Dominique Bonvin

Dynamic optimization of batch processes: II. Role of measurements in handling uncertainty

Abstract The main bottleneck in using optimization at the industrial level is the presence of uncertainty in the form of model mismatch and disturbances. The way uncertainty can be handled constitutes the subject of this series of two papers. The first part dealt with the characterization of the nominal solution and proposed an approach to separate the constraint-seeking from the sensitivity-seeking components of the inputs. This second part reviews various strategies for optimization under uncertainty, namely the robust and measurement-based optimization schemes. A novel scheme is proposed, where optimality is achieved by tracking the necessary conditions of optimality. The different approaches are compared via the simulation of a bioreactor for penicillin production.

Optimal operation of batch reactors—a personal view

Abstract This paper presents a personal, thus necessarily subjective, view of the operation of batch and semi-batch reactors. The emphasis is on safety, product quality and scale-up. Key characteristics of discontinuous reaction systems are discussed, along with the resulting implications for monitoring, control and optimization. The industrial needs are compared with the research solutions proposed by academia. It is argued that, in industry, measurement and modeling issues are often more important than the algorithmic aspects related to the computation of control and optimization strategies. Major challenges and selected research opportunities are discussed.

On the Rank Deficiency and Rank Augmentation of the Spectral Measurement Matrix

Abstract The analysis of spectral measurements using standard factor-analytical (FA) techniques requires the rank of the absorbance matrix to be equal to the number of absorbing species, S. However, in many practical reaction networks, such an assumption does not hold. This paper examines various scenarios where ‘rank deficiency’ can occur. The most important case is when the number of independent reactions, R, is less than S. In such a case, rank analysis can only reveal R and, hence, standard FA techniques will fail. Hence, one possibility is to perform rotation in the reaction-spectra space of dimension R. Another possibility is to augment the rank of the data matrix to S for which two experimental methods are developed. Rank augmentation is performed by (i) multiple process runs and (ii) addition of reactants or products during the reaction. The composite data matrices are of rank S and, hence, suited to factor analysis. The number of necessary runs or additions can be detected by determining the rank of both the original and column-mean-centered data matrices. With rank augmentation, it is possible to determine both the number of independent reactions and the number of absorbing species. Furthermore, the influence on the rank of data pretreatment such as mean centering, normalization, auto-scaling, and differentiation with respect to time or wavelength is examined.

Adaptation Strategies for Real-time Optimization

Challenges in real-time process optimization mainly arise from the inability to build and adapt accurate models for complex physico-chemical processes. This paper surveys different ways of using measurements to compensate for model uncertainty in the context of process optimization. Three approaches can be distinguished according to the quantities that are adapted: model-parameter adaptation updates the parameters of the process model and repeats the optimization, modifier adaptation modifies the constraints and gradients of the optimization problem and repeats the optimization, while direct input adaptation turns the optimization problem into a feedback control problem and implements optimality via tracking of appropriate controlled variables. This paper argues in favor of modifier adaptation, since it uses a model parameterization and an update criterion that are well tailored to meeting the KKT conditions of optimality. These considerations are illustrated with the real-time optimization of a semi-batch reactor system.

Implementation of adaptive optimal operation for a semi-batch reaction system

Abstract This paper presents the results of on-line optimization of the acetoacetylation of pyrrole with diketene in a laboratory-scale reactor. In addition to the desired reaction of pyrrole to 2-acetoacetyl pyrrole, there are several undesired side reactions. The selectivity can be controlled by adjusting the feed rate of diketene to a given solution of pyrrole. Variable amounts of impurities in the crude pyrrole imply different rate constants for each batch. Consequently, on-line estimation of some rate constants and subsequent adjustment of the feeding strategy through dynamic optimization are necessary to reach a desired objective. The nonlinear differential-algebraic optimization problems for both the estimation and the optimization are transformed into nonlinear algebraic optimization problems (AOP). Due to the different characteristics of the estimation and optimization problems, the resulting AOPs are solved using different techniques. Successive quadratic programming is applied to solve the AOP in the estimation, and successive linear programming is used for the optimization. Both are fast infeasible-path methods. The estimation and optimization problems are solved sequentially at given points in time. Results are presented for the minimization of batch time subject to endpoint constraints with respect to yield and two of the concentrations. Runs with and without on-line optimization are compared to demonstrate the effectiveness of the on-line strategy.

Optimal operation of fed-batch fermentations via adaptive control of overflow metabolite

The maximization of biomass productivity in the fed-batch fermentation of Saccharomyces cerevisiae is analyzed. Due to metabolic bottleneck, often attributed to limited oxygen capacity, ethanol is formed when the substrate concentration is above a critical value, which results in a decrease in biomass productivity. Thus, to maximize the production of biomass, the substrate concentration should be kept at the critical value. However, this value is unknown a priori and may change from experiment to experiment. A way to overcome this lack of knowledge is to allow the cells to produce a very small amount of ethanol. This way, the problem of maximizing the production of biomass is converted into that of regulating the concentration of ethanol, for which cell growth can be viewed as a perturbation. A novel adaptive control methodology based on the internal model principle is used to maintain the desired ethanol setpoint and reject the perturbation. Only a single parameter needs to be estimated on-line. Experimental results demonstrate the effectiveness of the proposed control methodology.

Optimization of Batch Reactor Operation under Parametric Uncertainty - Computational Aspects

Reference LA-ARTICLE-1995-002View record in Web of Science Record created on 2004-11-26, modified on 2017-05-10

A feedback-based implementation scheme for batch process optimization

The terminal-cost optimization of a control–affine nonlinear system leads to a discontinuous solution that can be characterized in a piecewise manner. To implement such an optimal trajectory despite disturbances and parametric uncertainty, a cascade optimization scheme is proposed in this paper, where optimal reference signals are tracked. Optimality is achieved by the appropriate definition of reference signals (input bounds, state constraints, or switching functions) to track in various sub-intervals. Furthermore, conservatism is introduced into the optimization problem to ensure satisfaction of path constraints in the presence of uncertainty. Finally, the proposed cascade optimization scheme is illustrated on a simulation of a fed-batch penicillin fermentation plant.

Iterative correlation-based controller tuning with application to a magnetic suspension system

Iterative tuning of the parameters of a restricted-order controller using the data acquired in closed-loop operation seems to be a promising idea, especially for tuning PID controllers in industrial applications. In this paper, a new tuning approach based on decorrelation is proposed. The basic idea is to make the output error between the designed and achieved closed-loop systems uncorrelated with the reference signal. The controller parameters are calculated as the solution of correlation equations involving instrumental variables. Different choices of instrumental variables are proposed and compared via simulation. The stochastic properties of the correlation approach are compared with those of standard IFT using Monte-Carlo simulation. The proposed approach is also implemented on an experimental magnetic suspension system, and excellent performance using only a few real-time experiments is achieved.

Brief paper: Global stabilization of an inverted pendulum-Control strategy and experimental verification

The problem of swinging up an inverted pendulum on a cart and controlling it around the upright position has traditionally been treated as two separate problems. This paper proposes a control strategy that is globally asymptotically stable under actuator saturation and, in addition, locally exponentially stable. The proposed methodology, which performs swing up and control simultaneously, uses elements from input-output linearization, energy control, and singular perturbation theory. Experimental results on a laboratory-scale setup are presented to illustrate the approach and its implementation.