Showing papers by "A. Vande Wouwer published in 2022"

Dynamic Modeling of Crop–Soil Systems to Design Monitoring and Automatic Irrigation Processes: A Review with Worked Examples

Abstract: The smart use of water is a key factor in increasing food production. Over the years, irrigation has relied on historical data and traditional management policies. Control techniques have been exploited to build automatic irrigation systems based on climatic records and weather forecasts. However, climate change and new sources of information motivate better irrigation strategies that might take advantage of the new sources of information in the spectrum of systems and control methodologies in a more systematic way. In this connection, two open questions deserve interest: (i) How can one deal with the space–time variability of soil conditions? (ii) How can one provide robustness to an irrigation system under unexpected environmental change? In this review, the different elements of an automatic control system are described, including the mathematical modeling of the crop–soil systems, instrumentation and actuation, model identification and validation from experimental data, estimation of non-measured variables and sensor fusion, and predictive control based on crop–soil and weather models. An overview of the literature is given, and several specific examples are worked out for illustration purposes.

Implementation and Tests of an INDI Control Strategy applied to the Parrot Mambo Minidrone

Abstract: In this work, a flight control scheme based on incremental nonlinear dynamic inversion (INDI) is implemented within the Mathworks Simulink environment dedicated to the Parrot Mambo minidrone. This implementation is tested both in simulation and in real-life tests, and compared to the original cascade PID control structure. Trajectory tracking, robustness to modeling uncertainties and instrumentation issues are discussed. The resulting implementation can be used for educational purposes related to feedback linearization and the INDI controller in flight control applications.

Evaluation of the Region of Attractions of Higher Dimensional Hyperbolic Systems using the Extended Dynamic Mode Decomposition

Abstract: This paper proposes an original methodology to compute the regions of attraction in hyperbolic and polynomial nonlinear dynamical systems using the eigenfunctions of the discrete-time approximation of the Koopman operator given by the extended dynamic mode decomposition algorithm. The proposed method relies on the spectral decomposition of the Koopman operator to build eigenfunctions that capture the boundary of the region of attraction. The algorithm relies solely on data that can be col-lected in experimental studies and does not require a mathematical model of the system. Two examples of dynamical systems, a population model and a higher dimensional chemical reaction system, allows demonstrating the reliability of the results.

A Matlab Toolbox for Extended Dynamic Mode Decomposition Based on Orthogonal Polynomials and p-q Quasi-Norm Order Reduction

Abstract: Extended Dynamic Mode Decomposition (EDMD) allows an approximation of the Koopman operator to be derived in the form of a truncated (finite dimensional) linear operator in a lifted space of (nonlinear) observable functions. EDMD can operate in a purely data-driven way using either data generated by a numerical simulator of arbitrary complexity or actual experimental data. An important question at this stage is the selection of basis functions to construct the observable functions, which in turn is determinant of the sparsity and efficiency of the approximation. In this study, attention is focused on orthogonal polynomial expansions and an order-reduction procedure called p-q quasi-norm reduction. The objective of this article is to present a Matlab library to automate the computation of the EDMD based on the above-mentioned tools and to illustrate the performance of this library with a few representative examples.

Data-Driven Predictive Control of Interconnected Systems Using the Koopman Operator

Abstract: Interconnected systems are widespread in modern technological systems. Designing a reliable control strategy requires modeling and analysis of the system, which can be a complicated, or even impossible, task in some cases. However, current technological developments in data sensing, processing, and storage make data-driven control techniques an appealing alternative solution. In this work, a design methodology of a decentralized control strategy is developed for interconnected systems based only on local and interconnection time series. Then, the optimization problem associated with the predictive control design is defined. Finally, an extension to interconnected systems coupled through their input signals is discussed. Simulations of two coupled Duffing oscillators, a bipedal locomotion model, and a four water tank system show the effectiveness of the approach.

