On Improving the Efficiency of Modifier Adaptation via Directional Information

In real-time optimization, the solution quality depends on the model ability to predict the plant Karush–Kuhn–Tucker (KKT) conditions. In the case of non-parametric plant-model mismatch, one can add input-affine modifiers to the model cost and constraints as is done in modifier adaptation (MA). These modifiers require estimating the plant cost and constraint gradients. This paper discusses two ways of reducing the number of input directions, thereby improving the efficiency of MA in practice. The first approach capitalizes on the knowledge of the active set to reduce the number of KKT conditions. The second approach determines the dominant gradients using sensitivity analysis. This way, MA reaches near plant optimality efficiently by adapting the first-order modifiers only along the dominant input directions. These approaches allow generating several alternative MA schemes, which are analyzed in terms of the number of degrees of freedom and compared in a simulated study of the Williams–Otto plant.Fil: Rodrigues, D.. Instituto Superior Tecnico; PortugalFil: Marchetti, Alejandro Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaFil: Bonvin, D.. Ecole Polytechnique Federale de Lausanne; Franci

Modifier Adaptation as a Feedback Control Scheme

As a real-time optimization technique, modifier adaptation (MA) has gained much significance in recent years. This is mainly due to the fact that MA can deal explicitly with structural plant-model mismatch and unknown disturbances. MA is an iterative technique that is ideally suited to real-life applications. Its two main features are the way measurements are used to correct the model and the role played by the model in actually computing the next inputs. This paper analyzes these two features and shows that, although MA computes the next inputs via numerical optimization, it can be viewed as a feedback control scheme, that is, optimization implements tracking of the plant Karush-Kuhn-Tucker (KKT) conditions. As a result, the role of the model is downplayed to the point that model accuracy is not an important issue. The key issues are gradient estimation and model adequacy, the latter requiring that the model possesses the correct curvature of the cost function at the plant optimum. The main role of optimization is to identify the proper set of controlled variables (the active constraints and reduced gradients) as these might change with the operating point and disturbances. Thanks to this reduced requirement on model accuracy, MA is ideally suited to drive real-life processes to optimality. This is illustrated through two experimental systems with very different optimization features, namely, a commercial fuel-cell system and an experimental kite setup for harnessing wind energy.Fil: Marchetti, Alejandro Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaFil: de Avila Ferreira, T.. Ecole Polytechnique Federale de Lausanne; FranciaFil: Costello, Sergio Gustavo. Ecole Polytechnique Federale de Lausanne; FranciaFil: Bonvin, Dominique. Ecole Polytechnique Federale de Lausanne; Franci

Modifier adaptation for process optimization with uncertainty

La gestión óptima de procesos suele realizarse en la capa de control RTO, que basándose en modelos del proceso y métodos de optimización proporciona las directrices óptimas. Sin embargo, los modelos nunca reflejan fielmente la realidad por lo que el óptimo calculado puede no corresponder al óptimo del proceso. La metodología adaptación de modificadores utiliza medidas para estimar gradientes y calcular modificadores del problema de optimización para conducir el proceso a su punto óptimo de operación. Sin embargo, presenta limitaciones como la dimensión del problema con respecto al número de variables de decisión y restricciones que aumentan los modificadores necesarios ralentizando la convergencia. La tesis presenta una formulación para que el número de modificadores dependa únicamente del número de entradas del proceso. Otra es la necesidad de esperar al estacionario para actualizar los modificadores. La tesis propone el uso de medidas transitorias para estimar los gradientes sin esperar al estacionario.Departamento de Ingeniería de Sistemas y AutomáticaDoctorado en Ingeniería Industria

On enforcing the necessary conditions of optimality under plant-model mismatch - What to measure and what to adapt?

