On‐line optimization of constrained multivariable chemical processes

2009

Ind. Eng. Chem. Res.

256

331

The ability of a model-based real-time optimization (RTO) scheme to converge to the plant optimum relies on the ability of the underlying process model to predict the plant’s necessary conditions of optimality (NCO). These include the values and gradients of the active constraints, as well as the gradient of the cost function. Hence, in the presence of plant−model mismatch or unmeasured disturbances, one could use (estimates of) the plant NCO to track the plant optimum. This paper shows how to formulate a modifed optimization problem that incorporates such information. The so-called modifiers, which express the difference between the measured or estimated plant NCO and those predicted by the model, are added to the constraints and the cost function of the modified optimization problem and are adapted iteratively. Local convergence and model-adequacy issues are analyzed. The modifier-adaptation scheme is tested experimentally via the RTO of a three-tank system.

Section: Real-time Optimization With Model Updatementioning

confidence: 99%

mentioning

confidence: 99%

Modifier-Adaptation Methodology for Real-Time Optimization

Marchetti

Chachuat

2009

Ind. Eng. Chem. Res.

256

331

“…Modifier adaptation (MA) is one of a family of techniques (see e.g. Jang et al (1987); Tatjewski (2002); Gao and Engell (2005); Skogestad (2000); Srinivasan and Bonvin (2007)) that combines these two radically different approaches by using experimental data to make up for inconsistencies between the model and the plant. For a more comprehensive introduction to this topic, the reader is invited to refer to a previous paper by the same authors (Costello et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Modifier Adaptation for Constrained Closed-Loop Systems

Costello

François

IFAC Proceedings Volumes

et al. 2014

The steady advance of computational methods makes model-based optimization an increasingly attractive method for process improvement. Unfortunately, the available models are often inaccurate. An iterative optimization method called "modifier adaptation" overcomes this obstacle by incorporating process information into the optimization framework. This paper extends this technique to constrained optimization problems, where the plant consists of a closedloop system but only a model of the open-loop system is available. The degrees of freedom of the closed-loop system are the setpoints provided to the controller, whereas the model degrees of freedom are the inputs of the open-loop plant. Using this open-loop model and process measurements, the proposed algorithm guarantees both optimality and constraint satisfaction for the closed-loop system upon convergence. A simulated CSTR example with constraints illustrates the method.

“…Increased computational power led to the development of the original modelbased algorithm, the so-called two-step approach (Chen and Joseph, 1987;Jang et al, 1987). Two steps are repeated online, namely, parameter estimation to update the model and optimization of the updated model to compute the optimal inputs.…”

Section: Introductionmentioning

confidence: 99%

A Directional Modifier-Adaptation Algorithm for Real-Time Optimization

Costello

François

Journal of Process Control

2016

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 Modifier 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.