Extended Predictive Control of Interconnected Oscillators

Abstract: This study shows how to combine the concepts of extended dynamic mode decomposition and model predictive control in a decentralized approach to drive interconnected oscillators. To achieve this goal, the predictive power of the decomposition algorithm is used to make an approximation of the state of the system, but also to predict the behavior of the interconnection input that affects a particular subsystem. As the prediction of the extended system captures the dynamics linearly, this approach is suitable for the design of local model predictive controllers such that each subsystem can be driven to a desired state despite not having complete knowledge of the other subsystems.

Minimizing Foaming and Bulking in Activated Sludge with Bacteriophage Treatment: A Review of Mathematical Modeling

Abstract: The interest in the ability of phages to control bacterial populations has extended from medical applications into the fields of agriculture, aquaculture, and the food industry. In particular, several authors have proposed using bacteriophages as an alternative method to control foaming and bulking in wastewater treatment. This strategy has shown successful results at the laboratory scale. However, this technology is still in development, and there are several challenges to overcome before bacteriophages can be widely used to control foaming and bulking in pilot or larger-scale treatment plants. Several models of the infection mechanisms in individual bacteria–phage pairs have been reported, i.e., for controlled systems with only one bacterium species in the presence of one phage species. However, activated sludge treatment systems largely differ from this situation, which opens a large horizon for future research. Mathematical models will play a key role in this development process, and this review offers an overview of the proposed models: their applications, potential, and challenges. A particular focus is placed on the model properties, such as parameter identifiability and states’ observability, which are essential for process prediction, monitoring, or dynamic optimization.

Maximum Likelihood pqEDMD Identification

Abstract: The ordinary least squares (OLS) regression for linear system identification might give biased results when noise affects some explicative variables. As OLS is at the core of the extended dynamic mode decomposition algorithm, it is interesting to pay attention to alternative methods, such as maximum likelihood estimation (MLE), to deal with the identification problem. This study explores this direction, discusses the question of defining the probability distribution of the observable functions, and illustrates the performance of the algorithm with two case studies. The first one shows a successful application of MLE to a simple reaction network, while the second, more complex example based on the Duffing equation highlights the method limitation in relation with the empirical construction of the probability distribution of the observables.

Experimental validation of a nonlinear model predictive controller regulating the acetate concentration in fed‐batch Escherichia coli BL21(DE3) cultures

Abstract: Fed‐batch cultures of Escherichia coli are commonly used for the production of biopharmaceuticals. However, productivity can be adversely affected by the production of acetate inhibiting the cell respiratory capacity. In this study, a nonlinear predictive control is developed based on a process model, and an unscented Kalman filter for estimating the evolution of the glucose and acetate concentrations. The control objective is to regulate the acetate concentration at a low level, so as to maintain the culture close to the edge between the fermentative and respirative regimes. The control strategy is tested in simulation and in lab‐scale experiments, demonstrating its feasibility and performance.

Parameter Estimation of Dynamic Beer Fermentation Models

Abstract: In this study, two dynamic models of beer fermentation are proposed, and their parameters are estimated using experimental data collected during several batch experiments initiated with different sugar concentrations. Biomass, sugar, ethanol, and vicinal diketone concentrations are measured off-line with an analytical system while two on-line immersed probes deliver temperature, ethanol concentration, and carbon dioxide exhaust rate measurements. Before proceeding to the estimation of the unknown model parameters, a structural identifiability analysis is carried out to investigate the measurement configuration and the kinetic model structure. The model predictive capability is investigated in cross-validation, in view of opening up new perspectives for monitoring and control purposes. For instance, the dynamic model could be used as a predictor in receding-horizon observers and controllers.

