Backstepping observer-based output feedback control for a class of coupled parabolic PDEs with the same diffusion
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- 英文论文题名：Backstepping observer-based output feedback control for a class of coupled parabolic PDEs with the same diffusion
- 论文作者：Bai-Nan Liu ; Driss Boutat ; Da-Yan Liu
- 英文论文作者：Bai-Nan Liu ; Driss Boutat ; Da-Yan Liu ; INSA Centre Val de Loire ; Université d'Orléans
- 年：2017
- 作者机构：INSA Centre Val de Loire,Université d'Orléans;
- 英文论文关键词：Coupled parabolic partial differential equations ; Observer-based output feedback control ; Backstepping controller ; Backstepping observer
- 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（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：O231
- 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：253k
- 原文格式：D
- 会议级别：全国
摘要
The objective of this paper is to extend the relaxed conditions on the existence of the backstepping controllers and observers obtained in a recent literature to the case of parabolic Partial Differential Equations(PDEs) with the same diffusion.Moreover, an observer-based output feedback controller is designed for the considered systems with the new conditions. Then,the corresponding exponential stability analysis is provided. Finally, the efficiency of the proposed method is shown by taking a simplified model of Chemical Tubular Reactor.
The objective of this paper is to extend the relaxed conditions on the existence of the backstepping controllers and observers obtained in a recent literature to the case of parabolic Partial Differential Equations(PDEs) with the same diffusion.Moreover, an observer-based output feedback controller is designed for the considered systems with the new conditions. Then,the corresponding exponential stability analysis is provided. Finally, the efficiency of the proposed method is shown by taking a simplified model of Chemical Tubular Reactor.
The objective of this paper is to extend the relaxed conditions on the existence of the backstepping controllers and observers obtained in a recent literature to the case of parabolic Partial Differential Equations(PDEs) with the same diffusion.Moreover, an observer-based output feedback controller is designed for the considered systems with the new conditions. Then,the corresponding exponential stability analysis is provided. Finally, the efficiency of the proposed method is shown by taking a simplified model of Chemical Tubular Reactor.
引文
[1]K.Kunish,G.Leugering,J.Sprekels and F.Troltzsh,Control of coupled partial differential equations,SpringerBrikhauser,vol.155,no.3,2007.
[2]A.Hasan,O.M.Aamo and M.Krstic,Boundary observer design for hyperbolic PDE-ODE cascade systems,Automatica,vol.68,no.12,pp.75-86,2016.
[3]Y.Lou,Q.Nie and F.Y.M.Wang,Nonlinear eigenvalue problems in the stability analysis of morphogen gradients,Studies in Applied Mathematics,vol.113,no.2,pp.183-215,2004.
[4]B.N.Liu,D.Boutat and D.Y.Liu,Backstepping observerbased output feedback control for a class of coupled parabolic PDEs with different diffusions,Systems&Control Letters,vol.97,2016.
[5]D.M.Boskovic,M.Krstic,and W.J.Liu,Boundary control of an unstable heat equation via measurement of domainaveraged temperature,IEEE Trans.Automat.Control,vol.46,no.12,pp.2022-2028,2001.
[6]A.Balogh and M.Krstic,Infinite-step backstepping for a heat equation-like PDE with arbitrarily many unstable eigenvalues,in Proceedings of the 2001 American Control Conference,vol.3,IEEE Press,Piscataway,pp.2480-2485,2001.
[7]A.Balogh and M.Krstic,Infinite dimensional backsteppingstyle feedback transformations for a heat equation with an arbitrary level of instability,European J.Control,vol.8,no.2,pp.165-176,2002.
[8]W.J.Liu,Boundary feedback stabilization of an unstable heat equation,SIAM J.Control optim,vol.42,no.3,pp.1033-1043,2003.
[9]A.Smyshlyaev and M.Krstic,Closed-Form Boundary Stated Feedbacks for a class of 1-D partial integro-differential equations,IEEE Transactions on automatic control,vol.49,no.12,pp.2185-2202,2004.
[10]T.Meurer and A.Kugi,Tracking control for boundary controlled parabolic PDEs with varying parameters:Combining backstepping and differential flatness,Automatica,vol.45,no.5,pp.1182-1194,2009.
