Optimal Control for Realizing Target Flow Velocity in 1D MHD Flow
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- 英文论文题名：Optimal Control for Realizing Target Flow Velocity in 1D MHD Flow
- 论文作者：Zhigang Ren ; Xiangguo Liu ; Chao Xu ; Tehuan Chen ; Zongze Wu
- 英文论文作者：Zhigang Ren ; Xiangguo Liu ; Chao Xu ; Tehuan Chen ; Zongze Wu ; School of Automation ; Guangdong University of Technology ; State Key Laboratory of Industrial Control Technology and Institute of Cyber-Systems & Control ; Zhejiang University ; Faculty of Mechanical Engineering and Mechanics ; Ningbo University
- 年：2017
- 作者机构：School of Automation,Guangdong University of Technology;State Key Laboratory of Industrial Control Technology and Institute of Cyber-Systems & Control,Zhejiang University;Faculty of Mechanical Engineering and Mechanics,Ningbo University;
- 英文论文关键词：Magnetohydrodynamic ; Flow Control ; Galerkin Method ; Control Parameterization ; Time-scaling Transformation
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O232
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：250k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, we consider an optimal control problem arising in a one-dimensional(1D) Magnetohydrodynam(MHD) flow, which can be modelled by a coupled partial differential equations(PDEs) where the external control input(externinduction of magnetic field) takes the multiplicative effect exerted on both state variables(momentum and magnetic componentsThe aim is to derive the flow velocity to within close proximity of a desired target flow velocity at the pre-indicated termintime. We first use the Galerkin method to obtain a low dimensional dynamical ordinary differential equation(ODE) model baseon the original coupled PDEs. Then, we combine the control parameterization method with the time-scaling transformatiotechnique to obtain an approximate optimal parameter selection problem, which can be solved using gradient-based optimizatiotechniques such as sequential quadratic programming(SQP). The exact gradients of the cost functional with respect to thdecision parameters are computed based on the analytical equations. Finally, we conclude the paper with simulation results fan example of the 1D MHD flow.
In this paper, we consider an optimal control problem arising in a one-dimensional(1D) Magnetohydrodynam(MHD) flow, which can be modelled by a coupled partial differential equations(PDEs) where the external control input(externinduction of magnetic field) takes the multiplicative effect exerted on both state variables(momentum and magnetic componentsThe aim is to derive the flow velocity to within close proximity of a desired target flow velocity at the pre-indicated termintime. We first use the Galerkin method to obtain a low dimensional dynamical ordinary differential equation(ODE) model baseon the original coupled PDEs. Then, we combine the control parameterization method with the time-scaling transformatiotechnique to obtain an approximate optimal parameter selection problem, which can be solved using gradient-based optimizatiotechniques such as sequential quadratic programming(SQP). The exact gradients of the cost functional with respect to thdecision parameters are computed based on the analytical equations. Finally, we conclude the paper with simulation results fan example of the 1D MHD flow.
In this paper, we consider an optimal control problem arising in a one-dimensional(1D) Magnetohydrodynam(MHD) flow, which can be modelled by a coupled partial differential equations(PDEs) where the external control input(externinduction of magnetic field) takes the multiplicative effect exerted on both state variables(momentum and magnetic componentsThe aim is to derive the flow velocity to within close proximity of a desired target flow velocity at the pre-indicated termintime. We first use the Galerkin method to obtain a low dimensional dynamical ordinary differential equation(ODE) model baseon the original coupled PDEs. Then, we combine the control parameterization method with the time-scaling transformatiotechnique to obtain an approximate optimal parameter selection problem, which can be solved using gradient-based optimizatiotechniques such as sequential quadratic programming(SQP). The exact gradients of the cost functional with respect to thdecision parameters are computed based on the analytical equations. Finally, we conclude the paper with simulation results fan example of the 1D MHD flow.
引文
[1]E.Schuster,L.X.Luo,and M.Krsti,MHD channel flow control in 2D:Mixing enhancement by boundary feedback,Automatica,44(10):2498-2507,2008.
[2]S.Qian and H.H.Bau,Magneto-hydrodynamics based microfluidics,Mechanics Research Communications,36(1):10-21,2009.
[3]C.Xu,E.Schuster,R.Vazquez,and M.Krstic,Stabilization of linearized 2D magnetohydrodynamic channel flow by backstepping boundary control,Systems&Control Letters,57(10):805-812,2008.
[4]R.Vazquez,E.Schuster,and M.Krstic,A closed-form fullstate feedback controller for stabilization of 3D magnetohydrodynamic channel flow,Journal of Dynamic Systems,Measurement,and Control,131(4):041001,2009.
[5]J.Baker and P.D.Christofides,Drag reduction in transitional linearized channel flow using distributed control,International Journal of Control,75(15):1213-1218,2002.
[6]K.Debbagh,P.Cathalifaud,and C.Airiau,Optimal and robust control of small disturbances in a channel flow with a normal magnetic field,Physics of Fluids,19(1):014103,2007.