Model Predictive Control of Simulated Moving Bed Chromatographic Processes Using Conservation Element/Solution Element Method

Abstract: Simulated moving bed chromatographic (SMB) processes are used for difficult separations in pharmaceutical, biotechnological and petrochemical industries. Due to high sensitivity to disturbances these processes are usually operated in open-loop mode under suboptimal conditions. In the present work, operation of such processes based on the online optimizing model predictive control (MPC) using the full blown chromatographic model is proposed. For the fast and accurate solution of the underlying model described by a system of partial differential algebraic equations, the so-called space-time conservation element/solution method (CE/SE) is used. As an application example, the separation of racemic mixture of bicalutamides, one of which is a valuable active pharmaceutical component, is considered. To evaluate the performance of the controller, reference tracking (change of the purity requirements) and disturbance rejection (change of the composition of the feed mixture) scenarios are simulated. Since there is no plant-model mismatch, the controller is able to follow the change of the reference from complete to reduced purity separation closely. However, the results of the disturbance rejection simulation shows that the controller requires an adaption mechanism in order to efficiently reject the disturbance.

Real-Time Optimization of Social Distancing to Mitigate COVID-19 Pandemic Using Quantized Extremum Seeking

Abstract: The application of extremum seeking control is investigated to mitigate the spread of the COVID-19 pandemic, maximizing social distancing while limiting the number of infections. The procedure does not rely on the accurate knowledge of an epidemiological model and takes realistic constraints into account, such as hospital capacities, the observation horizon of the pandemic evolution and the quantized government sanitary policy decisions. Based on the bifurcation analysis of a SEIARD compartmental model providing two possible types of equilibria, numerical simulation reveals the transient behaviour of the extremum of the constrained cost function, which, if rapidly caught by the algorithm, slowly drifts to the steady-state optimum. Specific features are easily incorporated in the real-time optimization procedure, such as quantized sanitary condition levels and long actuation (decision) periods (usually several weeks), requiring processing of the discrete control signal saturation and quantization. The performance of the proposed method is numerically assessed, considering the convergence rate and accuracy (quantization bias).

Two Simple Model-free Extremum Seeking Strategies with Convergence Acceleration through Hessian Estimation

Abstract: Recently, several Newton-based extremum seeking strategies have been proposed, which provide fast convergence. In this study, we focus attention on perturbation-based proportional-integral extremum seeking (PIES) and block-oriented model recursive least squares extremum seeking (BOM-RLSES), and we discuss stability and convergence, highlighting the impact of the quality of the Hessian estimation. A bioprocess application is used to compare the performance of PI and RLS Newton-based strategies with respect to the block-oriented RLSES. The results confirm the faster convergence of the Newton-based formulations for an input range contained in the region of attraction of the extremum.

Data-driven Linear Predictor based on Maximum Likelihood Nonnegative Matrix Decomposition for Batch Cultures of Hybridoma Cells

Abstract: This paper presents an original design of low-rank linear predictors of nonlinear process state variables based on nonnegative matrix decomposition (NMD). Therefore, this predictor is data-driven and does not require an accurate model description of the process. In addition, measurement errors are considered, conferring maximum likelihood (ML) properties to the estimator and resulting in a maximum likelihood nonnegative matrix decomposition (MLNMD) formulation. The latter is validated in simulation with a model developed by the authors, describing monoclonal antibody (MAb) production from sequential batch hybridoma cell cultures that are further validated with real-life experimental data. To this end, two available experimental data sets are used for direct and cross-validation, highlighting the good predictive properties of the method.

Application of a Nonlinear Model Predictive Controller to the Anaerobic Digestion of Readily Biodegradable Wastes

Abstract: A nonlinear model predictive controller for the anaerobic digestion of readily biodegradable substrates is presented. The controller aims to achieve a planned methane production, following a reference trajectory for the whole operation. Using an existing dynamic model of anaerobic digestion, the controller optimizes the operation conditions by conveniently manipulating a set of process variables such that the methane flow rate follows the reference trajectory. The controller works in a sequential approach, i.e., the plant trajectory is estimated over a prediction horizon with a simplified dynamic model of the process that includes only two biological reactions: acidogenesis and methanogenesis; then, the model predictions are optimized via a sequential quadratic programming method to match the desired trajectory. Due to the simplicity of the process model, the iterative optimization process is solved in a relatively short time. Both the dynamic model of the process and the optimization algorithm are implemented in MATLAB. The controller is tested in a simulation case study treating a readily biodegradable liquid effluent, where the same process model is used to mimic the measurements of the real plant.

