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ispartof: JOURNAL OF PROCESS CONTROL vol:117 pages:169-180 status: published

Second-generation biomass is an underexploited resource, which can lead to valuable products in a circular economy. Available locally as food waste, gardening and pruning waste or agricultural waste, second-generation biomass can be processed into high-valued products through a flexi-feed small-scale biorefinery. The flexi-feed and the use of local biomass ensure the continuous availability of feedstock at low logistic costs. However, the viability and sustainability of the biorefinery must be ensured by the design and optimal operation. While the design depends on the available feedstock and the desired products, the optimisation requires the availability of a mathematical model of the biorefinery. This paper details the design and modelling of a small-scale biorefinery in view of its optimisation at a later stage. The proposed biorefinery comprises the following processes: steam refining, anaerobic digestion, ammonia stripping and composting. The models’ integration and the overall biorefinery operation are emphasised. The simulation results assess the potential of the real biowaste collected in a commune in Flanders (Belgium) to produce oligosaccharides, lignin, fibres, biogas, fertiliser and compost. This represents a baseline scenario, which can be subsequently employed in the evaluation of optimised solutions. The outlined approach leads to better feedstocks utilisation and product diversification, raising awareness on the impact and importance of small-scale biorefineries at a commune level.

The demand for sustainable replacements for fossil-based products is steadily increasing, especially now that the effects of climate change are becoming more prominent. Lignocellulose, which is a sustainable and abundant carbon source, is dubbed to be the perfect replacement. Lignocellulose consists of lignin, hemicellulose, and cellulose. During the Simultaneous Saccharification and Fermentation (SSF) of cellulose, the hydrolysis and fermentation of the produced C6-sugars occurs simultaneously in the same vessel. The SSF process has mainly been developed to circumvent inhibitory effect and increase the overall product yield. Although the concept of the SSF process is promising, the applications are still limited. This contribution presents the trade-off-based multi-objective optimisation of an SSF process. Multi-objective optimisation allows for optimising (bio-)process with respect to multiple, and often conflicting, objectives. These optimisation problems do not render a unique optimal solution but instead an infinite set of so-called Pareto-optimal solutions, the Pareto front. From the Pareto front, the decision maker should select one working point. To aid decision makers in this selection process, the application of a novel genetic optimisation algorithm is presented in this contribution, i.e., tDOM, that is capable of filtering solutions using t-domination. This results in a less dense Pareto front that only contains solutions that are of interest for the decision maker. Additionally, by extending the t-domination concept to two subsequent solution populations, a novel problem-relevant stopping criterion is developed, resulting in a significant gain in the required computational time. A comparison to the well known NSGA-II is provided.

Anaerobic digestion systems are of increasing interest as they are able to produce biogas while treating waste/wastewater. However, their dynamics is complex and not fully understood, which makes their operation and optimization difficult. In this paper, an extremum seeking control algorithm is applied to a three-stage anaerobic digestion system to maximize the outflow rate of methane. In a first stage, the stability analysis of the three-stage model is performed, which provides valuable information on the type of steady states the system possesses, the occurrence of the optimal steady state and good practices to successfully operate the system. In a second stage, an extremum seeking controller, which employs a recursive least-squares algorithm for block-oriented models, is implemented and tested on the anaerobic digestion model. Simulation results show that the proposed controller globally stabilizes the process dynamics at the optimal operating point. Compared to the classical extremum seeking algorithms, the proposed technique allows for a faster convergence, in an imposed time period assigned by the designer.

The identification of accurate models for the anaerobic digestion process is essential for the characterization of the region that guarantees the conservation of the bacteria population. Traditional techniques involve the identification of nonlinear models based on data from the system. In this paper, we introduce data-driven techniques that allow the characterization of the system’s behavior via the approximation of the Koopman operator with the extended dynamic mode decomposition algorithm. We propose methods to reduce the order and dimension of the representation based on orthogonal polynomials.

ispartof: pages:403-408 ispartof: IFAC PAPERSONLINE vol:55 issue:20 pages:403-408 ispartof: 10th Vienna International Conference on Mathematical Modelling (MATHMOD) location:ELECTR NETWORK, Tech Univ Wien date:27 Jul - 29 Jul 2022 status: published

This paper investigates state and unknown input estimations in an Anaerobic Digestion Reactor (ADR) considering a simple two-stage reaction model describing acidogenesis and methanogenesis. From the sole methane outlet flow, this model allows to predict the inlet and outlet biodegradable suspended solid and volatile fatty acid concentrations, which are critical for process stability, as well as acidogenic and methanogenic biomasses. Continuous–discrete exogenous and unknown input formulations of the Extended Kalman Filter (EKF) are applied in this context and a numerical robustness analysis is achieved to characterize sensitivities to measurement noise and model uncertainties. The resulting observers are then validated experimentally with data from a lab-scale plant.

