Control and dynamics of a SDOF system with piecewise linear stiffness and combined external excitations

D. Yurchenko; R. Iwankiewicz; P. Alevras

doi:10.1016/j.probengmech.2013.09.007

Control and dynamics of a SDOF system with piecewise linear stiffness and combined external excitations

D. Yurchenko, R. Iwankiewicz, P. Alevras^*

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

The paper considers a problem of stochastic control and dynamics of a single-degree-of-freedom system with piecewise linear stiffness subjected to combined periodic and white noise external excitations. To minimize the system response energy a bounded in magnitude control force is applied to the systems. The stochastic optimal control problem is handled through the dynamic programming approach. Based on the solution to the Hamilton-Jacobi-Bellman equation it is proposed to use the dry friction control law in the non-resonant case. In the resonant case the stochastic averaging procedure has been used to derive stochastic differential equations for system response amplitude and phase. The joint PDF of response amplitude and phase is derived analytically and numerically using the Path Integration approach. (C) 2013 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	118-124
Number of pages	7
Journal	Probabilistic Engineering Mechanics
Volume	35
DOIs	https://doi.org/10.1016/j.probengmech.2013.09.007
Publication status	Published - Jan 2014

Keywords

Stochastic optimal control
Hamilton-Jacobi-Bellman equation
Fokker-Plank-Kolmogorov equation
Path integration method
Stochastic averaging
Piecewise linear
STRONGLY NONLINEAR OSCILLATORS
WHITE-NOISE EXCITATIONS
OPTIMAL BOUNDED CONTROL

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10.1016/j.probengmech.2013.09.007

Cite this

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title = "Control and dynamics of a SDOF system with piecewise linear stiffness and combined external excitations",

abstract = "The paper considers a problem of stochastic control and dynamics of a single-degree-of-freedom system with piecewise linear stiffness subjected to combined periodic and white noise external excitations. To minimize the system response energy a bounded in magnitude control force is applied to the systems. The stochastic optimal control problem is handled through the dynamic programming approach. Based on the solution to the Hamilton-Jacobi-Bellman equation it is proposed to use the dry friction control law in the non-resonant case. In the resonant case the stochastic averaging procedure has been used to derive stochastic differential equations for system response amplitude and phase. The joint PDF of response amplitude and phase is derived analytically and numerically using the Path Integration approach. (C) 2013 Elsevier Ltd. All rights reserved.",

keywords = "Stochastic optimal control, Hamilton-Jacobi-Bellman equation, Fokker-Plank-Kolmogorov equation, Path integration method, Stochastic averaging, Piecewise linear, STRONGLY NONLINEAR OSCILLATORS, WHITE-NOISE EXCITATIONS, OPTIMAL BOUNDED CONTROL",

author = "D. Yurchenko and R. Iwankiewicz and P. Alevras",

year = "2014",

month = jan,

doi = "10.1016/j.probengmech.2013.09.007",

language = "English",

volume = "35",

pages = "118--124",

journal = "Probabilistic Engineering Mechanics",

issn = "0266-8920",

publisher = "Elsevier",

}

TY - JOUR

T1 - Control and dynamics of a SDOF system with piecewise linear stiffness and combined external excitations

AU - Yurchenko, D.

AU - Iwankiewicz, R.

AU - Alevras, P.

PY - 2014/1

Y1 - 2014/1

N2 - The paper considers a problem of stochastic control and dynamics of a single-degree-of-freedom system with piecewise linear stiffness subjected to combined periodic and white noise external excitations. To minimize the system response energy a bounded in magnitude control force is applied to the systems. The stochastic optimal control problem is handled through the dynamic programming approach. Based on the solution to the Hamilton-Jacobi-Bellman equation it is proposed to use the dry friction control law in the non-resonant case. In the resonant case the stochastic averaging procedure has been used to derive stochastic differential equations for system response amplitude and phase. The joint PDF of response amplitude and phase is derived analytically and numerically using the Path Integration approach. (C) 2013 Elsevier Ltd. All rights reserved.

AB - The paper considers a problem of stochastic control and dynamics of a single-degree-of-freedom system with piecewise linear stiffness subjected to combined periodic and white noise external excitations. To minimize the system response energy a bounded in magnitude control force is applied to the systems. The stochastic optimal control problem is handled through the dynamic programming approach. Based on the solution to the Hamilton-Jacobi-Bellman equation it is proposed to use the dry friction control law in the non-resonant case. In the resonant case the stochastic averaging procedure has been used to derive stochastic differential equations for system response amplitude and phase. The joint PDF of response amplitude and phase is derived analytically and numerically using the Path Integration approach. (C) 2013 Elsevier Ltd. All rights reserved.

KW - Stochastic optimal control

KW - Hamilton-Jacobi-Bellman equation

KW - Fokker-Plank-Kolmogorov equation

KW - Path integration method

KW - Stochastic averaging

KW - Piecewise linear

KW - STRONGLY NONLINEAR OSCILLATORS

KW - WHITE-NOISE EXCITATIONS

KW - OPTIMAL BOUNDED CONTROL

U2 - 10.1016/j.probengmech.2013.09.007

DO - 10.1016/j.probengmech.2013.09.007

M3 - Article

SN - 0266-8920

VL - 35

SP - 118

EP - 124

JO - Probabilistic Engineering Mechanics

JF - Probabilistic Engineering Mechanics

ER -

Control and dynamics of a SDOF system with piecewise linear stiffness and combined external excitations

Abstract

Keywords

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