Sliding mode control of the Orr-Sommerfeld equation cascaded by both the Squire equation and ode in the presence of boundary disturbances

Jian Jun Gu; Jun Min Wang

doi:10.1137/15M1046952

Sliding mode control of the Orr-Sommerfeld equation cascaded by both the Squire equation and ode in the presence of boundary disturbances

Jian Jun Gu, Jun Min Wang^*

^*Corresponding author for this work

School of Mathematics and Statistics

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

26 Citations (Scopus)

Abstract

The sliding mode control (SMC) approach is proposed in this paper for the Orr- Sommerfeld equation cascaded by both the Squire equation and ODE, in which Orr-Sommerfeld and Squire equations are subject to boundary controls matched disturbances, respectively. A modified backstepping transformation with matrix kernel is integrated with SMC to reject the bounded disturbances. The well-posedness of the solution for the closed-loop system is obtained based on the Riesz basis method and the finite time "reaching condition" is verified. Finally, the numerical simulations are presented to illustrate the effectiveness of the control approach.

Original language	English
Pages (from-to)	837-867
Number of pages	31
Journal	SIAM Journal on Control and Optimization
Volume	56
Issue number	2
DOIs	https://doi.org/10.1137/15M1046952
Publication status	Published - 2018

Keywords

Disturbance rejection
Orr-Sommerfeld equation
Sliding mode control
Squire equation

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10.1137/15M1046952

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title = "Sliding mode control of the Orr-Sommerfeld equation cascaded by both the Squire equation and ode in the presence of boundary disturbances",

abstract = "The sliding mode control (SMC) approach is proposed in this paper for the Orr- Sommerfeld equation cascaded by both the Squire equation and ODE, in which Orr-Sommerfeld and Squire equations are subject to boundary controls matched disturbances, respectively. A modified backstepping transformation with matrix kernel is integrated with SMC to reject the bounded disturbances. The well-posedness of the solution for the closed-loop system is obtained based on the Riesz basis method and the finite time {"}reaching condition{"} is verified. Finally, the numerical simulations are presented to illustrate the effectiveness of the control approach.",

keywords = "Disturbance rejection, Orr-Sommerfeld equation, Sliding mode control, Squire equation",

author = "Gu, {Jian Jun} and Wang, {Jun Min}",

note = "Publisher Copyright: {\textcopyright} 2018 Society for Industrial and Applied Mathematics.",

year = "2018",

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language = "English",

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T1 - Sliding mode control of the Orr-Sommerfeld equation cascaded by both the Squire equation and ode in the presence of boundary disturbances

AU - Gu, Jian Jun

AU - Wang, Jun Min

PY - 2018

Y1 - 2018

N2 - The sliding mode control (SMC) approach is proposed in this paper for the Orr- Sommerfeld equation cascaded by both the Squire equation and ODE, in which Orr-Sommerfeld and Squire equations are subject to boundary controls matched disturbances, respectively. A modified backstepping transformation with matrix kernel is integrated with SMC to reject the bounded disturbances. The well-posedness of the solution for the closed-loop system is obtained based on the Riesz basis method and the finite time "reaching condition" is verified. Finally, the numerical simulations are presented to illustrate the effectiveness of the control approach.

AB - The sliding mode control (SMC) approach is proposed in this paper for the Orr- Sommerfeld equation cascaded by both the Squire equation and ODE, in which Orr-Sommerfeld and Squire equations are subject to boundary controls matched disturbances, respectively. A modified backstepping transformation with matrix kernel is integrated with SMC to reject the bounded disturbances. The well-posedness of the solution for the closed-loop system is obtained based on the Riesz basis method and the finite time "reaching condition" is verified. Finally, the numerical simulations are presented to illustrate the effectiveness of the control approach.

KW - Disturbance rejection

KW - Orr-Sommerfeld equation

KW - Sliding mode control

KW - Squire equation

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JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 2

ER -

Sliding mode control of the Orr-Sommerfeld equation cascaded by both the Squire equation and ode in the presence of boundary disturbances

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Keywords

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