[11]S.X.Tang and C.K.Xie,Stabilization for a coupled PDE-ODE control system,Journal of the Franklin Institute,vol.348,no.8,pp.2142-2155,2011.
[12]F.D.Meglio,R.Vazquez and M.Krstic,Stabilization of a system of n+1 coupled first-order hyperbolic linear PDEs with a signle boundary input,IEEE Trans.Automat.Control,vol.58,no.12,pp.3097-31111,2013.
[13]R.Vazquez and M.Krstic,A closed-form full-state feedback controller for stabilization of 3D magnetohydrodynamic channel flow,Journal of Dynamic Systems,Measurement and Control,vol.131,no.4,2009.
[14]D.Tsubakino,M.Krstic and Y.Yamashita,Boundary control of a cascade of two parabolic PDEs with different diffusion coefficients,52rd IEEE Conference on Decision and Control,Florence,Italy,2013.
[15]A.Baccoli and A.Pisano,On the boundary control of coupled reaction-diffusion equations having the same diffusivity parameters,53rd IEEE Conference on Decision and Control,Los Angeles,USA,2014.
[16]J.M.Wang,L.L.Su and H.X.Li,Stabilization of an unstable reaction-diffusion PDE cascaded with a heat equation,Systems&Control Letters,vol.76,pp.8-18,2015.
[17]B.B.Ren,J.M.Wang and M.Krstic,Stabilization of an ODE-Schrodinger cascade,Systems&Control Letters,vol.62,no.6,pp.503-510,2013.
[18]A.Baccoli,A.Pisano and Y.Orlov,Boundary control of coupled reaction-diffusion processes with constant parameters,Automatica,vol.54,pp.80-90,2015.
[19]A.Smyshlyaev and M.Krstic,Backstepping observers for a class of parabolic PDEs,Systems&Control Letters,vol.54,no.7,pp.613-625,2005.
[20]D.Tsubakino and S.Hara,Backstepping observer design for parabolic PDEs with measurements of wighted spatial averages,Automatica,vol.53,pp.179-187,2015.
[21]L.Jadachowski,T.Meurer and A.Kugi,Backstepping observers for linear PDEs on higher-dimensional spatial domains,Automatica,vol.51,no.1,pp.179-187,2015.
[22]S.X.Tang and C.K.Xie,State and output feedback boundary control for a coupled PDE-ODE system,System&Control Letters,vol.60,no.8,pp.540-545,2011.
[23]R.Vazquez and M.Krstic,Boundary observer for outputfeedback stabilization of thermal-fluid convection loop,IEEETrans.on Control Systems Technology,vol.18,no.4,pp.789-797,2010.
[24]A.Baccoli and A.Pisano,Anti-collocated backstepping observer design for a class of coupled reaction-diffusion PDEs,Journal of Control Science and Engineering,vol.2015,pp.1-10,2015.
[25]M.Krstic and A.Smyshlyaev,Boundary control of PDEs:ACourse on Backstepping Designs,Singapore:SIAM,2008.
[26]Y.Orlov and D.Dochain,Discontinuous feedback stabilization of minimum-phase semilinear infinite-dimensional systems with application to chemical tubular reactor,IEEETransactions on Automatic Control,vol.47,no.8,pp.1293-1304,2002.
[2]A.Hasan,O.M.Aamo and M.Krstic,Boundary observer design for hyperbolic PDE-ODE cascade systems,Automatica,vol.68,no.12,pp.75-86,2016.
[3]Y.Lou,Q.Nie and F.Y.M.Wang,Nonlinear eigenvalue problems in the stability analysis of morphogen gradients,Studies in Applied Mathematics,vol.113,no.2,pp.183-215,2004.
[4]B.N.Liu,D.Boutat and D.Y.Liu,Backstepping observerbased output feedback control for a class of coupled parabolic PDEs with different diffusions,Systems&Control Letters,vol.97,2016.
[5]D.M.Boskovic,M.Krstic,and W.J.Liu,Boundary control of an unstable heat equation via measurement of domainaveraged temperature,IEEE Trans.Automat.Control,vol.46,no.12,pp.2022-2028,2001.
