Use of Transient Measurements for Static Real-Time Optimization

Dominique Bonvin, Tafarel de Avila Ferreira, Grégory François, Alejandro Gabriel Marchetti
2017
Article de conférence

Résumé

Modifier adaptation (MA) is a real-time optimization (RTO) method characterized by its ability to enforce plant optimality upon convergence despite the presence of model uncertainty. The approach is based on correcting the available model using gradient estimates computed at each iteration. MA uses steady-state measurements and solves a static optimization problem. Hence, after every input change, one typically waits for the plant to reach steady state before measurements are taken. With many iterations, this can make convergence to the plant optimum rather slow. Recently, an approach that uses transient measurements for steady-state MA has been proposed. This way, plant optimality can be reached in a single transient operation. This paper proposes to improve this approach by using a dynamic model to process transient measurements for gradient computations. The approach is illustrated through the simulated example of a CSTR. Furthermore, the proposed method is less dependent on the choice of the RTO period. The time needed to reach plant optimality is of the order of the plant settling time, whereas several transitions to steady state would have been necessary using the standard static MA scheme.

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https://infoscience.epfl.ch/record/222922?ln=fr

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Optimization of industrial processes aims at minimizing operating cost or maximizing economic profit while respecting plant constraints. In process industry, real-time optimization (RTO) is often considered to ensure optimal plant operation and constraint satisfaction. Solid-oxide fuel-cell (SOFC) devices oxidize fuels such as hydrogen and methane to produce electric energy through electrochemical reactions at very high efficiency. To reduce the emission of carbon dioxide and the high cost of non-renewable energies, fuel cells have become popular as an alternative energy source with a wide range of applications. The optimal operation of SOFC systems, while being subjected to changing operating conditions such as variations in the electrical power demand, remains a challenging problem in the field of control and optimization. In addition, these types of devices are characterized by slow dynamics and drifts such as degradation. This motivates the use of real-time optimization for optimizing and controlling the operation of SOFC systems. The most popular RTO technique in industry is the so-called two-step approach. This approach consists in estimating the model parameters based on measurements by solving a parameter estimation problem, and computing the next operating point by solving an optimization problem using the updated model. However, this technique is highly dependent on model accuracy and tends to fail in the presence of structural plant-model mismatch. As an alternative, modifier adaptation has been developed to enforce convergence to the plant optimum even in presence of structural plant-model mismatch. Since plant optimality is often characterized by active constraints, it is possible to use a simpler version of modifier adaptation, called constraint adaptation (CA). This approach corrects the constraints in the model-based optimization problem by means of bias terms computed from the differences between the measured and predicted values of the constraints. The active plant constraintsâi.e. the intersection of the constraints where the plant opti- mum liesâfor each mode of operation is typically known from experience. Therefore, as the optimum of SOFC systems typically lies on active plant constraints, we can apply constraint adaptation. One of the drawbacks of static RTO is the fact that it is necessary to wait until the plant reaches its steady state. Since this may be inappropriate for slow processes, we propose an RTO approach that can speed up the procedure by using transient measurements combined with a dynamic tendency model. In this work, we apply constraint adaptation combined with transient measurements and a dynamic model to experimental SOFC systems. The proposed approach is applied to two SOFC systems: (i) an SOFC system with 6 cells that consists of both hardware and software components; (ii) a commercial SOFC system named BlueGEN. The results obtained are very promising. For both systems, the proposed approach can reach the power demand much faster than the time it takes for the process to settle to steady state. The optimizer is quick at finding and tracking the correct set of active constraints, thus avoiding large constraint violations. In addition, we study the effect of the RTO period on the convergence rate. Finally, we show that CA acts simultaneously as a controller and an optimizer that is able to efficiently detect and track the correct set of active constraints.

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Use of Transient Measurements for Real-Time Optimization via Modifier Adaptation

Dominique Bonvin, Grégory François

Real-time optimization (RTO) methods use measurements to offset the effect of uncertainty and drive the plant to optimality. Explicit RTO schemes, which are characterized by solving a static optimization problem repeatedly, typically require multiple iterations to steady state. In contrast, implicit RTO methods, which do not solve an optimization problem explicitly, can use transient measurements and gradient control to bring the plant to steady state optimality in a single iteration, provided the set of active constraints is known. This paper investigates the explicit RTO scheme “modifier adaptation” (RTO-MA) and proposes a framework that uses transient measurements. Convergence to the true plant optimum can be achieved in a single iteration provided the plant gradients can be estimated appropriately, for which we propose a linearization-based method. The approach is illustrated through the simulated example of a continuous stirred-tank reactor. It is shown that the time needed for convergence is of the order of the plant settling time, while more than five iterations to steady state are required when MA is applied in its classical form. In other words, RTO-MA is able to compete in performance with RTO schemes based on gradient control, with the additional ability to handle process constraints.

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Real-time optimization (RTO) methods use measurements to offset the effect of uncertainty and drive the plant to optimality. RTO schemes differ in the way measurements are incorporated in the optimization framework. Explicit RTO schemes solve a static optimization problem repeatedly, with each iteration requiring transient operation of the plant to steady state. In contrast, implicit RTO methods use transient measurements to bring the plant to steady-state optimality in a single iteration, provided the set of active constraints is known. This paper considers the explicit RTO scheme "modifier adaptation" (MA) and proposes a framework that allows using transient measurements for the purpose of steady-state optimization. It is shown that convergence to the plant optimum can be achieved in a single transient operation provided the plant gradients can be estimated accurately. The approach is illustrated through the simulated example of a continuous stirred-tank reactor. The time needed for convergence is of the order of the plant settling time, while more than five iterations to steady state are required with conventional static MA. In other words, MA using transient information is able to compete in performance with RTO schemes based on gradient control, with the additional ability to handle plant constraints.

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