SISO model‐based control of separated flows: Sliding mode and optimal control approaches

The challenging problem of active control of separated flows is tackled in the present paper using model-based design principles, and applied to data issued from a two-dimensional separated flow experiment. First, a bilinear state and input delay model of the system has been obtained from experimental data by means of a modified identification procedure. Adequacy and precision of the obtained model are demonstrated and compared with existing results. Next, two control problems (setpoint tracking and optimal control) have been formulated and studied using sliding mode control methodology and averaging analysis. The theoretical control results are supported with numerical simulations.

[1]  F. G. Howard,et al.  Control of low-speed turbulent separated flow using jet vortex generators , 1992 .

[2]  Emilia Fridman,et al.  Introduction to Time-Delay Systems , 2014 .

[3]  Charles Audet,et al.  Globalization strategies for Mesh Adaptive Direct Search , 2008, Comput. Optim. Appl..

[4]  Emilia Fridman,et al.  Delay-dependent positivity: Application to interval observers , 2015, 2015 European Control Conference (ECC).

[5]  Louis N. Cattafesta,et al.  Passive Flow Control over a Three-Dimensional Turret with a Flat Aperture , 2011 .

[6]  Jean-Paul Gauthier,et al.  A separation principle for bilinear systems with dissipative drift , 1992 .

[7]  Leonid Fridman,et al.  Nonlocal stabilization via delayed relay control rejecting uncertainty in a time delay , 2004 .

[8]  Sergio Guerrero,et al.  Local exact controllability of the Navier-Stokes system ✩ , 2004 .

[9]  Sébastien Le Digabel,et al.  Algorithm xxx : NOMAD : Nonlinear Optimization with the MADS algorithm , 2010 .

[10]  Christopher Edwards,et al.  Static output feedback sliding mode control for time‐varying delay systems with time‐delayed nonlinear disturbances , 2010 .

[11]  Omar Ghattas,et al.  Optimal Control of Two- and Three-Dimensional Incompressible Navier-Stokes Flows , 1997 .

[12]  Z. Artstein Linear systems with delayed controls: A reduction , 1982 .

[13]  Eric Garnier,et al.  NARX modelling of unsteady separation control , 2013 .

[14]  Andrey Polyakov,et al.  A bilinear input-output model with state-dependent delay for separated flow control , 2016, 2016 European Control Conference (ECC).

[15]  Eric Garnier,et al.  Experimental detection of flow separation over a plain flap by wall shear stress analysis with and without steady blowing , 2014 .

[16]  Emmanuel Cid,et al.  Wave patterns generated by an axisymmetric obstacle in a two-layer flow , 2013 .

[17]  Clarence W. Rowley,et al.  Active control of flow-induced cavity oscillations , 2008 .

[18]  E. Davies,et al.  Linear Operators and their Spectra , 2007 .

[19]  Michel Stanislas,et al.  Closed-loop control of experimental shear flows using machine learning , 2014 .

[20]  R. Eldredge,et al.  Active Control of a Separating Boundary Layer with Steady Vortex Generating Jets - Detailed Flow Measurements , 2004 .

[21]  Charles Audet,et al.  Mesh Adaptive Direct Search Algorithms for Constrained Optimization , 2006, SIAM J. Optim..

[22]  R. Volino Separation Control on Low-Pressure Turbine Airfoils Using Synthetic Vortex Generator Jets , 2003 .

[23]  Eric Garnier,et al.  Experimental closed-loop control of flow separation over a plain flap using slope seeking , 2014 .

[24]  Andrei Polyakov,et al.  Minimization of disturbances effects in time delay predictor-based sliding mode control systems , 2012, J. Frankl. Inst..

[25]  Dan S. Henningson,et al.  Model Reduction and Control of a Cavity-Driven Separated Boundary Layer , 2008 .

[26]  Wei Xing Zheng,et al.  Dissipativity-Based Sliding Mode Control of Switched Stochastic Systems , 2013, IEEE Transactions on Automatic Control.

[27]  K. McManus,et al.  Pulsed vortex generator jets for active control of flow separation , 1994 .

[28]  H. Sung,et al.  Control of turbulent separated flow over a backward-facing step by local forcing , 1996 .

[29]  Qi Song,et al.  Adaptive Feedback Control of Flow Separation , 2006 .

[30]  Feingesicht Maxime,et al.  A bilinear input-output model with state-dependent delay for separated flow control , 2016 .

[31]  Li Tiancheng,et al.  アルゴリズム906: elrint3d―組み込み格子ルールのシーケンスを用いる三次元非適応自動立体求積法ルーチン , 2011 .

[32]  Charles Audet,et al.  Nonsmooth optimization through Mesh Adaptive Direct Search and Variable Neighborhood Search , 2006, J. Glob. Optim..

[33]  Louis N. Cattafesta,et al.  Adaptive Control of Separated Flow , 2006 .

[34]  Michel Stanislas,et al.  Open and closed-loop experiments to identify the separated flow dynamics of a thick turbulent boundary layer , 2013 .

[35]  Michel Stanislas,et al.  Characterisation of the Transient Dynamics of a Controlled Separated Flow Using Phase Averaged PIV , 2015 .

[36]  Christian J. Kähler,et al.  Ultra-high-speed 3D astigmatic particle tracking velocimetry: application to particle-laden supersonic impinging jets , 2014 .

[37]  Daniel Wachsmuth,et al.  Optimal control of the unsteady Navier-Stokes equations , 2006 .

[38]  Xiaozhan Yang,et al.  Robust Model-Based Fault Diagnosis for PEM Fuel Cell Air-Feed System , 2016, IEEE Transactions on Industrial Electronics.

[39]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

[40]  Huijun Gao,et al.  Extended State Observer-Based Sliding-Mode Control for Three-Phase Power Converters , 2017, IEEE Transactions on Industrial Electronics.

[41]  B. R. Noack,et al.  Closed-Loop Turbulence Control: Progress and Challenges , 2015 .