[6]A.Balogh and M.Krstic,Infinite-step backstepping for a heat equation-like PDE with arbitrarily many unstable eigenvalues,in Proceedings of the 2001 American Control Conference,vol.3,IEEE Press,Piscataway,pp.2480-2485,2001.
[7]A.Balogh and M.Krstic,Infinite dimensional backsteppingstyle feedback transformations for a heat equation with an arbitrary level of instability,European J.Control,vol.8,no.2,pp.165-176,2002.
[8]W.J.Liu,Boundary feedback stabilization of an unstable heat equation,SIAM J.Control optim,vol.42,no.3,pp.1033-1043,2003.
[9]A.Smyshlyaev and M.Krstic,Closed-Form Boundary Stated Feedbacks for a class of 1-D partial integro-differential equations,IEEE Transactions on automatic control,vol.49,no.12,pp.2185-2202,2004.
[10]T.Meurer and A.Kugi,Tracking control for boundary controlled parabolic PDEs with varying parameters:Combining backstepping and differential flatness,Automatica,vol.45,no.5,pp.1182-1194,2009.
[11]S.X.Tang and C.K.Xie,Stabilization for a coupled PDE-ODE control system,Journal of the Franklin Institute,vol.348,no.8,pp.2142-2155,2011.
[12]F.D.Meglio,R.Vazquez and M.Krstic,Stabilization of a system of n+1 coupled first-order hyperbolic linear PDEs with a signle boundary input,IEEE Trans.Automat.Control,vol.58,no.12,pp.3097-31111,2013.
[13]R.Vazquez and M.Krstic,A closed-form full-state feedback controller for stabilization of 3D magnetohydrodynamic channel flow,Journal of Dynamic Systems,Measurement and Control,vol.131,no.4,2009.
[14]D.Tsubakino,M.Krstic and Y.Yamashita,Boundary control of a cascade of two parabolic PDEs with different diffusion coefficients,52rd IEEE Conference on Decision and Control,Florence,Italy,2013.
[15]A.Baccoli and A.Pisano,On the boundary control of coupled reaction-diffusion equations having the same diffusivity parameters,53rd IEEE Conference on Decision and Control,Los Angeles,USA,2014.
[16]J.M.Wang,L.L.Su and H.X.Li,Stabilization of an unstable reaction-diffusion PDE cascaded with a heat equation,Systems&Control Letters,vol.76,pp.8-18,2015.
[17]B.B.Ren,J.M.Wang and M.Krstic,Stabilization of an ODE-Schrodinger cascade,Systems&Control Letters,vol.62,no.6,pp.503-510,2013.
[18]A.Baccoli,A.Pisano and Y.Orlov,Boundary control of coupled reaction-diffusion processes with constant parameters,Automatica,vol.54,pp.80-90,2015.
[19]A.Smyshlyaev and M.Krstic,Backstepping observers for a class of parabolic PDEs,Systems&Control Letters,vol.54,no.7,pp.613-625,2005.
[20]D.Tsubakino and S.Hara,Backstepping observer design for parabolic PDEs with measurements of wighted spatial averages,Automatica,vol.53,pp.179-187,2015.
[21]L.Jadachowski,T.Meurer and A.Kugi,Backstepping observers for linear PDEs on higher-dimensional spatial domains,Automatica,vol.51,no.1,pp.179-187,2015.
[22]S.X.Tang and C.K.Xie,State and output feedback boundary control for a coupled PDE-ODE system,System&Control Letters,vol.60,no.8,pp.540-545,2011.
[23]R.Vazquez and M.Krstic,Boundary observer for outputfeedback stabilization of thermal-fluid convection loop,IEEETrans.on Control Systems Technology,vol.18,no.4,pp.789-797,2010.
[24]A.Baccoli and A.Pisano,Anti-collocated backstepping observer design for a class of coupled reaction-diffusion PDEs,Journal of Control Science and Engineering,vol.2015,pp.1-10,2015.
[25]M.Krstic and A.Smyshlyaev,Boundary control of PDEs:ACourse on Backstepping Designs,Singapore:SIAM,2008.
[26]Y.Orlov and D.Dochain,Discontinuous feedback stabilization of minimum-phase semilinear infinite-dimensional systems with application to chemical tubular reactor,IEEETransactions on Automatic Control,vol.47,no.8,pp.1293-1304,2002.