Jan Van Impe

Tuning of predictive controllers for drinking water networked systems

Abstract In this paper, two tuning strategies for a multi-objective predictive controller applied to a drinking water network (DWN) are proposed. A control-oriented DWN model is briefly reviewed, together with its management objectives. A comparison of methods to explore the Pareto front of the multi-objective optimisation (MOO) problem behind the predictive controller is presented with an effective normalisation method for the model predictive control (MPC) objectives. The proposed tuning strategies, applied to a real-life case study, are compared. Finally, simulation results show that the proposed MPC tuning strategies outperform the baseline results.

Multi-objective optimal control of dynamic bioprocesses using ACADO Toolkit

The optimal design and operation of dynamic bioprocesses gives in practice often rise to optimisation problems with multiple and conflicting objectives. As a result typically not a single optimal solution but a set of Pareto optimal solutions exist. From this set of Pareto optimal solutions, one has to be chosen by the decision maker. Hence, efficient approaches are required for a fast and accurate generation of the Pareto set such that the decision maker can easily and systematically evaluate optimal alternatives. In the current paper the multi-objective optimisation of several dynamic bioprocess examples is performed using the freely available ACADO Multi-Objective Toolkit (http://www.acadotoolkit.org). This toolkit integrates efficient multiple objective scalarisation strategies (e.g., Normal Boundary Intersection and (Enhanced) Normalised Normal Constraint) with fast deterministic approaches for dynamic optimisation (e.g., single and multiple shooting). It has been found that the toolkit is able to efficiently and accurately produce the Pareto sets for all bioprocess examples. The resulting Pareto sets are added as supplementary material to this paper.

Robust optimal control of a biochemical reactor with multiple objectives

Abstract This paper studies the optimal control of a fed-batch fermentor with conflicting productivity and yield objectives under uncertainty. To generate the robustified Pareto sets for different uncertainty levels, a novel scalarisation based multi-objective approach (i.e., normalised normal constraint) is combined with a recent linearisation based robust optimal control approximation method. This combination allows the use of fast gradient based optimisation routines and ensures an accurate and efficient Pareto set generation.

Robust Optimal Experiment Design: A Multi-Objective Approach

Abstract Optimal Experiment Design (OED) is an indispensable tool in order to reduce the amount of labour and cost intensive experiments in the modelling phase. The unknown parameters are often non-linearly present in the dynamic process models. This means that the Fisher Information Matrix also depends on the current guess for the parameters. In the early stage of the modelling phase these estimates are often highly uncertain. So designing an optimal experiment without taking this uncertainty into account is troublesome. In order to obtain an informative experiment, a robust optimisation approach is necessary. In recent work a formulation using an implicit weighted sum approach is proposed where the objective function is split in a nominal optimal experiment design part and a robust counterpart. This weighted sum has well known drawbacks in a Multi-Objective Optimisation approach. In this work these objectives are studied using advanced methods like the Normal Boundary Intersection and the Normalised Normal Constraint. In this way, the experimenter gets an overview of the different experiments possible. Furthermore, in past work the necessary third order derivatives are approximated using a finite different approach. The results in this work are obtained using exact third order and fourth order derivatives by exploiting the symbolic and automatic derivation methods implemented in the ACADO-toolkit.

Numerical strategies for optimal experimental design for parameter identification of non-linear dynamic (Bio-)chemical processes

Abstract The problem of optimal experimental design (OED) for parameter estimation of non-linear dynamic systems is considered. It is shown how this problem can be formulated as a dynamic optimization (optimal control) problem where the performance index is usually a scalar function of the Fisher informatioin matrix. Numerical solutions can be obtained using direct methods, which transform the original problem into a non-linear programming (NLP) problem via discretizations. However, due to the frequent non-smoothness of the cost functions, the use of gradient-based methods to solve this NLP might lead to local solutions. Stochastic methods of global optimization are suggested as robust alternatives. A case study considering the OED for parameter estimation in a fed-batch bioreactor is used to illustrate the performance and advantages of two selected stochastic algorithms.

