Economic MPC of Wastewater Treatment Plants Based on Model Reduction
Department of Chemical & Materials Engineering, University of Alberta, Edmonton, AB T6G 2R3, Canada
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Processes 2019, 7(10), 682; https://doi.org/10.3390/pr7100682
Received: 14 August 2019
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Revised: 26 September 2019
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Accepted: 27 September 2019
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Published: 1 October 2019
(This article belongs to the Special Issue Design and Control of Sustainable Systems)
In this paper, we consider the problem of economic model predictive control of wastewater treatment plants based on model reduction. We apply two model approximation methods to a wastewater treatment plant (WWTP) described by a modified Benchmark Simulation Model No.1 to overcome the intensive computation associated with economic model predictive control (MPC). Two computationally efficient models are obtained based on trajectory piecewise linearization (TPWL) and reduced order TPWL. To obtain the reduced order TPWL model, a proper orthogonal decomposition (POD)-based method is utilized. Further, the reduced order model is linearized to obtain a TPWL-POD model. The objective is to design controllers which minimize the overall economic cost. Accordingly, we design economic MPC (EMPC) controllers based on each of the models. The economic control cost can be described as a weighted summation of effluent quality and overall operating cost. We compare the accuracy of the two proposed approximation models with different linearization point numbers. We evaluate the average evaluation time for the two proposed EMPC controllers and make comparisons with the EMPC based on the original nonlinear model. We also investigate how the number of linearization points involved in the TPWL model and TPWL-POD model affects the control performance in terms of average performance cost and the average evaluation time.
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Keywords:
economic model predictive control; wastewater treatment plant; model reduction; trajectory piecewise linearization
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MDPI and ACS Style
Zhang, A.; Liu, J. Economic MPC of Wastewater Treatment Plants Based on Model Reduction. Processes 2019, 7, 682. https://doi.org/10.3390/pr7100682
AMA Style
Zhang A, Liu J. Economic MPC of Wastewater Treatment Plants Based on Model Reduction. Processes. 2019; 7(10):682. https://doi.org/10.3390/pr7100682
Chicago/Turabian StyleZhang, An, and Jinfeng Liu. 2019. "Economic MPC of Wastewater Treatment Plants Based on Model Reduction" Processes 7, no. 10: 682. https://doi.org/10.3390/pr7100682
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