A Linear Systems Approach to Flow Control

The objective of this paper is to introduce the essential ingredients of linear systems and control theory to the fluid mechanics community, to discuss the relevance of this theory to important open problems in the optimization, control, and forecasting of practical flow systems of engineering interest, and to outline some of the key ideas that have been put forward to make this connection tractable. Although many significant advances have already been made, many new challenges lie ahead before the full potential of this synthesis of disciplines can be realized.

[1]  Parviz Moin,et al.  Active turbulence control for drag reduction in wall-bounded flows , 1994, Journal of Fluid Mechanics.

[2]  P. Ioannou,et al.  Turbulence suppression by active control , 1996 .

[3]  V. Wertz,et al.  Adaptive Optimal Control: The Thinking Man's G.P.C. , 1991 .

[4]  Frank L. Lewis,et al.  Optimal Control , 1986 .

[5]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[6]  A. Laub.  A schur method for solving algebraic Riccati equations , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[7]  Ronald D. Joslin,et al.  Issues in active flow control: theory, control, simulation, and experiment , 2004 .

[8]  Danny C. Sorensen,et al.  Implicit Application of Polynomial Filters in a k-Step Arnoldi Method , 1992, SIAM J. Matrix Anal. Appl..

[9]  L. Hou,et al.  Boundary velocity control of incompressible flow with an application to viscous drag reduction , 1992 .

[10]  Jason L. Speyer,et al.  Application of reduced-order controller to turbulent flows for drag reduction , 2001 .

[11]  Thomas R. Bewley,et al.  A noncausal framework for model-based feedback control of spatially developing perturbations in boundary-layer flow systems. Part II: numerical simulations using state feedback , 2004, Syst. Control. Lett..

[12]  R. Chris Camphouse,et al.  Feedback Control for a Two-Dimensional Burgers' Equation System Model , 2004 .

[13]  Thomas Bewley,et al.  The decay of stabilizability with Reynolds number in a linear model of spatially developing flows , 2003, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[14]  T. Bewley,et al.  Skin friction and pressure: the “footprints” of turbulence , 2004 .

[15]  J. Corbett,et al.  Updated emissions from ocean shipping , 2003 .

[16]  Dan S. Henningson,et al.  Linear feedback control and estimation of transition in plane channel flow , 2003, Journal of Fluid Mechanics.

[17]  Thomas R. Bewley,et al.  A Fundamental Limit on the Heat Flux in the Control of Incompressible Channel Flow , 2007, IEEE Transactions on Automatic Control.

[18]  Clarence W. Rowley,et al.  Model Reduction for fluids, Using Balanced Proper Orthogonal Decomposition , 2005, Int. J. Bifurc. Chaos.

[19]  Javier Jiménez,et al.  The autonomous cycle of near-wall turbulence , 1999, Journal of Fluid Mechanics.

[20]  Sanjay S. Joshi,et al.  Finite Dimensional Optimal Control of Poiseuille Flow , 1999 .

[21]  P. Moin,et al.  Turbulence statistics in fully developed channel flow at low Reynolds number , 1987, Journal of Fluid Mechanics.

[22]  T. Bewley,et al.  State estimation in wall-bounded flow systems. Part 1. Perturbed laminar flows , 2005, Journal of Fluid Mechanics.

[23]  Junwoo Lim,et al.  A linear process in wall-bounded turbulent shear flows , 2000 .

[24]  Gene F. Franklin,et al.  Digital control of dynamic systems , 1980 .

[25]  Fernando Paganini,et al.  Distributed control of spatially invariant systems , 2002, IEEE Trans. Autom. Control..

[26]  Kathryn M. Butler,et al.  Optimal perturbations and streak spacing in wall‐bounded turbulent shear flow , 1993 .

[27]  B. Moore.  Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

[28]  Ole Morten Aamo,et al.  A ‘win–win’ mechanism for low-drag transients in controlled two-dimensional channel flow and its implications for sustained drag reduction , 2004, Journal of Fluid Mechanics.

[29]  Haecheon Choi,et al.  Suboptimal control of turbulent channel flow for drag reduction , 1998, Journal of Fluid Mechanics.

[30]  John Kim,et al.  Control of turbulent boundary layers , 2003 .

[31]  Roger Temam,et al.  A general framework for robust control in fluid mechanics , 2000 .

