Economic MPC of Wastewater Treatment Plants Based on Model Reduction

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.