Optimal control for a distributed parameter system with delayed-time. Application to onesided heat conduction system

International Journal of Electrical and Electronics Engineering

© 2019 by SSRG - IJEEE Journal

Volume 6 Issue 5

Year of Publication : 2019

Authors : Mai Trung Thai

10.14445/23488379/IJEEE-V6I5P102

How to Cite?

Mai Trung Thai, "Optimal control for a distributed parameter system with delayed-time. Application to onesided heat conduction system," SSRG International Journal of Electrical and Electronics Engineering, vol. 6,  no. 5, pp. 7-14, 2019. Crossref, https://doi.org/10.14445/23488379/IJEEE-V6I5P102

Abstract:

This paper gives a solution of an optimal control problem for a distributed parameter system (DPS) with delayed-time, governed by a heatconduction
equation, using the numerical method. In which, the delayed object e^-is is replaced by using first-order Pade approximation model. The system is
applied to a specific one-sided heat-conduction system in a heating furnace to control temperature for the objects which have flat-slab shape following
the most accurate burning standards [2], [6]. The aim of problem is to find an optimal control signal (optimal voltage) so that the error between the
distribution of real temperature of the object and the desired temperature is minimum after a given period of time tf [2], [6], [9]. To verify the solution of the problem, we have proceeded to run the simulation programs on a flat-slab of Carbon steel and a flatslab of Samot.

Keywords:

optimal control, distributed parameter systems, delay,numerical method, Pade approximation

References:

[1] P.K.C.Wang, "Optimum control of distributed parameter systems", Presented at the Joint Automatic Control Conference, Minneapolis, Minn.June, pp.19-21. 1963
[2] Y. Sakawa, “Solution of an optimal control problem in a distributed parameter system”, Trans. IEEE, 1964, AC-9, pp. 420-426.
[3] E. Celik and M. Bayram, “On the numerical solution of differential algebraic equation by Pade series”, Applied mathematics and computation, 137, pp. 151-160, 2003.
[4] J. H. Mathews and K. K. Fink, “Numerical Methods Using Matlab”, 4th Edition, Upper saddle River, New Jersey, 2004
[5] N..H.Cong, “ A research replaces a delayed object by appropriate models”, 6th Viet Nam International Conference on Automation, (VICA6-2005)
[6] N.H.Cong, N.H.Nam, “Optimal control for a distributed parameter system with time delay based on the numerical method”, 10th International Conference on Control, Automation, Robotics and Vision, IEEE Conference, pp.1612-1615, 2008.
[7] M. Subasi, “Optimal Control of Heat Source in a Heat Conductivity Problem”, Optimization Methods and Software, Vol 17, pp. 239-250, Turkey, 2010.
[8] B. Talaei, H. Xu and S. Jagannathan, “Neural network dynamic progamming constrained control of distributed parameter systems governed by parabolic partial differential equations with application to diffusion-reaction processes”, IEEE Conference Publications, pp. 1861 - 1866, 2014.
[9] Mai.T.Thai, Nguyen.H.Cong, Nguyen.V.Chi, Vu.V.Dam, “Applying pade approximation model in optimal control problem for a distributed parameter system with time delay”, International Journal of Computing and Optimization, Hikari Ltd, vol 4, no.1, pp.19-30, 2017.
[10] Cong Huu Nguyen, Mai Trung Thai (2018), “Optimal control for a distributed parameter system with time-delay, non-linear using the numerical method. Application to one-sided heat conduction system”, ISSN 2395-0250, International Journal of Thermal Engineering (IJTE), Vol 4, Issue 1, Jan-Feb 2018.