Nonlinear biochemical systems such as the anaerobic digestion process experience the problem of the multi-stability phenomena, and thus, the dynamic spectrum of the system has several undesired equilibrium states. As a result, the selection of initial conditions and operating parameters to avoid such states is of importance. In this work, we present a data-driven approach, which relies on the generation of several system trajectories of the anaerobic digestion system and the construction of a data-driven Koopman operator to give a concise criterion for the classification of arbitrary initial conditions in the state space. Unlike other approximation methods, the criterion does not rely on difficult geometrical analysis of the identified boundaries to produce the classification.

This paper is dedicated to the experimental validation of a cascade control strategy for simultaneously regulating the glucose and biomass levels in continuously perfused HEK-293 cell cultures. The inner loop consists of a partial feedback linearization, which requires the estimation of the biomass specific growth rate and glucose uptake rate. This latter task is achieved by sliding mode observers, which do not require a priori process knowledge in the form of a process model. The linearized process is then regulated by the outer loop, including two classical PI controllers with autotuning. The four manipulated variables are a feed flow rate with low glucose concentration, another feed flow with a higher glucose content, a bleed flow, and a perfusion stream. The experimental results demonstrate the ability of the control strategy to reach and regulate the prescribed setpoints. The main advantage of the strategy is that it can be applied in a plug and play manner and shows satisfactory robustness. To the best of our knowledge, this is the first time that such a multivariable control strategy, together with sliding mode observers, is applied at the lab scale to an industrial process in the pharmaceutical sector.

The anaerobic digestion (AD) technology is widely used in the treatment of waste and wastewater. To ensure the treatment efficiency and to increase the production of biogas, which can be reused as a renewable energy source, a good understanding of the process and tight control are needed. This paper presents an estimation and control scheme, which can be successfully used in the operation of the AD process. The process is simulated by the ADM1 model, the most complex and detailed model developed so far to characterize AD. The controller and the observer, which provides estimates of the unmeasurable variables needed in the computation of the control law, are designed based on a simplified model developed in a previous work. Since it has been shown that hydrogen concentration is an accurate and fast indicator of process stability, it was chosen as controlled variable. Aside from the hydrogen concentration, the only measurement employed by the proposed control structure is the volatile fatty acids concentration. Simulation results prove the effectiveness of the proposed control structure.

This paper presents an original model for calcium phosphate crystallization from acidic wastewater. The model is developed using classical principles of chemistry and population balance modeling. The aim is to further use the model for analysis, control and optimization of the crystallization process for phosphate recovery. The proposed model consists of one population balance equation coupled with four mass balance equations and a set of algebraic equations, which can be easily integrated with Matlab and MatMOL toolbox. The model is validated against PHREEQC, a software for speciation and geochemical calculations.

In this study, the steady states of an anaerobic digestion model are analytically computed and characterized. The influence of the dilution rate on the system states and methane outflow rate is illustrated by means of one-parameter bifurcation diagrams. A two-parameter bifurcation diagram is also computed. This diagram illustrates the combined effect of the dilution rate and inlet substrate concentration on the system steady states and allows to determine corrective actions (in terms of selecting appropriated inputs) for preserving system stability and efficiency. Expressions for all the boundaries and critical points appearing in the diagram are provided. Furthermore, the complex system behavior is illustrated by means of phase portraits. The paper emphasizes the methodology, which can also be applied to other bioprocesses taking place in continuously stirred tank reactors. The method allows practitioners to build two-parameter bifurcation diagrams by solving a set of algebraic equations. This implies low computational requirements.

