Feedback control for distributed heat transfer mechanisms in direct-contact membrane distillation system

In this paper, the problem of stabilization and production rate reference tracking for a Direct-Contact Membrane Distillation (DCMD) system is addressed. Sufficient conditions for the asymptotic and exponential stabilization for DCMD system are presented using the Gronwall-Bellman lemma and Linear Matrix Inequalities (LMIs) approaches, respectively. A nonlinear observer is then proposed to estimate the temperature distribution among the DCMD domain. This contributes to propose a reference production rate control design for the DCMD process via observer-based output control approach. Finally, numerical simulations are given to show the effectiveness of the proposed methods.

[1]  M. Darouach,et al.  Exponential stabilization of a class of nonlinear systems: A generalized GronwallBellman lemma appr , 2011 .

[2]  D. Debeljkovic,et al.  Finite-time stability of linear singular systems: Bellman-Gronwall approach , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[3]  Å. Björck Solving linear least squares problems by Gram-Schmidt orthogonalization , 1967 .

[4]  V. Jurdjevic,et al.  Controllability and stability , 1978 .

[5]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in System and Control Theory , 1994, Studies in Applied Mathematics.

[6]  B. G. Pachpatte,et al.  A note on Gronwall-Bellman inequality , 1973 .

[7]  Ludovic F. Dumée,et al.  Advances in Membrane Distillation for Water Desalination and Purification Applications , 2013 .

[8]  M. Gryta Water Desalination by Membrane Distillation , 2011 .

[9]  C. A. Desoer,et al.  Nonlinear Systems Analysis , 1978 .

[10]  Alexandre Trofino,et al.  Sufficient LMI conditions for output feedback control problems , 1999, IEEE Trans. Autom. Control..

[11]  D. H. Jacobson,et al.  Stabilization and Optimal Control of Nonlinear Systems Homogeneous-in-the-Input , 1976 .

[12]  H. Hammouri,et al.  Nonlinear implicit on-line observer : application to the estimation in binary distillation columns , 2008 .

[13]  Ioan Doré Landau,et al.  Reduced order bilinear models for distillation columns , 1978, Autom..

[14]  Alexandr A. Zevin,et al.  Exponential stability and solution bounds for systems with bounded nonlinearities , 2003, IEEE Trans. Autom. Control..

[15]  Stanislaw H. Zak,et al.  On the stabilization and observation of nonlinear/uncertain dynamic systems , 1990 .

[16]  J. Gauthier,et al.  A simple observer for nonlinear systems applications to bioreactors , 1992 .

[17]  C. Desoer,et al.  Feedback Systems: Input-Output Properties , 1975 .

[18]  Vahid Johari Majd,et al.  A Nonlinear Adaptive Resilient Observer Design for a Class of Lipschitz Systems Using LMI , 2011, Circuits Syst. Signal Process..

[19]  Panagiotis D. Christofides,et al.  Model predictive control of feed flow reversal in a reverse osmosis desalination process , 2009, 2009 American Control Conference.

[20]  H. Shim,et al.  A Simple Observer for Nonlinear Systems in x-coordinate using Lipschitz Extension Technique , 2000 .

[21]  Marshall Slemrod,et al.  Stabilization of Bilinear Control Systems with Applications to Nonconservative Problems in Elasticity , 1978 .

[22]  Kiyotaka Shimizu,et al.  Nonlinear state observers by gradient descent method , 2000, Proceedings of the 2000. IEEE International Conference on Control Applications. Conference Proceedings (Cat. No.00CH37162).

[23]  T. Laleg‐Kirati,et al.  Membrane Distillation Process Modeling: Dynamical Approach , 2014 .

[24]  Roland Longchamp,et al.  Stable feedback control of bilinear systems , 1980 .

[25]  Bor-Sen Chen,et al.  Robust linear controller design: Time domain approach , 1987 .

[26]  Taous-Meriem Laleg-Kirati,et al.  Nonlinear Lyapunov-based boundary control of distributed heat transfer mechanisms in membrane distillation plant , 2015, 2015 American Control Conference (ACC).

[27]  Dale E. Seborg,et al.  Characterization of equilibrium sets for bilinear systems with feedback control , 1983, Autom..

[28]  Taous-Meriem Laleg-Kirati,et al.  Dynamic modeling and optimization in membrane distillation system , 2014 .

[29]  Valentina Orsini,et al.  Relaxed sufficient conditions for the stability of continuous and discrete-time linear time-varying systems , 2007, 2007 46th IEEE Conference on Decision and Control.

[30]  Michael Schorr,et al.  Desalination, Trends and Technologies , 2011 .

[31]  E. Ryan,et al.  On asymptotically stabilizing feedback control of bilinear systems , 1983 .

[32]  Colin A. Scholes Advanced Membrane Technology and Applications [Book Review] , 2011 .

[33]  Noreddine Ghaffour,et al.  Performance evaluation of the DCMD desalination process under bench scale and large scale module operating conditions , 2014 .