MODEL PREDICTIVE CONTROL FOR DISTRIBUTED PARAMETER SYSTEMS USING RBF NEURAL NETWORKS

Eleni Aggelogiannaki, Haralambos Sarimveis

Abstract

A new approach for the identification and control of distributed parameter systems is presented in this paper. A radial basis neural network is used to model the distribution of the system output variables over space and time. The neural network model is then used for synthesizing a non linear model predictive control configuration. The resulting framework is particular useful for control problems that pose constraints on the controlled variables over space. The proposed scheme is demonstrated through a tubular reactor, where the concentration and the temperature distributions are controlled using the wall temperature as the manipulated variable. The results illustrate the efficiency of the proposed methodology.

References

  1. Armaou, A., Christofides, P. (2002). Dynamic optimization of dissipative PDE systems using nonlinear order reduction. Chem. Eng. Sc., 57, 5083- 5114.
  2. Baker, J., Christofides, P. (1999). Output feedback control of parabolic PDE systems with nonlinear spatial differential operators. Ind. Eng. Chem. Res., 38, 4372- 4380.
  3. Chatterjee, A. (2000). An introduction to the proper orthogonal decomposition. Current Science, 78, 808- 817.
  4. Chiu, T., Christofides, P. (1999). Nonlinear control of particulate processes. AIChE Journal, 45, 1279-1297.
  5. Christofides, P. (1998). Robust control of parabolic PDE systems. Chem. Eng. Sc., 53, 2949-2965.
  6. Christofides, P. (2001a). Control of nonlinear distributed process systems: recent developments and challenges. AIChE Journal, 47, 514-518.
  7. Christofides, P. (2001b). Nonlinear and Robust Control of PDE Systems: Methods and Applications to transport reaction processes. Birkhäuser, Boston.
  8. Christofides, P. J. Baker, (1999). Robust output feedback control of quasi-linear parabolic PDE systems. In Systems & Control Letters, 36, 307-316.
  9. Christofides, P., Daoutidis, P. (1996). Nonlinear control of Diffusion-Convection-Reaction processes. Comp. Chem. Eng., 20, 1071-1076.
  10. Christofides, P., Daoutidis, P. (1997). Finite-Dimensional Control of Parabolic PDE Systems Using Approximate Inertial Manifolds. Journal of mathematical analysis and applications, 216, 398-420.
  11. El-Farra, N., Armaou, A., Christofides, P. (2003). Analysis and control of parabolic PDE systems with input constraints. Automatica, 19, 715-725.
  12. El-Farra, N., Christofides, P. (2004). Coordinating feedback and switching for control of spatially distributed process. Comp. Chem. Eng.,28, 111-128.
  13. Gay, D., Ray, W. (1995). Identification and control of distributed parameter systems by means of the singular value decomposition. Chem. Eng. Sc., 50, 1519-1539.
  14. Gonzáles-García, R., Rico-Martínez, R., Kevrekidis, I. (1998). Identification of distributed parameter systems: A neural net based approach. Comp. Chem. Eng., 22, 965-968.
  15. Hoo, K., Zheng, D. (2001). Low order control-relevant models for a class of distributed parameter systems. Chem. Eng. Sc., 56, 6683-6710.
  16. Newman, A. (1996a). Model reduction via the KarhunenLoève Expansion Part I: An exposition. Technical Report 96-32, University of Maryland, College Park, MD.
  17. Newman, A. (1996b). Model reduction via the KarhunenLoève Expansion Part II: Some elementary examples. Technical Report 96-33, University of Maryland, College Park, MD.
  18. Padhi, R., Balakrishnan, S. (2003). Proper orthogonal decomposition based optimal neurocontrol synthesis of a chemical reactor process using approximate dynamic programming. Neural Networks, 16, 719-728.
  19. Padhi, R., Balakrishnan, S., Randolph, T. (2001). Adaptive-critic based optimal neuro control synthesis for distributed parameter systems. Automatica, 37, 1223-1234.
  20. Park, H., Cho, D. (1996a). The use of Karhunen-Loeve decomposition for the modelling of distributed parameter systems. Chem. Eng. Sc., 51, 81-89.
  21. Park, H., Cho, D. (1996b). Low dimensional modelling of flow reactors. Int. J. Heat Mass Transfer, 39, 3311- 3323.
  22. Park, H., Kim, O. (2000). A reduction method for the boundary control of the heat conduction equation. Journal of Dynamic Systems Measurement and Control, 122, 435-444.
  23. Sarimveis, H., Alexandridis, A., Tsekouras, G., Bafas, G. (2002). A fast and efficient algorithm for training radial basis function neural networks based on a fuzzy partition of the input space. Ind. Eng. Chem. Res., 41, 751-759.
  24. Shvartsman, S., Kevrekidis, I. (1998). Nonlinear model reduction for control of distributed systems: a computer -assisted study. AIChE Journal, 44, 1579- 1595
  25. Shvartsman, S., Theodoropoulos, C., Rico-Martínez, R. Kevrekidis, I., Titi, E., Mountziaris, T. (2000). Order reduction for nonlinear dynamic models of distributed reacting systems. Journal of Process Control, 10, 177- 184.
  26. Zheng D., Hoo, K. (2002). Low-order model identification for implementable control solutions of distributed parameter systems. Comp. Chem. Eng., 26, 1049- 1076.
  27. Zheng, D., Hoo, K. (2004). System identification and model-based control for distributed parameter systems. Comp. Chem. Eng., 28, 1361-1375.
  28. Zheng, D., Hoo, K., Piovoso, M. (2002a). Low-order model identification of distributed parameter systems by a combination of singular value decomposition and the Karhunen-Loève expansion. Ind. Eng. Chem. Res., 41, 1545-1556.
  29. Zheng, D., Hoo, K., Piovoso, M. (2002b). Finite dimensional modeling and control of distributed parameter systems. In 2002 American Automatic Control Conference, A.A.C.C.
Download


Paper Citation


in Harvard Style

Aggelogiannaki E. and Sarimveis H. (2005). MODEL PREDICTIVE CONTROL FOR DISTRIBUTED PARAMETER SYSTEMS USING RBF NEURAL NETWORKS . In Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 972-8865-29-5, pages 19-24. DOI: 10.5220/0001156700190024


in Bibtex Style

@conference{icinco05,
author={Eleni Aggelogiannaki and Haralambos Sarimveis},
title={MODEL PREDICTIVE CONTROL FOR DISTRIBUTED PARAMETER SYSTEMS USING RBF NEURAL NETWORKS},
booktitle={Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2005},
pages={19-24},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001156700190024},
isbn={972-8865-29-5},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - MODEL PREDICTIVE CONTROL FOR DISTRIBUTED PARAMETER SYSTEMS USING RBF NEURAL NETWORKS
SN - 972-8865-29-5
AU - Aggelogiannaki E.
AU - Sarimveis H.
PY - 2005
SP - 19
EP - 24
DO - 10.5220/0001156700190024