[7]P.Moresco and T.Alboussiere,Experimental study of the instability of the hartmann layer,Journal of Fluid Mechanics,504:167-181,2004.
[8]J.Pang and K.-S.Choi,Turbulent drag reduction by lorentz force oscillation,Physics of Fluids,16(5):L35-L38,2004.
[9]K.L.Teo,C.J.Goh,and K.H.Wong,A Unified Computational Approach to Optimal Control Problems.Longman Scientific and Technical,1991.
[10]L.D.Landau,J.Bell,M.Kearsley,L.Pitaevskii,E.Lifshitz,and J.Sykes,Electrodynamics of Continuous Media.Elsevier,2013.
[11]V.Thomée,Galerkin Finite Element Methods for Parabolic Problems.Springer,2006.
[12]N.U.Ahmed and K.L.Teo,Optimal Control of Distributed Parameter Systems.Elsevier Science Inc,1984.
[13]K.L.Teo and Z.S.Wu,Computational Methods for Optimizing Distributed Systems.Academic Press,1984.
[14]Q.Lin,Y.H.Wu,R.Loxton,and S.Y.Lai,Linear B-spline finite element method for the improved Boussinesq equation,Journal of Computational and Applied Mathematics,224(2):658-667,2009.
[15]Q.Lin,R.Loxton,and K.L.Teo,The control parameterization method for nonlinear optimal control:A survey,Journal of Industrial and Management Optimization,10(1):275-309,2013.
[16]R.Loxton,Q.Lin,and K.L.Teo,Switching time optimization for nonlinear switched systems:Direct optimization and the time-scaling transformation,Pacific Journal of Optimization,10(3):537-560,2014.
[17]Z.Ren,C.Xu,Q.Lin,R.Loxton,and K.L.Teo,Dynamic optimization of open-loop input signals for ramp-up current profiles in tokamak plasmas,Communications in Nonlinear Science and Numerical Simulation,32:31-48,2016.
[2]S.Qian and H.H.Bau,Magneto-hydrodynamics based microfluidics,Mechanics Research Communications,36(1):10-21,2009.
[3]C.Xu,E.Schuster,R.Vazquez,and M.Krstic,Stabilization of linearized 2D magnetohydrodynamic channel flow by backstepping boundary control,Systems&Control Letters,57(10):805-812,2008.
[4]R.Vazquez,E.Schuster,and M.Krstic,A closed-form fullstate feedback controller for stabilization of 3D magnetohydrodynamic channel flow,Journal of Dynamic Systems,Measurement,and Control,131(4):041001,2009.
[5]J.Baker and P.D.Christofides,Drag reduction in transitional linearized channel flow using distributed control,International Journal of Control,75(15):1213-1218,2002.
[6]K.Debbagh,P.Cathalifaud,and C.Airiau,Optimal and robust control of small disturbances in a channel flow with a normal magnetic field,Physics of Fluids,19(1):014103,2007.
[7]P.Moresco and T.Alboussiere,Experimental study of the instability of the hartmann layer,Journal of Fluid Mechanics,504:167-181,2004.
[8]J.Pang and K.-S.Choi,Turbulent drag reduction by lorentz force oscillation,Physics of Fluids,16(5):L35-L38,2004.
[9]K.L.Teo,C.J.Goh,and K.H.Wong,A Unified Computational Approach to Optimal Control Problems.Longman Scientific and Technical,1991.
[10]L.D.Landau,J.Bell,M.Kearsley,L.Pitaevskii,E.Lifshitz,and J.Sykes,Electrodynamics of Continuous Media.Elsevier,2013.
[11]V.Thomée,Galerkin Finite Element Methods for Parabolic Problems.Springer,2006.
[12]N.U.Ahmed and K.L.Teo,Optimal Control of Distributed Parameter Systems.Elsevier Science Inc,1984.
[13]K.L.Teo and Z.S.Wu,Computational Methods for Optimizing Distributed Systems.Academic Press,1984.
[14]Q.Lin,Y.H.Wu,R.Loxton,and S.Y.Lai,Linear B-spline finite element method for the improved Boussinesq equation,Journal of Computational and Applied Mathematics,224(2):658-667,2009.
[15]Q.Lin,R.Loxton,and K.L.Teo,The control parameterization method for nonlinear optimal control:A survey,Journal of Industrial and Management Optimization,10(1):275-309,2013.
[16]R.Loxton,Q.Lin,and K.L.Teo,Switching time optimization for nonlinear switched systems:Direct optimization and the time-scaling transformation,Pacific Journal of Optimization,10(3):537-560,2014.
[17]Z.Ren,C.Xu,Q.Lin,R.Loxton,and K.L.Teo,Dynamic optimization of open-loop input signals for ramp-up current profiles in tokamak plasmas,Communications in Nonlinear Science and Numerical Simulation,32:31-48,2016.