(170d) A Model Reduction and Decomposition Approach for Economic MPC of Wastewater Treatment Plants
In the literature, several control approaches have been proposed for WWTPs. One commonly adopted solution is to design a proportional-integral (PI) regulator. Another regulating approach is based on the combination of feedforward control and PI control. Despite the simple structures, the above approaches may not handle system constraints and provide optimal control actions. To address these shortcomings, more and more research attention has been given to model predictive control (MPC) algorithms during the last decade. However, the computational complexity of these algorithms is non-negligible. In our previous work , an economic MPC algorithm was developed for the control of WWTPs. It was demonstrated that economic MPC can improve the effluent quality while reducing the operational costs compared with the classical set-point tracking MPC. While economic MPC has the potential to improve the control of WWTPs, one critical issue is its high computational complexity. Note that in the implementation of set-point tracking MPC, the computational issue may be overcome by using identified linear input-output models around the set-point. However, these input-output models may not be suitable for economic MPC if the objective function in the economic MPC is a function of the entire process state (instead of the outputs) and the process exhibits time-varying (instead of steady-state) operation like in WWTPs.
In this work, we present an objective-oriented model reduction and subsystem decomposition approach for the control of WWTPs. A benchmark simulation model for a WWTP of five activated sludge reactors and a secondary reactor is used. In the proposed approach, the nonlinear model is reduced and simplified through a few steps. First, the model is reduced by considering the time-scale multiplicity in the process dynamics; second, the dynamic sensitivities of the objective function (effluent quality and operational cost) with respect to all the process states are evaluated along typical operating trajectories and the most important states are determined according to the dynamic sensitivities; third, a hybrid model is developed based on linearizing those not so important states around a steady-state and piecewise linearizing those important states (with high dynamic sensitivities). Based on the simplified hybrid model, we also illustrate how recent results on input-output pairing  and subsystem decomposition  may be applied to the WWTP. Simulation results are also provided to demonstrate the effectiveness of the proposed approach.
 J. Zeng and J. Liu. Economic model predictive control of wastewater treatment processes. Industrial & Engineering Chemistry Research, 54:5710-5721, 2015.
 X. Yin and J. Liu. Input-output paring accounting for both structure and strength in coupling. AIChE Journal, 63:1226-1235, 2017.
 X. Yin, K. Arulmaran, J. Liu and J. Zeng. Subsystem decomposition and configuration for distributed state estimation. AIChE Journal, 62:1995-2003, 2016.