Advanced monitoring of viral amplification process by soft sensing

Abstract: In this study, a software sensor monitoring a viral amplification process is developed and validated. First, a dynamic model structure is proposed, describing Vero cell growth as well as the impact of viral infection, in accordance with the considered industrial application. A parameter identification procedure is set up based on a nonlinear least-square optimization criterion using several data sets provided by Sanofi Pasteur (Lyon, France). Second, an extended Kalman filter is designed considering a specific measurement configuration including a Raman probe sensing biomass, glucose, lactate and glutamine concentrations, and the estimation of exogenous variables such as the cell growth rate and viral amplification parameters. The obtained results validate the possibility to consider the EKF software sensor as a useful tool to monitor and report on viral amplification dynamics.

Hybrid Dynamic Models of Bioprocesses Based on Elementary Flux Modes and Multilayer Perceptrons

Abstract: The derivation of minimal bioreaction models is of primary importance to develop monitoring and control strategies of cell/microorganism culture production. These minimal bioreaction models can be obtained based on the selection of a basis of elementary flux modes (EFMs) using an algorithm starting from a relatively large set of EFMs and progressively reducing their numbers based on geometric and least-squares residual criteria. The reaction rates associated with the selected EFMs usually have complex features resulting from the combination of different activation, inhibition and saturation effects from several culture species. Multilayer perceptrons (MLPs) are used in order to undertake the representation of these rates, resulting in a hybrid dynamic model combining the mass-balance equations provided by the EFMs to the rate equations described by the MLPs. To further reduce the number of kinetic parameters of the model, pruning algorithms for the MLPs are also considered. The whole procedure ends up with reduced-order macroscopic models that show promising prediction results, as illustrated with data of perfusion cultures of hybridoma cell line HB-58.

Distributed multi-objective state-dependent MPC for mapping mission with multiple UAVs

Abstract: This paper presents a Distributed Model Predictive Control approach for UAVs trajectory optimization with the state-dependent collision avoidance criterion. While classical trajectory tracking optimization criterion ensures accuracy of arrival points for the multi-agent system, risk of collision is evaluated at every optimization step, and collision avoidance is included or neglected in the cost function accordingly. Proposed solution is finally evaluated in simulation tests with two scenarios, intersecting and parallel paths of two UAVs. It is, therefore, applicable for different planned path configurations.

Agent-Based Crop Model for Smart Irrigation: Design of a State Estimator

Abstract: In the design of smart irrigation systems, there are several open challenges, among which: i) the modeling of heterogeneity of cropping land, and ii) the estimation of non-measured state variables to control crop development. This work addresses both challenges by an agent-based model (ABM) of a discretized field and by using state estimation techniques. For the last challenge, two software sensors, i.e., an extended Kalman filter (EKF) and an unscented Kalman filter (UKF) are used and compared to estimate on-line the states of homogeneous portions of land assigned to the agents of an ABM model. The agent-based crop model is presented and simulated under two different climatic scenarios to assess the performance of the estimation techniques. Simulation results of a testbed in Colombia shows the advantages of UKF over the EKF.

Special Issue: Mathematical Modeling and Control of Bioprocesses

Abstract: This Special Issue (SI) of Processes on Mathematical Modeling and Control of Bioprocesses (MMCB) contains papers focusing, on the one hand, on mathematical modeling of biological processes at different scales ranging from microscopic to macroscopic levels and, on the other hand, on model-based estimation, optimization and control of these processes [...]