Alejandro Marchetti

A new dual modifier-adaptation approach for iterative process optimization with inaccurate models

Abstract In order to deal with plant-model mismatch, iterative process optimization schemes use some adaptation strategy based on measurements. The modifier-adaptation approach consists in performing first-order corrections of the cost and constraint functions in the model-based optimization problem. The approach has the ability to converge to the true process optimum but the first-order corrections require the experimental estimation of the process gradients. Dual modifier-adaptation algorithms estimate the gradients by finite difference approximation based on the measurements obtained at the current and past operating points. In order to guarantee the accuracy of the estimated gradients a constraint is added to the optimization problem in order to position the next operating points with respect to the previous ones. This paper presents an alternative first-order correction, which provides an improved approximation of the cost and constraint functions, together with a new gradient error constraint for use in dual modifier adaptation. By means of the Williams–Otto reactor case study, the new dual modifier-adaptation approach is compared in simulation with a previous approach found in the literature showing faster convergence to a neighborhood of the plant optimum.

Robust Real-Time Optimization of a Solid Oxide Fuel Cell Stack

On-line control and optimization can improve the efficiency of fuel cell systems whilst simultaneously ensuring that the operation remains within a safe region. Also, fuel cells are subject to frequent variations in their power demand. This paper investigates the real-time optimization (RTO) of a solid oxide fuel cell (SOFC) stack. An optimization problem maximizing the efficiency subject to operating constraints is defined. Due to inevitable model inaccuracies, the open-loop implementation of optimal inputs evaluated off-line may be suboptimal, or worse, infeasible. Infeasibility can be avoided by controlling the constrained quantities. However, the constraints that determine optimal operation might switch with varying power demand, thus requiring a change in the regulator structure.

A New Dual Modifier-Adaptation Approach for Real-Time Optimization with Inaccurate Models

Abstract In order to deal with plant-model mismatch, real-time optimization schemes use some adaptation strategy based on measurements. The modifier-adaptation approach has the ability to converge to the true process optimum but it requires the experimental estimation of the process gradients. Dual modifier-adaptation algorithms estimate the gradients based on the current and past operating points. This paper presents a new dual modifier-adaptation approach. The approach is compared with a previous approach found in the literature showing faster convergence to a neighborhood of the plant optimum.

REAL-TIME OPTIMIZATION OF CONTINUOUS PROCESSES VIA CONSTRAINTS ADAPTATION

In the framework of process optimization, measurements can be used to compensate for the effect of uncertainty. The method studied in this paper combines a process model and measurements to iteratively improve the operation of continuous processes. Unlike many existing real-time optimization schemes, the measurements are not used to update the process model, but to adapt the constraints in the optimization problem. Upon convergence, all the constraints are respected even in the presence of large model mismatch. Moreover, it is shown that constraints adaptation can handle changes in the set of active constraints. The approach is illustrated, via numerical simulation, for the optimization of a continuous stirred-tank reactor.

Real-Time Optimization via Modifier Adaptation Integrated with Model Predictive Control

Abstract In order to deal with plant-model mismatch, real-time optimization schemes use some adaptation strategy based on measurements. The modifier-adaptation approach is to correct the constraints and gradients in the optimization problem by adapting the values of bias modifiers expressing the difference between the constraints and gradients of the plant and the model. The approach has the ability to converge to the plant optimum but does not guarantee feasibility prior to convergence if the evaluated optimal inputs are applied directly to the plant. In this paper, an approach for integrating modifier adaptation with model predictive control is presented where both automation layers use the same decision variables. The control targets are included as equality constraints in the real-time optimization problem, and are continuously enforced by the model predictive controller. In order to apply modifier adaptation, new gradient modifiers are defined that correct the projected gradients in the tangent space of the equality constraints, rather than the full gradients. An illustrative case study shows the applicability of the approach.

Scale-up of batch processes via decentralized control

The economic environment in the specialty chemicals industry requires short times to market and thus the ability to develop new products and processes very rapidly. This, in turn, calls for large scale-ups from laboratory to production. Due to scale-related differences in operating conditions, direct extrapolation of conditions obtained in the laboratory is often impossible, especially when terminal objectives must be met and path constraints respected. This paper proposes a decentralized control scheme for scaling-up the operation of batch and semi-batch processes. The targets to be reached are either taken directly from laboratory experiments or adjusted to account for production constraints. Some targets are reached on-line within a given run, while others are implemented on a run-to-run basis. The methodology is illustrated in simulation via the scale-up of a semi-batch reactor.

Modifier adaptation with guaranteed feasibility in the presence of gradient uncertainty

Abstract In the context of real-time optimization, modifier-adaptation schemes use estimates of the plant gradients to achieve plant optimality despite plant-model mismatch. Plant feasibility is guaranteed upon convergence, but not at the successive operating points computed by the algorithm prior to convergence. This paper presents a strategy for guaranteeing rigorous constraint satisfaction of all iterates in the presence of plant-model mismatch and uncertainty in the gradient estimates. The proposed strategy relies on constructing constraint upper-bounding functions that are robust to the gradient uncertainty that results when the gradients are estimated by finite differences from noisy measurements. The performance of the approach is illustrated for the optimization of a continuous stirred-tank reactor.

Time-optimal path-following operation in the presence of uncertainty

Path-following tasks, which refer to dynamic motion planning along pre-specified geometric references, are frequently encountered in applications such as milling, robot-supported measurements, and trajectory planning for autonomous vehicles. Different convex and non-convex optimal control formulations have been proposed to tackle these problems for the case of perfect models. This paper analyzes path-following problems in the presence of plant-model mismatch. The proposed adaptation strategies rely on concepts that are well known in the field of real-time optimization. We present conditions guaranteeing that, upon convergence, a minimumtime solution is attained despite the presence of plant-model mismatch. We draw upon a simulated robotic example to illustrate our results.

Real-time Optimization with Estimation of Experimental Gradients

For good performance in practice, real-time optimization schemes need to be able to deal with the inevitable model-mismatch problem. Unlike the two-step schemes combining parameter estimation and optimization, the modifier-adaptation approach uses experimental gradient information and does not require the model parameters to be estimated on-line. The dual modifier-adaptation approach presented in this paper drives the process towards optimality, while paying attention to the accuracy of the estimated gradients. The gradients are estimated from the successive operating points generated by the optimization algorithm. The novelty lies in the development of an upper bound on the gradient estimation error, which is used as a constraint for locating the next operating point. The proposed approach is demonstrated in simulation by the real-time optimization of a continuous reactor.

Real-Time Optimization via Adaptation and Control of the Constraints

In the framework of real-time optimization, measurements are used to compensate for effects of uncertainty. The main approach uses measurements to update the parameters of a process model. In contrast, the constraint-adaptation scheme uses the measurements to bias the constraints in the optimization problem. In this paper, an algorithm combining constraint adaptation with a constraint controller is presented. The former detects shifts in the set of active constraints and passes the set points of the active constraints to the latter. In order to avoid constraint violation, the set points are moved gradually during the iterative process. Moreover, the constraint controller manipulates linear combinations of the original input variables. The approach is illustrated for a simple case study.