Research Papers

Moving-Horizon Modulating Functions-Based Algorithm for Online Source Estimation in a First-Order Hyperbolic Partial Differential Equation

[+] Author and Article Information
Sharefa Asiri

Computer, Electrical and Mathematical Science
and Engineering Division (CEMSE),
King Abdullah University of Science and
Technology (KAUST),
Thuwal 23955-6900, Saudi Arabia
e-mail: sharefa.asiri@kaust.edu.sa

Shahrazed Elmetennani

Computer, Electrical and Mathematical Science
and Engineering Division (CEMSE),
King Abdullah University of Science and
Technology (KAUST),
Thuwal 23955-6900, Saudi Arabia
e-mail: shahrazed.elmetennani@kaust.edu.sa

Taous-Meriem Laleg-Kirati

Computer, Electrical and Mathematical Science
and Engineering Division (CEMSE),
King Abdullah University of Science and
Technology (KAUST),
Thuwal 23955-6900, Saudi Arabia
e-mail: taousmeriem.laleg@kaust.edu.sa

1Corresponding author.

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received October 23, 2016; final manuscript received August 8, 2017; published online September 28, 2017. Assoc. Editor: M. Keith Sharp.

J. Sol. Energy Eng 139(6), 061007 (Sep 28, 2017) (7 pages) Paper No: SOL-16-1452; doi: 10.1115/1.4037743 History: Received October 23, 2016; Revised August 08, 2017

In this paper, an online estimation algorithm of the source term in a first-order hyperbolic partial differential equation (PDE) is proposed. This equation describes heat transport dynamics in concentrated solar collectors where the source term represents the received energy. This energy depends on the solar irradiance intensity and the collector characteristics affected by the environmental changes. Control strategies are usually used to enhance the efficiency of heat production; however, these strategies often depend on the source term which is highly affected by the external working conditions. Hence, efficient source estimation methods are required. The proposed algorithm is based on modulating functions method (MFM) where a moving-horizon strategy is introduced. Numerical results are provided to illustrate the performance of the proposed estimator in open-and closed-loops.

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Fig. 1

A schematic diagram of the hydraulic circuit of a distributed solar collector

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Fig. 2

Indirect adaptive control block diagram

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Fig. 3

A schematic diagram for Algorithm 1

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Fig. 4

The estimated source Ŝ(t) using synthetic data. The subfigures correspond to the cases presented in Table 2. (a) Case 1, (b) Case 2, (c) Case 3, and (d) Case 4.

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Fig. 5

The estimation error, S−Ŝ, for the cases in Fig. 4: (a) Case 1, (b) Case 2, (c) Case 3, and (d) Case 4

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Fig. 6

The control input profile for the open-loop test

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Fig. 7

The estimated source Ŝ(t) in open-loop

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Fig. 8

The estimation error, S−Ŝ, for the result in Fig. 7

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Fig. 9

Results of the indirect adaptive controller in closed-loop

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Fig. 10

The estimated source Ŝ(t) in closed-loop

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Fig. 11

Generated control input



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