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Design of poiseuille flow controllers using the method of inequalities

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Abstract

This paper investigates the use of the method of inequalities (MoI) to design output-feedback compensators for the problem of the control of instabilities in a laminar plane Poiseuille flow. In common with many flows, the dynamics of streamwise vortices in plane Poiseuille flow are very non-normal. Consequently, small perturbations grow rapidly with a large transient that may trigger nonlinearities and lead to turbulence even though such perturbations would, in a linear flow model, eventually decay. Such a system can be described as a conditionally linear system. The sensitivity is measured using the maximum transient energy growth, which is widely used in the fluid dynamics community. The paper considers two approaches. In the first approach, the MoI is used to design low-order proportional and proportional-integral (PI) controllers. In the second one, the MoI is combined with McFarlane and Glover’s H ∞ loop-shaping design procedure in a mixed-optimization approach.

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Authors and Affiliations

  1. Department of Mechanical Engineering, King’s College London, Strand, London, WC2R 2LS, UK

    John McKernan & George Papadakis

  2. Department of Aerospace Sciences, Cranfield University, Bedfordshire, MK43 0AL, UK

    James F. Whidborne

Authors
  1. John McKernan
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  2. James F. Whidborne
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  3. George Papadakis
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Correspondence to James F. Whidborne.

Additional information

John McKernan received the B.A. degree in engineering from Cambridge University, UK, in 1980. From 1980 to 2001, he worked in industry. In 2002, he received the M. Sc. degree in computer aided mechanical engineering from King’s College London, UK, and the Ph.D. degree in 2006 from Cranfield University, UK. He joined the Division of Engineering, King’s College London as a research associate in 2007, where he is currently in the Experimental and Computational Laboratory for the Analysis of Turbulence. He is an associate member of the Institute of Mechanical Engineers.

His research interest is the control of transition to turbulence of Poiseuille flow by the application of linear control.

James F. Whidborne received the B.A. degree in engineering from Cambridge University, UK, in 1982, and the M. Sc. and the Ph.D. degrees in systems and control from University of Manchester Institute of Science and Technology (UMIST), UK, in 1987 and 1992, respectively. From 1982 to 1985, he worked in industry, and from 1986 to 1991, he was with the Control Systems Centre, UMIST. From 1991 to 1994, he held a position of research associate with the Department of Engineering, at the University of Leicester, UK. From 1994 to 2003, he was a lecturer, then senior lecturer with the Department of Mechanical Engineering, King’s College London. He is currently a senior lecturer in the Department of Aerospace Sciences at Cranfield University, UK. He has over 100 research publications, including three books. He is a chartered engineer, and a member of the IET and IEEE.

His research interests include optimal finite-precision controller implementations, multi-objective robust control design, fluid flow control, and control of UAVs.

George Papadakis received the Dipl.Eng. degree in mechanical engineering from the National Technical University of Athens, Greece, in 1990, and was awarded the Ph.D. degree from the same university in 1996. He is a senior lecturer in computational fluid dynamics in the Department of Mechanical Engineering of King’s College London, UK, since 2006, and member of the Experimental and Computational Laboratory for the Analysis of Turbulence (ECLAT) group. He has over 13 years experience in the development and use of numerical methods for the solution of problems that involve laminar or turbulent flows, with or without heat transfer.

His research interests include numerical simulation of turbulent flows (mainly in stirred vessels and heat exchangers) using the large eddy simulation technique in unstructured grids, flow control of unstable flows using optimal control theory to prevent transition to turbulence as well as turbulence modelling with emphasis on improved predictions in the near wall region. His work has been supported by Engineering and Physical Sciences Research Council (EPSRC) and the European Union.

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McKernan, J., Whidborne, J.F. & Papadakis, G. Design of poiseuille flow controllers using the method of inequalities. Int. J. Autom. Comput. 6, 14–21 (2009). https://doi.org/10.1007/s11633-009-0014-x

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  • DOI: https://doi.org/10.1007/s11633-009-0014-x

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