapunov direct method and the comparison method, conditions are derived under which we can guarantee stability or asymptotic stability of an equilibrium position of the body despite the vanishing of the restoring torque. A numerical simulation is provided to demonstrate the effectiveness of analytical results.

AB - The problem of attitude stabilization of a rigid body with the use of restoring and dissipative torques is studied. The possibility of implementing a control system in which the restoring torque tends to zero as time increases, and the only remaining control torque is a linear time-invariant dissipative one, is investigated. Both cases of linear and essentially nonlinear restoring torques are considered. With the aid of the Lyapunov direct method and the comparison method, conditions are derived under which we can guarantee stability or asymptotic stability of an equilibrium position of the body despite the vanishing of the restoring torque. A numerical simulation is provided to demonstrate the effectiveness of analytical results.

KW - Asymptotic stability

KW - Attitude stabilization

KW - Decomposition

KW - Lyapunov function

KW - Rigid body

KW - Time-varying control

UR - http://www.scopus.com/inward/record.url?scp=85043390419&partnerID=8YFLogxK

U2 - 10.1007/s11071-018-4191-4

DO - 10.1007/s11071-018-4191-4

M3 - Article

VL - 93

SP - 285

EP - 293

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 2

ER -