The objective of this paper is to address the problem of state estimation in an Anaerobic Digestion Reactor (ADR) with unknown inputs - typically some influent concentrations, and to compare two different state and input estimation schemes. The first one is the classical Extended Kalman Filter (EKF) based on an augmented system that considers a slowly varying input (approach that has been already applied to this system and reported in the literature), whereas the second one is a recently proposed Unknown Input Observer (UIO), formulated in the spirit of a Kalman Filter, for continuous estimation with discrete measurements. The two filters are evaluated in simulation, demonstrating the superiority of the UIO.

This paper describes the implementation and validation of a model predictive controller (MPC) for a photobioreactor system. The microalgae concentration, the solution pH and the illumination index, which is related to the lit PBR volume, are simultaneously controlled at imposed setpoint values by manipulating the dilution rate, the flow of CO 2 supplied to the culture and the incident light. The complex, time consuming nonlinear optimization is replaced by iterative quadratic programming optimizations. With a reduced number of tuning parameters and no demand for dynamics decoupling, the proposed controller improves considerably the speed of the control loop compared to the results available in literature.

This paper presents a framework for the multivariable robust control of perfusion animal cell cultures. It consists of a cascade control structure and an estimation algorithm, which provides the unmeasurable variables needed in the design of the control law, and ensures the regulation of the cell and glucose concentrations at imposed levels by manipulating the bleed and the dilution rates. The cascade control structure uses a feedback linearizing controller in the inner loop and linear (PI) controllers in the outer loops, and requires the measurement of the cell concentration and the glucose concentration in the bioreactor. Two approaches are provided: the first one assumes the availability of an approximate model of the process kinetics and uses an extended Kalman filter (EKF) to estimate the system states; the second approach does not require the prior knowledge of the process kinetics. These are estimated from the available measurements using sliding mode observers (SMO). A receding horizon optimization algorithm is employed to (periodically) tune the gains of the outer loop controllers. The proposed framework is easy to implement and tune, and may be applied to a general class of perfusion cell culture systems. Its effectiveness and robustness are illustrated by means of simulation results.

This paper presents the estimation of the unknown states and inputs of an anaerobic digestion system characterized by a two-step reaction model. The estimation is based on the measurement of the two substrate concentrations and of the outflow rate of biogas and relies on the use of an observer, consisting of three parts. The first is a generalized super-twisting observer, which estimates a linear combination of the two input concentrations. The second is an asymptotic observer, which provides one of the two biomass concentrations, whereas the third is a super-twisting observer for one of the input concentrations and the second biomass concentration.

This paper presents a brief evaluation of a start-up strategy for multi-species anaerobic digestion systems modelled as two-step reaction systems, where acidogenesis is described by Monod kinetics while the methanogenesis is described by Haldane kinetics. The start-up policy has been developed originally for single species systems with the aim of maximizing the biogas outflow rate. It consists of switching the dilution rate from minimum to maximum and then to the optimal value (bang-bang control) in order to bring the system from an arbitrary initial condition to the optimal set-point. This start-up strategy is applied to the multi-species system using an averaged model, which is usually the only model that can be identified for a multi-species system, as measuring individual biomasses is almost impossible in practice. Even the development of an accurate averaged model, fully characterizing the system dynamics based on the variation of the species proportions is difficult. The averaged models used in this...

This paper presents an effective and robust structure for the estimation and control of perfusion cell cultures, in which the cells and glucose concentrations are simultaneously controlled by manipulating the dilution and bleed rates. Firstly, a partially linearizing feedback controller is designed to ensure an approximately linear decoupled dynamics between the controlled outputs and the manipulated inputs. Then the model of the inner loop is used to design an extended Kalman filter, which estimates all the system states used in the implementation of the linearizing feedback control law from the (possibly noisy) measurements of cells and glucose concentrations. Two PI controllers are used in the outer loop for a good tracking performance, which are tuned using a receding horizon optimization procedure. The proposed structure shows good performance and robustness with respect to parameter uncertainties, non-cancelled nonlinearities and measurement noise.

In this study, a multivariable control structure is developed to simultaneously control the concentrations of cells and of one of the nutrients in an animal cell cultivation system operated in perfusion. A cascade control structure is considered consisting of (i) an inner loop with a partially linearizing feedback controller, tuned so as to ensure robustness with respect to parameter uncertainties and non-canceled nonlinearities; and (ii) an outer loop involving two linear predictive controllers. The resulting control strategy shows robustness and performance properties similar to more computationally demanding strategies (such as a multivariable nonlinear MPC strategy), while requiring less measurements and involving an easier implementation.

