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Outline

Robust/Optimal Temperature Profile Control Using Neural Networks

2006, 2006 IEEE International Conference on Control Applications

https://doi.org/10.1109/CACSD-CCA-ISIC.2006.4777145

Abstract

An approximate dynamic programming (ADP) based neurocontroller is developed for a heat transfer application. Heat transfer problem for a fin in a car's electronic module is modeled as a nonlinear distributed parameter (infinite-dimensional) system by taking into account heat loss and generation due to conduction, convection and radiation. A low-order, finite-dimensional lumped parameter model for this problem is obtained by using Galerkin projection and basis functions designed through the 'Proper Orthogonal Decomposition' technique (POD) and the 'snap-shot' solutions. A suboptimal neurocontroller is obtained with a single-network-adaptivecritic (SNAC). Further contribution of this paper is to develop an online robust controller to account for unmodeled dynamics and parametric uncertainties. A weight update rule is presented that guarantees boundedness of the weights and eliminates the need for persistence of excitation (PE) condition to be satisfied. Since, the ADP and neural network based controllers are of fairly general structure, they appear to have the potential to be controller synthesis tools for nonlinear distributed parameter systems especially where it is difficult to obtain an accurate model. Most of the real-world engineering problems are distributed in nature and can be described by a set of partial differential equations (PDEs) (e.g. heat transfer, fluid flow, flexible structures etc.) for which one must take the spatial distribution into account. The analysis and controller design for such systems are often far more complex than for the Manuscript received February 10, 2006. This research was supported by NSF grant 0324428. We gratefully acknowledge the heat transfer related discussions with Dr. D.C. Look, Emeritus professor, University of Missouri-Rolla.

References (8)

  1. Bryson A. E. and Ho Y. C., Applied Optimal Control, London: Taylor and Francis, 1975
  2. Curtain R. F. and Zwart H. J., An Introduction to Infinite Dimensional Linear Systems Theory, Springer-Verlag, New York, 1995.
  3. Holmes P., Lumley J. L. and Berkooz G., Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge University Press, 1996, pp. 87-154.
  4. Miller A. F., Basic Heat and Mass Transfer, Richard D. Irwin Inc., Concord, MA, 1995.
  5. Padhi, R., Unnikrishnan N. and Balakrishnan, S. N., Optimal Control Synthesis of a Class of Nonlinear Systems Using Single Network Adaptive Critics, Submitted to ACC, 2004.
  6. aRavindran S. S., Proper Orthogonal Decomposition in Optimal Control of Fluids, NASA/TM-1999-209113.
  7. Slotine J-J. E. and Li W., Applied Nonlinear Control, Prentice Hall Inc, New Jersey, 1991.
  8. Yadav V, Padhi R, Balakrishnan S.N. Robust/Optimal Temperature Profile Control of a Re-Entry Vehicle Using Neural Networks. AIAA AFM, Keystone, Colorado. 21-24 Aug 2006