Distributed economic model predictive control of wastewater treatment plants

Distributed Economic MPC for Dynamically Coupled Linear Systems With Uncertainties

In this article, we propose a novel economic model-predictive control (MPC) algorithm for a group of disturbed linear systems and implement it in a distributed manner. The system consists of multiple subsystems interacting with each other via dynamics and aims to optimize an economic objective. Each subsystem is subject to constraints both on states and inputs as well as unknown but bounded disturbances. First, we divide the computation of control inputs into several local optimization problems based on each subsystem's local information. This is done by introducing compatibility constraints to confine the difference between the actual information and the previously published reference information of each subsystem, which is the key feature of the proposed distributed algorithm. Then, to ensure the satisfaction of both state and input constraints under disturbances, constraints are tightened on the state and the input of nominal systems by considering explicitly the effect of uncertainties. Moreover, based on an overall optimal steady state, a dissipativity constraint and a terminal constraint are designed and incorporated in the local optimization problems to establish recursive feasibility and guarantee stability for the resulting closed-loop system. Finally, the efficiency of the distributed economic MPC algorithm is demonstrated in a building temperature control case study.

Real-Time Optimization of Wastewater Treatment Plants via Constraint Adaptation

An important requirement of wastewater treatment plants (WWTPs) is compliance with the local regulations on effluent discharge, which are going to become more stringent in the future. The operation of WWTPs exhibits a trade-off between operational cost and effluent quality, which provides a scope for optimization. Process optimization is usually done by optimizing a model of the process. However, due to inevitable plant–model mismatch, the computed optimal solution is usually not optimal for the plant. This study represents the first attempt to handle plant–model mismatch via constraint adaptation (CA) for the real-time optimization of WWTPs. In this simulation study, the “plant” is a model adopted from the BSM1 benchmark, while a reduced-order “model” is used for making predictions and computing the optimal inputs. A first implementation uses steady-state measurements of the plant constraints to adjust the model in the optimization framework. A fast CA technique is also proposed, which adjusts the model using transient measurements. It is observed that, even in the presence of significant plant–model mismatch, the two proposed techniques are able to meet the active plant constraints. These techniques are found to reduce the pumping and aeration energy by 20%, as compared to that adopted in BSM1.

New approach for regulation of the internal recirculation flow rate by fuzzy logic in biological wastewater treatments

The internal recirculation plays an important role on the different biological processes of wastewater treatment plants because it has a great influence on the concentration of pollutants, especially nutrients. Usually, the internal recirculation flow rate is kept fixed or manipulated by control techniques to maintain a fixed nitrate set-point in the last anoxic tank. This work proposes a new control strategy to manipulate the internal recirculation flow rate by applying a fuzzy controller. The proposed controller takes into account the effects of the internal recirculation flow rate on the inlet of the biological treatment and on the denitrification and nitrification processes with the aim of reducing violations of legally established limits of nitrogen and ammonia and also reducing operational costs. The proposed fuzzy controller is tested by simulation with the internationally known benchmark simulation model no. 2. The objective is to apply the proposed fuzzy controller in any control strategy, only replacing the manipulation of the internal recirculation flow rate, to improve the plant operation.Therefore, it has been implemented in five operation strategies from the literature, replacing their original internal recirculation flow rate control, and simulation results are compared with those of the original strategies. Results show improvements with the application of the proposed fuzzy controller of between 2.25 and 57.94% in reduction of total nitrogen limit violations, between 55.22 and 79.69% in reduction of ammonia limit violations and between 0.84 and 38.06% in cost reduction of pumping energy.

Global Internal Recirculation Alternative Operation to Reduce Nitrogen and Ammonia Limit Violations and Pumping Energy Costs in Wastewater Treatment Plants

The internal recirculation plays an important role in different areas of the biological treatment of wastewater treatment plants because it has a great influence on the concentration of pollutants, especially nutrients. A usual manipulation of the internal recirculation flow rate is based on the target of controlling the nitrate concentration in the last anoxic tank. This work proposes an alternative for the manipulation of the internal recirculation flow rate instead of nitrate control, with the objective of avoiding limit violations of nitrogen and ammonia concentrations and reducing operational costs. A fuzzy controller is proposed to achieve it based on the effects of the internal recirculation flow rate in different areas of the biological treatment. The proposed manipulation of the internal recirculation flow rate is compared to the application of the usual nitrate control in an already established and published operation strategy by using the internationally known benchmark simulation model no. 2 as a working scenario. The results show improvements with reductions of 59.40% in ammonia limit violations, 2.35% in total nitrogen limit violations, and 38% in pumping energy costs.

Collaborative Control Applied to BSM1 for Wastewater Treatment Plants

This paper describes a design procedure for a collaborative control structure in Plant Wide Control (PWC), taking into account the existing controllable parameters as a novelty in the procedure. The collaborative control structure includes two layers, supervisory and regulatory, which are determined according to the dynamics hierarchy obtained by means of the Hankel matrix. The supervisory layer is determined by the main dynamics of the process and the regulatory layer comprises the secondary dynamics and controllable parameters. The methodology proposed is applied to a wastewater treatment plant, particularly to the Benchmark Simulation Model No 1 (BSM1) for the activated sludge process, comparing the results with the use of a Model Predictive Controller in the supervisory layer. For determining controllable parameters in the BSM1 control, a new specific oxygen mass transfer model in the biological reactor has been developed, separating the kLa volumetric mass transfer coefficient into two controllable parameters, kL and a.

Responsive Economic Model Predictive Control for Next-Generation Manufacturing

There is an increasing push to make automated systems capable of carrying out tasks which humans perform, such as driving, speech recognition, and anomaly detection. Automated systems, therefore, are increasingly required to respond to unexpected conditions. Two types of unexpected conditions of relevance in the chemical process industries are anomalous conditions and the responses of operators and engineers to controller behavior. Enhancing responsiveness of an advanced control design known as economic model predictive control (EMPC) (which uses predictions of future process behavior to determine an economically optimal manner in which to operate a process) to unexpected conditions of these types would advance the move toward artificial intelligence properties for this controller beyond those which it has today and would provide new thoughts on interpretability and verification for the controller. This work provides theoretical studies which relate nonlinear systems considerations for EMPC to these higher-level concepts using two ideas for EMPC formulations motivated by specific situations related to self-modification of a control design after human perceptions of the process response are received and to controller handling of anomalies.

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