Daniel Navia

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.

Nested Modifier-Adaptation for RTO in the Otto Williams Reactor

Abstract This paper deals with the problem of uncertainty management in real time optimization (RTO). It proposes a new architecture in the modifier-adaptation methodology, reformulating the algorithm as a nested optimization problem with two layers. Using this approach, it is possible to find a point that satisfies the KKT conditions of a process using an inaccurate model, but unlike the original modifier method, with no need to estimate the experimental gradients of the process. The proposed method has been tested in the Otto Williams Reactor considering structural mismatches and perfect and noisy measurements. The results are compared with the previous modifier adaptation methodology using dual control optimization showing that the method finds a KKT point of the process with the advantage that no experimental gradient information is required and with less sensitivity to process noise.

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.

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.

Real-time optimization for a laboratory-scale flotation column

Abstract In this paper, a supervisory layer with real-time optimization (RTO) has been implemented in an experimental laboratory-scale flotation column for copper concentration. A two-stage and modifier adaptation (MA) methodology for RTO has been compared under structural, experimental and dynamic uncertainty. In addition, a gradient-free alternative for MA, called nested modifier optimization, has been proposed and tested. The results show that the KKT updates of the MA approach allow the process optimum to be determined under uncertain scenarios, unlike the two-stage approach. From the perspective of gradient modifiers, the performance of the nested methodology is comparable to the dual approach because previous past values are used to update the modifiers without requiring the gradient estimation step. In addition, the interaction of RTO with the regulatory layer must be considered to propose an optimal implementation.

Shared Resources Management by Price Coordination

Abstract This work presents an approach to optimal operation of a system with shared resources based on price coordination. The system consists of three consumer units where oxygen is the shared limited resource. They are operated by local optimizers minimizing local costs where the prices associated to the shared resources, the flows of oxygen from the distribution lines, have different values that are set up by an upper level. This level operates like a market-like mechanism modifying the prices of the consumers according to the demand of the shared resources. The market is asymmetric, and operates like an anti-windup system to correct prices in case a resource is exceeded. Results on simulation of price coordination method are compared with fully decentralized NMPC structure and a centralized one.

Distributed Stochastic Optimization of a Process Plant Start-up

Abstract This paper presents a decentralized solution to the stochastic optimization problems that appear when uncertainty is considered explicitly using a set of scenarios in model based control and optimization. In particular, the paper deals with two-stage optimization problems, where the first-stage solution has to fulfil the constraints for all multiple scenarios simultaneously. To deal with the large size of the problem, a reformulation has been performed solving the optimization in parallel for as many deterministic problems as scenarios are, and coordinating their solutions in order to force a common decision for all of them, using a price-driven methodology followed by a sensitivity-based update. The methodology is illustrated with an example involving the optimal start-up of a hydrodesulphurization plant.

Laboratory Plant of a Gas Distribution Network

Abstract This work shows the implementation of a laboratory – scale oxygen distribution plant built with the aim of being used as a benchmark for control and optimization of networked processes. The plant emulates the architecture and the main problems that can be found in real facilities which combine several complex processes linked with shared resources that impose the need of coordinated operation and control. The paper describes the plant and the corresponding models and its control system. Additionally several applications and test are suggested to be performed, including methods for optimization of large scale systems handling uncertain behaviour of process, parameter estimation techniques and distributed model predictive control.

A Proposal to Include the Information of Disturbances in Modifier Adaptation Methodology for Real Time Optimization

Abstract This work presents an extension of the Modifier-Adaptation (MA) methodology for Real-Time Optimization (RTO), to include the available information of uncontrolled input variables in the estimation of plant gradients. The idea is to extend the applicability of this method for processes where disturbances affect the quantities involved in the necessary conditions of optimality of the process. The implementation was carried out in a simulated flotation column, including the effect disturbances coming from of contiguous units. The dual approach was used to estimate the process gradients. Results show that the system is able to follow the trajectory of the real optimum of the process under continuously changing scenario, unlike traditional MA.

Modifier-Adaptation Based on Transient Measurements Applied to a Laboratory-Scale Flotation Column

Abstract Real-Time Optimization (RTO) is not always able to achieve optimal process operation due to the presence of significant uncertainty. To overcome this issue, the economic optimization problem is modified following the Modifier-Adaptation methodology (MA) to bring the process to a point that satisfies the necessary optimality conditions (NCO) despite the presence of uncertainty. Traditionally, modifiers are updated only at the steady state using static information. This may imply a slow convergence of MA, or undesired interactions with side units. This issue is considered in this paper, where a transient-based methodology (TMA) is applied to estimate the modifiers in a laboratory-scale flotation column for copper concentration. As flotation columns interact with up and down stream units, waiting several steady states to find the optimum of the process can produce undesired effects. Experimental results show that TMA allows saving 10 steady states to find a point that satisfies the NCO of the process which is translated into a 64% reduction in time compared to dual MA (DMA).