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This paper considers the problem of simulating the humidity distributions of a grain storage system. The distributions are described by partial differential equations (PDE). It is quite difficult to obtain the humidity profiles from the PDE model. Hence, a discretization method is applied to obtain an equivalent ordinary differential equation model. However, after applying the discretization technique, the cost of solving the system increases as the size increases to a few thousands. It may be noted that after discretization, the degree of freedom of the system remain the same while the order increases. The large dynamic model is reduced using a proper orthogonal decomposition based technique and an equivalent model but of much reduced size is obtained. A controller based on optimal control theory is designed to obtain an input such that the output humidity reaches a desired profile and also its stability is analyzed. Numerical results are presented to show the validity of the reduced model and possible further extensions are identified.
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B. N. Datta. Numerical Methods for Linear Control Systems: Design and Analysis, New York: Elsevier Academic Press, 2003.
T. Roubíček. Nonlinear Partial Differential Equations with Applications, New York: Springer, 2005. MATH
D. W. Sun, J. L. Woods. Low temperature moisture transfer characteristics of wheat in thin layers. Transactions of the American Society of Agricultural Engineers, vol. 37, no. 6, pp. 1919–1926, 1994. CrossRef
J.N. Reddy. An Introduction to the Finite Element Method, New York, USA: McGraw Hill, Inc., 1993.
T. T. Lee, F. Y. Wang, R. B. Newell. Robust model-order reduction of complex biological processes. Journal of Process Control, vol. 12, no. 7, pp. 807–821, 2002. CrossRef
Z. Li, X. Lu, W. P. Shi. Process variation dimension reduction based on SVD. In Proceedings of the 2003 International Symposium on Circuits and Systems, IEEE, Bangkok, vol. 4, pp. IV–672–IV–675, 2003.
B. N. Datta. Krylov subspace methods for large-scale matrix problems in control. Future Generation Computer Systems, vol. 19, no. 7, pp. 1253–1263, 2003. CrossRef
E. J. Grimme. Krylov Projection Methods for Model Reduction, Ph. D. dissertation, University of Illinios at Urbana Champaign, Urbana, IL, USA, 1997.
S. Gugercin. An iterative SVD-Krylov based method for model reduction of large-scale dynamical systems. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, IEEE, Spain, pp. 5905–5910, 2005.
A. Chatterjee. An introduction to the proper orthogonal decomposition. Special Section: Computational Science, Current Science, vol. 78, no. 7, pp. 808–817, 2000.
S. Y. Shvartsman, C. Theodoropoulos, R. Rico-Martinez, I. G. Kevrekidis, E. S. Titi, T. J. Mountziaris. Order reduction for nonlinear dynamic models of distributed reacting systems. Journal of Process Control, vol. 10, no. 2–3, pp. 177–184, 2000. CrossRef
Y. Zhai, L. Vu-Quoc. Analysis of power magnetic components with nonlinear static hysteresis: Proper orthogonal decomposition and model reduction. IEEE Transactions on Magnetics, vol. 43, no. 5, pp. 1888–1897, 2007. CrossRef
Y. Tenne. An optimization algorithm employing multiple metamodels and optimizers. International Journal of Automation and Computing, vol. 10, no. 3, pp. 227–241, 2013. CrossRef
E. M. Jafarov. On stability delay bounds of simple input-delayed linear and non-linear systems: Computational results. International Journal of Automation and Computing, vol. 10, no. 4, pp. 327–334, 2013. CrossRef
N. J. Thakor, S. C. Patil, A. A. Sawant, S. D. Sawant. Influence of storage period on physical properties and quality of paddy stored in GIC silo and bag storage under humid Konkan climatic conditions. Journal of Agricultural Engineering, vol. 49, no. 1, pp. 43–47, 2012.
J. Zhang. Modelling and multi-objective optimal control of batch processes using recurrent neuro-fuzzy networks. International Journal of Automation and Computing, vol. 3, no. 1, pp. 1–7, 2006. CrossRef
P. Chakraborty, S. Banerjee. Optimization of extrusion process for production of expanded product from green gram and rice by response surface methodology. Journal of Scientific and Industrial Research, vol. 68, no. 2, pp. 140–148, 2009.
J. C. Alvarez. Evaluation of Moisture Diffusion Theories in Porous Materials, Master dissertation, Virginia Polytechnic Institute and State University, USA, 1998.
P. Guha, M. un Nabi. Model reduction and controller design for a nonlinear heat conduction problem using finite element method. International Journal of Automation and Computing, vol. 9, no. 5, pp. 474–479, 2012. CrossRef
M. un Nabi, P. Guha. A control law for a nonlinear heat conduction problem on nontrivial domains using FEM. In Proceedings of the 17th Mediterranean Conference on Control and Automation, IEEE, Thessaloniki, pp. 320–323, 2009.
D. S. Naidu. Optimal Control Systems, London, UK: CRC Press, 2002.
P. Guha, M. un Nabi. Optimal control of a nonlinear induction heating system using a proper orthogonal decomposition based reduced order model. Journal of Process Control, vol. 22, no. 9, pp. 1681–1687, 2012. CrossRef
- Reduced Order Modeling & Controller Design for Mass Transfer in a Grain Storage System
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