[32]  Parviz Moin,et al.  On the relation of near‐wall streamwise vortices to wall skin friction in turbulent boundary layers , 1993 .

[33]  Mohamed Gad-el-Hak.  Flow Control: Contents , 2000 .

[34]  Koji Fukagata,et al.  Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows , 2002 .

[35]  B. Bamieh,et al.  Modeling flow statistics using the linearized Navier-Stokes equations , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[37]  Jason L. Speyer,et al.  Sustained sub-laminar drag in a fully developed channel flow , 2006, Journal of Fluid Mechanics.

[38]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[39]  S. C. Reddy,et al.  Energy growth in viscous channel flows , 1993, Journal of Fluid Mechanics.

[40]  Max Gunzburger,et al.  Perspectives in flow control and optimization , 1987 .

[41]  Fazle Hussain,et al.  Coherent structure generation in near-wall turbulence , 2002, Journal of Fluid Mechanics.

[42]  B. Anderson,et al.  Model reduction for control system design , 1984 .

[43]  Thomas Bewley,et al.  Optimal and robust control and estimation of linear paths to transition , 1998, Journal of Fluid Mechanics.

[44]  J. Lumley,et al.  CONTROL OF TURBULENCE , 1998 .

[45]  Thomas Bewley,et al.  Flow control: new challenges for a new Renaissance , 2001 .

[46]  Dan S. Henningson,et al.  Relaminarization of Reτ=100 turbulence using gain scheduling and linear state-feedback control , 2003 .

[47]  G. Stein,et al.  Multivariable feedback design: Concepts for a classical/modern synthesis , 1981 .

[48]  D. Sorensen,et al.  Approximation of large-scale dynamical systems: an overview , 2004 .

[49]  Thomas Kailath,et al.  Some new algorithms for recursive estimation in constant linear systems , 1973, IEEE Trans. Inf. Theory.

[50]  Satish C. Reddy,et al.  A MATLAB differentiation matrix suite , 2000, TOMS.

[51]  P. Schmid,et al.  Stability and Transition in Shear Flows. By P. J. SCHMID & D. S. HENNINGSON. Springer, 2001. 556 pp. ISBN 0-387-98985-4. £ 59.50 or $79.95 , 2000, Journal of Fluid Mechanics.

[52]  R. Temam,et al.  On some control problems in fluid mechanics , 1990 .

[53]  Mohamed Gad-el-Hak,et al.  Flow Control: Passive, Active, and Reactive Flow Management , 2000 .

[54]  J. Burns,et al.  A control problem for Burgers' equation with bounded input/output , 1991 .

[55]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[56]  Mohamed Gad-el-Hak.  Flow Control: Flow Control , 2000 .

[57]  T. Bewley,et al.  A computational framework for the regularization of adjoint analysis in multiscale PDE systems , 2004 .

[58]  David J. N. Limebeer,et al.  Linear Robust Control , 1994 .

[59]  Thomas R. Bewley,et al.  A noncausal framework for model-based feedback control of spatially developing perturbations in boundary-layer flow systems. Part I: formulation , 2004, Syst. Control. Lett..

[60]  Thomas Bewley,et al.  Performance of a linear robust control strategy on a nonlinear model of spatially developing flows , 2004, Journal of Fluid Mechanics.

[61]  Roger Temam,et al.  DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithms , 2001, Journal of Fluid Mechanics.

[62]  Wesley H. Huang,et al.  The pseudospectral method for solving di8erential eigenvalue problems , 1994 .

[63]  Thomas Bewley,et al.  On the extension of the complex-step derivative technique to pseudospectral algorithms , 2003 .

[64]  Sanjay S. Joshi,et al.  A systems theory approach to the feedback stabilization of infinitesimal and finite-amplitude disturbances in plane Poiseuille flow , 1997, Journal of Fluid Mechanics.

[65]  J. Hunt,et al.  Perturbed vortical layers and shear sheltering , 1999 .

[66]  John Kim,et al.  Regeneration mechanisms of near-wall turbulence structures , 1995, Journal of Fluid Mechanics.

[67]  Dan S. Henningson,et al.  State estimation in wall-bounded flow systems. Part 2. Turbulent flows , 2006, Journal of Fluid Mechanics.