A Tutorial on Numerical Methods for State and Parameter Estimation in Nonlinear Dynamic Systems

In this chapter we provide a tutorial on state of the art numerical methods for state and parameter estimation in nonlinear dynamic systems. Here, we concentrate on the case that the underlying models are based on first-principles, giving rise to systems of ordinary differential equations (ODEs). As a general introduction the different dynamic model types, the generic modeling cycle and several approaches for dynamic optimization, i.e., optimization problems with dynamic systems as constraints, are briefly mentioned. Then, the estimation problem is posed as a maximum likelihood dynamic optimization problem. Afterwards, we review Multiple Shooting techniques and generalized Gauss-Newton methods for general least-squares and L1-norm optimization problems and discuss the benefits of the recently developed Lifted Newton Method in the context of state and parameter estimation. Finally, we present an illustrative example involving the estimation of the states and parameters of a pendulum using the freely available software environment ACADO Toolkit in which many of the discussed algorithms are implemented.

Multi-objective optimisation approach to optimal experiment design in dynamic bioprocesses using ACADO toolkit

Abstract Mathematical models are valuable tools for optimizing dynamic biochemical processes. However, experimental data collection is often labour and cost intensive and can give rise to production losses. The current paper studies the trade-offs between objectives for production and optimally designing experiments in view of parameter estimation for a bioreactor benchmark. Recent deterministic multi-objective optimal control approaches (i.e., the freeware toolkit ACADO Multi-objective www.acadotoolkit.org ) are used to efficiently produce the set of trade-off or so-called Pareto optimal solutions. These trade-offs are clearly reflected when the obtained optimal control solutions are exploited to estimate the parameters from virtual experiments, while also trying to maximise the biomass production.

Conceptual modelling and optimization of jacketed tubular reactors for the production of LDPE

Abstract This paper deals with the model based optimization of tubular reactors for the production of LDPE. Due to the high complexity, solving an optimization problem of an industrial application is not straightforward. Often researchers seek the shortest way to reach their final goal by going directly to the development of a high-complexity model and optimize this with respect to a certain objective. Although this approach seems the fastest way to success, it can be a bumpy road with a lot of dead ends. Therefore, a divide and conquer strategy is adopted, i.e., first develop a conceptual low-complexity model, set up the optimization problem and then use the obtained knowledge during the optimization of more complex models. The aim of this paper is to give the results of the three steps which have to be accomplished in order to achieve this subgoal. First, the multizone process of LDPE production is modelled as a sequence of conceptual modules which simulate the steady-state characteristics of one reaction and cooling zone. Then, this model is fitted to industrial data such that it quantitatively describes the real process. Finally, a multiple objective design optimization problem is formulated, i.e., where along the reactor and which amount of initiator has to be injected to maximize the profit at different economic situations.

A general method to predict pH and lactic acid dissociation during fermentation processes

Abstract During food fermentation processing, the biochemical activity of microbial starter cultures is exploited to obtain a product with optimal sensorial quality, stability and safety. This activity principally involves the production of lactic acid. To develop a suitable mathematical model of the fermentation process, the typicaltime-dependent profile of pH and undissociated lactic acid should be incorporated. This contribution introduces a novel, robust computation method for the acidifying behaviour of lactic acid in a complex growth medium. In combination with a model from literature for microbial growth and lactic acid production, the method is successfully appliedto experimental data of Lactococcus lactis SL05.

Model based optimisation of tubular reactors for LDPE production

This paper presents a study on the model based optimisation of an industrial tubular reactor for the production of low-density polyethylene (LDPE). First a detailed reactor simulator is presented. Second, a well-posed optimisation problem is formulated. To this end, an economic cost function consisting of conversion and energy terms is derived and constraints due to operational and safety reasons are added. The degrees of freedom involve parameters such as the initiator feed rates, the cooling water temperatures and the switching position between hot and cold cooling water. The optimal design of a dual water circuit operating at a low and a high temperature achieved in this work allows significant improvements in conversion with respect to the reference case of a single temperature circuit, while maintaining similar molecular characteristics.