Nonlinear Control with Distributed Delay for the Angular Stabilization of a Rigid Body

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Nonlinear Control with Distributed Delay for the Angular Stabilization of a Rigid Body. / Aleksandrov, A. Yu. ; Tikhonov, A. A. .

In: Vestnik St. Petersburg University: Mathematics, Vol. 55, No. 4, 2022, p. 426-433.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{ffa3e24557f64257ab04506c0e988b54,

title = "Nonlinear Control with Distributed Delay for the Angular Stabilization of a Rigid Body",

abstract = "The problem of the angular stabilization of a rigid body with an arbitrary triaxial ellipsoid of inertia is solved. The control strategy is based on a kind of a proportional integral derivative (PID) controller, where the conventional integral element is replaced with a more flexible control option, which assumes the presence of a distributed delay (integral term) in the control torque. In addition, a nonlinear uniform restoring torque is used for the first time instead of the usual linear restoring torque. Analytical substantiation of the asymptotic stability of the program motion involves a special construction of the Lyapunov–Krasovskii functional. A theorem is proved that provides sufficient conditions for the asymptotic stability of the program mode of angular motion of the body in the form of constructive inequalities with respect to the control parameters. The effectiveness of the constructed control is demonstrated, which provides both the high speed and smoothness of transient processes.",

keywords = "rigid body, stabilization, attitude motion, asymptotic stability, Lyapunov–Krasovskii functionals",

author = "Aleksandrov, {A. Yu.} and Tikhonov, {A. A.}",

note = "Aleksandrov, A.Y., Tikhonov, A.A. Nonlinear Control with Distributed Delay for the Angular Stabilization of a Rigid Body. Vestnik St.Petersb. Univ.Math. 55, 426–433 (2022). https://doi.org/10.1134/S1063454122040021",

year = "2022",

doi = "10.1134/S1063454122040021",

language = "English",

volume = "55",

pages = "426--433",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "4",

}

RIS

TY - JOUR

T1 - Nonlinear Control with Distributed Delay for the Angular Stabilization of a Rigid Body

AU - Aleksandrov, A. Yu.

AU - Tikhonov, A. A.

N1 - Aleksandrov, A.Y., Tikhonov, A.A. Nonlinear Control with Distributed Delay for the Angular Stabilization of a Rigid Body. Vestnik St.Petersb. Univ.Math. 55, 426–433 (2022). https://doi.org/10.1134/S1063454122040021

PY - 2022

Y1 - 2022

N2 - The problem of the angular stabilization of a rigid body with an arbitrary triaxial ellipsoid of inertia is solved. The control strategy is based on a kind of a proportional integral derivative (PID) controller, where the conventional integral element is replaced with a more flexible control option, which assumes the presence of a distributed delay (integral term) in the control torque. In addition, a nonlinear uniform restoring torque is used for the first time instead of the usual linear restoring torque. Analytical substantiation of the asymptotic stability of the program motion involves a special construction of the Lyapunov–Krasovskii functional. A theorem is proved that provides sufficient conditions for the asymptotic stability of the program mode of angular motion of the body in the form of constructive inequalities with respect to the control parameters. The effectiveness of the constructed control is demonstrated, which provides both the high speed and smoothness of transient processes.

AB - The problem of the angular stabilization of a rigid body with an arbitrary triaxial ellipsoid of inertia is solved. The control strategy is based on a kind of a proportional integral derivative (PID) controller, where the conventional integral element is replaced with a more flexible control option, which assumes the presence of a distributed delay (integral term) in the control torque. In addition, a nonlinear uniform restoring torque is used for the first time instead of the usual linear restoring torque. Analytical substantiation of the asymptotic stability of the program motion involves a special construction of the Lyapunov–Krasovskii functional. A theorem is proved that provides sufficient conditions for the asymptotic stability of the program mode of angular motion of the body in the form of constructive inequalities with respect to the control parameters. The effectiveness of the constructed control is demonstrated, which provides both the high speed and smoothness of transient processes.

KW - rigid body

KW - stabilization

KW - attitude motion

KW - asymptotic stability

KW - Lyapunov–Krasovskii functionals

UR - https://link.springer.com/article/10.1134/S1063454122040021

U2 - 10.1134/S1063454122040021

DO - 10.1134/S1063454122040021

M3 - Article

VL - 55

SP - 426

EP - 433

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -

ID: 102616050