Industrial processes are run with the aim of maximizing economic profit while simultaneously meeting process-critical constraints. To this end, model-based optimization can be performed to ensure optimal plant operations. Usually, inevitable model inaccuracies are dealt by collecting the plant measurements at the local operating conditions in order to adapt model parameters, followed by numerical re-optimization. This iterative two-step procedure often results in a sub-optimal solution, since the models are typically not designed for optimization. Modifier Adaptation (MA) is a Real-Time Optimization (RTO) technique that directly adds the affine-correction terms to the model. The affine corrections are parametrized in modifiers that are tailored to the optimization needs. This enables modifier adaptation to guarantee, upon convergence, matching the plant and the modified model's optimality conditions. However, computing the modifiers requires estimates of the plant gradients that are obtained via expensive plant experiments. The experimental cost can be reduced by relying more on the model of the considered plant. For example, Directional Modifier Adaptation (DMA) relies on offline-computed local parametric sensitivity analysis performed on the gradient of the Lagrangian function of the model resulting in reduced number of input directions that describe the gradient uncertainty in the model. Thereby, plant gradients are estimated only in a low-dimensional space of privileged input directions considerably reducing the experimental costs. However, local sensitivity analysis is often ineffective when the gradient of the model is considerably nonlinear in parameters. This thesis proposes an online procedure based on global sensitivity analysis for finding the most promising privileged directions that adequately compensates for the model deficiencies in predicting the plant optimality conditions. The discovered privileged directions are such that, upon parametric perturbations, the gradient varies a lot along the privileged directions and varies only a little along the remaining input directions. Consequently, the gradients of the model cost and constraints are corrected only along the privileged directions by adapting modifiers. The resulting methodology is named as Active Directional Modifier Adaptation (ADMA). Several simulation studies conducted show that the proposed approach reaches the near-optimality conditions at a considerably reduced experimental cost. In addition, this thesis attempts to establish a direct relation between the optimality conditions and the parameters of a given model. Model parameters are analyzed to discover mirror parameters that mimic the behavior of modifiers in influencing the optimality conditions. It is proposed to adapt mirror parameters instead of modifiers yielding the benefit of both, modifier adaptation in enforcing optimality conditions and of parameter adaptation in better noise handling and convergence. Moreover, it is investigated how to establish the synergies between privileged input directions with model parameters in order to reduce experimental efforts. The steady-state optimization of a simulated chemical process shows that the privileged directions and the selected parameters work together to reach near-optimal performance. Finally, the study on the power maximization of flying kites leads to the development of trust-region based ADMA method to better control the input step size

Offset-free economic mpc based on modifier adaptation: Investigation of several gradient-estimation techniques

Various offset-free economic model predictive control schemes that include a disturbance model and the modifier-adaptation principle have been proposed in recent years. These schemes are able to reach plant optimality asymptotically even in the presence of plant–model mismatch. All schemes are affected by a major issue that is common to all modifier-adaptation formulations, namely, plant optimality (note that convergence per se does not require perfect plant gradients) requires perfect knowledge of static plant gradients, which is a piece of information not known in most practical applications. To address this issue, we present two gradient-estimation techniques, one based on Broyden’s update and the other one on linear regression. We apply these techniques for the estimation of either the plant gradients or the modifiers directly. The resulting economic MPC schemes are tested in a simulation and compared on two benchmark examples of different complexity with respect to both convergence speed and robustness to measurement noise

Handling Uncertainties in Process Optimization

Esta tesis doctoral presenta el estudio de técnicas que permiten manejar las incertidumbres en la optimización de procesos, desde el punto de vista del comportamiento aleatorio de las variables y de los errores en los modelos utilizados en la optimización. Para el tratamiento de las variables inciertas, se presenta la aplicación de la Programación de dos Etapas y Optimización Probabilística a un proceso de hidrodesulfuración. Los resultados permiten asegurar factibilidad en la operación, independiente del valor que tome la variable aleatoria dentro de su distribución de probabilidad. Acerca del manejo de la incertidumbre derivada del conocimiento parcial del proceso, se ha estudiado el método de Optimización en Tiempo Real con adaptación de modificadores, proponiendo mejoras que permiten: (1) evitar infactibilidades en su evolución, (2) obtener el óptimo real del proceso sin necesidad de estimar sus gradientes y (3) identificar las limitaciones para su aplicación en sistemas dinámicos de horizonteDepartamento de Ingeniería de Sistemas y Automátic

A Directional Modifier-Adaptation Algorithm for Real-Time Optimization

The steady advances of computational methods make model-based optimization an increasingly attractive method for process improvement. Unfortunately, the available models are often inaccurate. The traditional remedy is to update the model parameters, but this generally leads to a difficult parameter estimation problem that must be solved on-line. In addition, the resulting model may poorly represent the plant when there is structural mismatch between the two. The iterative optimization method called Modifier Adaptation overcomes these obstacles by directly incorporating plant measurements into the optimization framework, principally in the form of constraint values and gradients. However, the experimental cost (i.e. the number of experiments required) to estimate these gradients increases linearly with the number of process inputs, which tends to make the method intractable for processes with many inputs. This paper presents a new algorithm, called Directional Modier Adaptation, that overcomes this limitation by only estimating the plant gradients in certain privileged directions. It is proven that plant optimality with respect to these privileged directions can be guaranteed upon convergence. A novel, statistically optimal, gradient estimation technique is developed. The algorithm is illustrated through the simulation of a realistic airborne wind-energy system, a promising renewable energy technology that harnesses wind energy using large kites. It is shown that Directional Modifier Adaptation can optimize in real time the path followed by the dynamically flying kite