D. Sarabia

Aeration control of a wastewater treatment plant using hybrid NMPC

In the operation of wastewater treatment plants a key variable is dissolved oxygen (DO) content in the bioreactors. As oxygen is consumed by the microorganisms, more oxygen has to be added to the water in order to comply with the required minimum dissolved oxygen concentration. This is done using a set of aerators working on/off that represents most of the plant energy consumption. In this paper a hybrid nonlinear predictive control algorithm is proposed, based on economic and control aims. Specifically, the controller minimizes the energy use while satisfying the time-varying oxygen demand of the plant and considering several operation constraints. A parameterization of the binary control signals in terms of occurrence time of events allows the optimization problem to be re-formulated as an nonlinear programming (NLP) problem at every sampling time. Realistic simulation results considering real perturbations data sets for the inlet variables are presented.

Hybrid Control of a Supermarket Refrigeration Systems

This paper presents a non-linear model predictive control (NMPC) of a supermarket refrigeration system. This is a hybrid process involving switching nonlinear dynamics and discrete events, on/off manipulated variables, like valves and compressors, continuous controlled variables like goods temperatures and finally, several operation constraints. The hybrid controller is based on a parameterization of the on/off control signals in terms of time of occurrence of events instead of using directly binary values, on this way, we can reformulate the optimization problem as a NLP problem. A rigorous model of a real supermarket refrigeration system provided by Danfoss is presented as well as results of the hybrid controller operating on it. The paper describes the hybrid process, presents the control problem formulation and provides some results of the proposed approach and comparisons with the traditional control.

A method to coordinate decentralized NMPC controllers in oxygen distribution networks

Abstract This paper deals with the optimal operation of large scale systems composed by local processes liked by shared resources. A decentralized architecture plus a coordinator, which guarantees the satisfaction of the global constraints of the process, is presented. The decomposition of the control problem into smaller ones is based on Lagrangean decomposition and on price coordination methods to update the prices. A coordination method that allows formulating the price assignment as a control problem is presented besides a formulation based on market behaviour. Both approaches are driven by the difference between the total shared resources available and demanded by the local NMPC controllers. One advantage of this approach is that in the low layer only requires adding an extra term in the cost function of the existing NMPC controllers. Moreover, there is no communication between local controllers, only between each local controller and the coordinator.

Handling Infeasibilities in Dual Modifier-Adaptation Methodology for Real-Time Optimization

This work shows an extension of dual-modifier adaptation methodology for RTO to reduce the infeasibilities. The main idea is to add a PI controller that is activated only when the measurements shows a violation in the constraints. Since the dual problem is solved to estimate the gradients of the process, an additional controller must be considered in order to increase the inverse of the condition number of the matrix formed with past values. The methodology presented has been applied in a simulated oxygen consumption plant. The results show that, under modelling mismatch, the method finds the real optimum of the process in a feasible path.

Hybrid control of a mixed continuous-batch process

Abstract This paper deals with a control problem related with a mixed continuous-batch process, a pilot plant of our Lab, where both continuous decisions and scheduling takes place. We tried to find a solution in the framework of non-linear model predictive control formulating the control problem by means of an hybrid model in terms of integer and continuous variables. As the system must be controlled in real-time, mixed integer optimization algorithms proved to be too slow, so, an alternative formulation in terms of real variables was set up. The paper describes the process, the control problem formulation, and the optimization alternatives and provides results of some test for evaluation of the proposed approach.

Improving scenario decomposition algorithms for robust nonlinear model predictive control

Abstract This paper deals with the efficient computation of solutions of robust nonlinear model predictive control problems that are formulated using multi-stage stochastic programming via the generation of a scenario tree. Such a formulation makes it possible to consider explicitly the concept of recourse, which is inherent to any receding horizon approach, but it results in large-scale optimization problems. One possibility to solve these problems in an efficient manner is to decompose the large-scale optimization problem into several subproblems that are iteratively modified and repeatedly solved until a solution to the original problem is achieved. In this paper we review the most common methods used for such decomposition and apply them to solve robust nonlinear model predictive control problems in a distributed fashion. We also propose a novel method to reduce the number of iterations of the coordination algorithm needed for the decomposition methods to converge. The performance of the different approaches is evaluated in extensive simulation studies of two nonlinear case studies.

A comparison between two methods of stochastic optimization for a dynamic hydrogen consuming plant

Abstract The following work shows the application of two methods of stochastic economic optimization in a hydrogen consuming plant: two-stage programming and chance constrained optimization. The system presents two main sources of uncertainty described with a binormal probability distribution function (PDF). Both methods are formulated in the continuous domain. For calculating the probabilistic constraints the inverse mapping method was written as a nested parameter estimation problem. On the other hand, to solve the two stage optimization, a discretization of the PDF in scenarios was applied with a scenario aggregation formulation to take into account the nonanticipativity constraints. Finally, a framework generalizing this solution based on interpolation was proposed. Both optimization methods, two-stage programming and chance constrained optimization, were tested using Monte Carlo simulation in terms of feasibility and optimality for the application considered. The main problem appears to be the large computation times associated.

Hybrid model predictive control of a sugar end section

Abstract This paper deals with the MPC control of an industrial hybrid process where continuous and batch units operate jointly: the crystallization section of a sugar factory. The paper describes a plant-wide predictive controller that takes into account, both, the continuous objectives and manipulated variables, as well as the ones related to the scheduling of the batch units. The MPC is formulated avoiding the use of integer variables, so that a NLP optimization technique could be applied. Simulation results of the controller operation are provided *

Modifier Adaptation methodology based on transient and static measurements for RTO to cope with structural uncertainty

Abstract Optimal process operation is carried out by a Real-Time Optimization (RTO) layer which is not always able to achieve its targets due to the presence of plant-model mismatch. To overcome this issue, the economic optimization problem solved in the RTO is changed following the Modifier Adaptation methodology (MA), which uses plant measurements to find a point that satisfies the necessary optimality conditions (NCO) of an uncertain process. MA proceeds by iteratively adjusting the optimization problem with first and zeroth order corrections, calculated from steady-state information at each RTO execution. This implies a long convergence time. This paper presents a new method based on a recursive identification algorithm to estimate process gradients from transient measurements to speed up the convergence of MA. The proposed approach is implemented in a simulated depropanizer column that incorporates a simplified model in the RTO, reducing by 8 the convergence time compared with traditional MA.

Price-driven Coordination for Distributed NMPC Using a Feedback Control Law

This chapter presents a distributed coordinated control algorithm based on a hierarchical scheme for systems consisting of nonlinear subsystems coupled by input constraints: the bottom layer is composed of several non-linear model predictive controllers (NMPC) working in parallel, and in a top layer, a price-driven coordination technique is used to coordinate these controllers. The price coordination problem is formulated as a feedback control law to fulfill the global constraints that affect all NMPC controllers. To illustrate this approach, the price-driven coordination method is used to control a four-tank process in a distributed manner and is compared with centralized and fully decentralized approaches.