Reduced-order model based feedback control of the modified Hasegawa-Wakatani model

I. R. Goumiri; Clarence Worth Rowley; Z. Ma; D. A. Gates; J. A. Krommes; J. B. Parker

doi:10.1063/1.4796190

Reduced-order model based feedback control of the modified Hasegawa-Wakatani model

I. R. Goumiri, Clarence Worth Rowley, Z. Ma, D. A. Gates, J. A. Krommes, J. B. Parker

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Abstract

In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modified Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in flow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then, a model-based feedback controller is designed for the reduced order model using linear quadratic regulators. Finally, a linear quadratic Gaussian controller which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHW equations to stabilize the equilibrium and suppress the transition to drift-wave induced turbulence.

Original language	English (US)
Article number	042501
Journal	Physics of Plasmas
Volume	20
Issue number	4
DOIs	https://doi.org/10.1063/1.4796190
State	Published - Apr 2013

All Science Journal Classification (ASJC) codes

Condensed Matter Physics

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10.1063/1.4796190

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title = "Reduced-order model based feedback control of the modified Hasegawa-Wakatani model",

abstract = "In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modified Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in flow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then, a model-based feedback controller is designed for the reduced order model using linear quadratic regulators. Finally, a linear quadratic Gaussian controller which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHW equations to stabilize the equilibrium and suppress the transition to drift-wave induced turbulence.",

author = "Goumiri, {I. R.} and Rowley, {Clarence Worth} and Z. Ma and Gates, {D. A.} and Krommes, {J. A.} and Parker, {J. B.}",

note = "Funding Information: The authors would like to acknowledge Professor R. B. White and E. Kolemen for helpful discussions. This work was supported by the U.S. Department of Energy Grant under Contract No. DEAC02-76CH03073.",

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language = "English (US)",

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journal = "Physics of Plasmas",

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AU - Goumiri, I. R.

AU - Rowley, Clarence Worth

AU - Ma, Z.

AU - Gates, D. A.

AU - Krommes, J. A.

AU - Parker, J. B.

N1 - Funding Information: The authors would like to acknowledge Professor R. B. White and E. Kolemen for helpful discussions. This work was supported by the U.S. Department of Energy Grant under Contract No. DEAC02-76CH03073.

PY - 2013/4

Y1 - 2013/4

N2 - In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modified Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in flow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then, a model-based feedback controller is designed for the reduced order model using linear quadratic regulators. Finally, a linear quadratic Gaussian controller which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHW equations to stabilize the equilibrium and suppress the transition to drift-wave induced turbulence.

AB - In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modified Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in flow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then, a model-based feedback controller is designed for the reduced order model using linear quadratic regulators. Finally, a linear quadratic Gaussian controller which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHW equations to stabilize the equilibrium and suppress the transition to drift-wave induced turbulence.

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Reduced-order model based feedback control of the modified Hasegawa-Wakatani model

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