Economic MPC with Modifier Adaptation using Transient Measurements

Producción CientíficaThis paper presents a method to estimate process dynamic gradients along the transient that combined with the idea of Modifier Adaptation (MA) improves the economic cost fuction of the examples presented. The gradient estimation method, called TMA, aims to reduce the large convergence time required to traditional MA in processes of slow dynamics. TMA is used with an economic predictive control with MA (eMPC+TMA) and was applied in two case studies: a simulation of the Williams-Otto reactor and a hybrid laboratory plant based on the Van de Vusse reactor. The results show that eMPC+TMA could reach the plant real steady-state optimum despite process-model mismatch, due to the inclusion of the effect of process dynamics in the TMA algorithm. Despite the estimation errors, the proposed methodology improved the profit of the experimental case study, with respect to the use of an eMPC with no modifiers, by about 20% for the unconstrained case, and by 130% in the constrained case.Junta de Castilla y León (CLU 2017-09 and UIC 233)FEDER - AEI (PGC2018-099312-B-C31

Nonlinear Estimation for Model Based Fault Diagnosis of Nonlinear Chemical Systems

Nonlinear estimation techniques play an important role for process monitoring since some states and most of the parameters cannot be directly measured. There are many techniques available for nonlinear state and parameter estimation, i.e., extended Kalman filter (EKF), unscented Kalman filter (UKF), particle filtering (PF) and moving horizon estimation (MHE) etc. However, many issues related to the available techniques are to be solved. This dissertation discusses three important techniques in nonlinear estimation, which are the application of unscented Kalman filters, improvement of moving horizon estimation via computation of the arrival cost and different implementations of extended Kalman filters. First the use of several estimation algorithms such as linearized Kalman filter (LKF), extended Kalman filter (EKF), unscented Kalman filter (UKF) and moving horizon estimation (MHE) are investigated for nonlinear systems with special emphasis on UKF as it is a relatively new technique. Detailed case studies show that UKF has advantages over EKF for highly nonlinear unconstrained estimation problems while MHE performs better for systems with constraints. Moving horizon estimation alleviates the computational burden of solving a full information estimation problem by considering a finite horizon of the measurement data; however, it is non-trivial to determine the arrival cost. A commonly used approach for computing the arrival cost is to use a first order Taylor series approximation of the nonlinear model and then apply an extended Kalman filter. The second contribution of this dissertation is that an approach to compute the arrival cost for moving horizon estimation based on an unscented Kalman filter is proposed. It is found that such a moving horizon estimator performs better in some cases than if one based on an extended Kalman filter. It is a promising alternative for approximating the arrival cost for MHE. Many comparative studies, often based upon simulation results, between extended Kalman filters (EKF) and other estimation methodologies such as moving horizon estimation, unscented Kalman filter, or particle filtering have been published over the last few years. However, the results returned by the extended Kalman filter are affected by the algorithm used for its implementation and some implementations of EKF may lead to inaccurate results. In order to address this point, this dissertation investigates several different algorithms for implementing extended Kalman filters. Advantages and drawbacks of different EKF implementations are discussed in detail and illustrated in some comparative simulation studies. Continuously predicting covariance matrix for EKF results in an accurate implementation. Evaluating covariance matrix at discrete times can also be applied. Good performance can be expected if covariance matrix is obtained from integrating the continuous-time equation or if the sensitivity equation is used for computing the Jacobian matrix

Comparison of two identification models used in adaptive control of continuous-stirred tank reactor

The goal of this paper is to compare two identification methods continuous-time and discrete-time. The continuous-time identification model is more accurate but not very suitable for on-line identification. This disadvantage was overcome with the use of differential filters. On the other hand, discrete-time identification model has is more suitable for identification but less accurate. Compromise can be found in the delta model as a special type of the discrete-time model parameters of which are related to the sampling period. The adaptive approach is based on the choice of the External Linear Model, parameters of which are identified recursively which satisfies the adaptivity of this system. Proposed control strategy was applied on the mathematical model of the Continuous Stirred-Tank reactor as a typical nonlinear lumped-parameters system used in the industry

Integration of economic MPC and modifier adaptation in slow dynamic processes with structural model uncertainty

Real-Time Optimization, known by its acronym RTO, uses a steady-state nonlinear model of the process to optimize a plant's economic objective subject to process constraints. This is the technology currently used in commercial RTO applications. However, no model is a perfect representation of reality, and structural and parametric model uncertainties make the optimum calculated by RTO do not match those of the actual process. One way to address this problem is to modify the optimization problem so that the Necessary Conditions of Optimality (NCO) of the problem match those of the actual plant. This strategy is known as Modifier Adaptation (MA) methodology. The MA methodology requires the gradient values of the real plant and the model to calculate the modifiers. There are several ways to accurately estimate model gradients, but estimation of the real process gradients are more difficult. In addition, the need to use stationary data is a limitation of RTO with MA, especially for slow dynamic systems. This thesis focuses on ways to mitigate the weaknesses of RTO and MA unification that we consider most critical for its application in industry. To this end, it is proposed to couple the RTO and control layers with the concepts of the Modifier Adaptation (MA) methodology by estimating process gradients or directly the MA modifiers using transient data.La Optimización en Tiempo Real, conocida por la sigla en inglés RTO usa un modelo no lineal estacionario del proceso para optimizar un objetivo económico de la planta frente a restricciones del proceso. Esta es la tecnología usada actualmente por las aplicaciones comerciales de RTO. Sin embargo, ningún modelo es una representación perfecta de la realidad y las incertidumbres estructurales y paramétricas de los modelos hacen que los óptimos calculados por la RTO no coincidan con los del proceso real. Una forma de abordar este problema es modificar el problema de optimización de modo que las condiciones necesarias de optimalidad del problema (NCO) se igualen a los de la planta real. Esa estrategia es conocida como la metodología de adaptación de modificadores (Modifier Adaptation, MA). La metodología MA necesita de los valores de gradiente de la planta real y del modelo para el cálculo de los modificadores. Hay diversas formas de estimar los gradientes del modelo con exactitud, sin embargo, la estimación en proceso real es más difícil. Además, la necesidad de usar datos en estacionario sigue siendo una limitación fundamental de la RTO con MA, principalmente para sistemas dinámicos lentos. Esta tesis se enfoca en formas de mitigar las debilidades de la unificación RTO y MA que consideramos las más críticas para su aplicación en la industria. Para eso se propone que las capas de RTO y control se unan con los conceptos de la metodología de adaptación de modificadores (Modifier Adaptation, MA) estimando los gradientes de proceso o directamente los modificadores de MA usando datos de transitorio.Escuela de DoctoradoDoctorado en Ingeniería Industria