This paper presents the bifurcation analysis of an anaerobic digestion model, which includes hydrogen production along with methane production. Analytical expressions of the equilibria are given and the conditions for their occurrence are provided. The analytical developments are validated by means of bifurcation diagrams built with specialized continuation software. Special emphasis is put on revealing the relationship between hydrogen and methane outflow rate. The complex system behavior is illustrated by means of phase portraits.

This paper presents a brief evaluation of a start-up strategy for multispecies anaerobic digestion systems modelled as two-step reaction systems, in which acidogenesis is described by Monod kinetics while the methanogenesis is described by Haldane kinetics. The start-up policy has been developed originally for single species systems with the aim of maximizing the biogas outflow rate. It consists of switching the dilution rate from minimum to maximum and then to the optimal value in order to bring the system from an arbitrary initial condition to the optimal setpoint. This start-up strategy is applied to the multispecies system using an averaged model, which is usually the only model that can be identified for a multispecies system, as measuring individual biomasses is quite difficult in practice. This study shows that the start-up policy leads to an efficient ecosystem, characterized by high outflow rate of biogas, even in the case of an inaccurate averaged model. It can be viewed as a robustness evaluation of the single species start-up strategy, as the process changes from the averaged kinetics to the kinetics of the winning species during species selection.

This paper presents a simple switching control policy for driving an anaerobic digestion system from an arbitrary initial state to an optimal setpoint, characterized by the maximum biogas production. A high wastewater treatment efficiency is achieved and a fast convergence to the optimal setpoint is obtained. The main features of this control strategy are its simplicity and ease of implementation, as it is based on the measurement of the biogas outflow rate, which is commonly available in anaerobic digestion systems.

This paper presents a strategy for the optimization of biogas outflow rate in an anaerobic digestion process described by a two-population model. The methodology relies on the solution of two optimization problems: steady state optimization for determining the optimal operating point and transient optimization. The latter is solved using the maximum principle of Pontryagin. The proposed control law, which drives the process from an initial state to the optimal steady state while maximizing the biogas outflow rate, consists of switching the manipulated variable (dilution rate) from the minimum to the maximum value and then to the optimal value at well defined instants. This control law substantially increases the stability region of the optimal equilibrium point, enlarging it in some cases to almost the entire state space. Aside its efficiency, the strategy is also characterized by simplicity, being thus appropriate for implementation in real-life systems. Another important advantage is its generality: this technique may be applied to any anaerobic digestion process, for which the acidogenesis and methanogenesis are respectively characterized by Monod and Haldane kinetics.

In this paper, the influence of microbial growth kinetics on the number and the stability of steady states for a nitrogen removal process is addressed. A two-step nitrification model is studied, in which the maximum growth rate of ammonium oxidizers is larger than the one of nitrite oxidizers. This model describes the behavior of a SHARON reactor for the treatment of wastewater streams with high ammonium concentrations. Steady states are identified through direct calculation using a canonical state space model representation, for several types of microbial kinetics. The stability of the steady states is assessed and the corresponding phase portraits are analyzed. Practical operation of a SHARON reactor aims at reaching ammonium conversion to nitrite while suppressing further conversion to nitrate. Regions in the input space are identified that result in this desired behavior, with only nitrite formation. It is demonstrated that not only the dilution rate plays a role, as is commonly known, but also the influent ammonium concentration. Besides, the type of microbial (inhibition) kinetics has a nonnegligible influence. While the results indicate that product inhibition does not affect the number of steady states of a (bio)reactor model, it is shown that substrate inhibition clearly yields additional steady states. Particular attention is devoted to the physical interpretation of these phenomena. Biotechnol. Bioeng. 2007;98: 882–893. © 2007 Wiley Periodicals, Inc.

The paper deals with the design of a predictive controller for a wastewa- ter treatment process. In the considered process, the wastewater is treated in order to obtain an effluent having the substrate concentration within the standard limits estab- lished by law (below 20 mg/l). This goal is achieved by controlling the concentration of dissolved oxygen to a certain value. The predictive controller uses a neural net- work as internal model of the process and alters the dilution rate in order to fulfill the control objective. This control strategy offers various possibilities for the control law adjustment by means of the following parameters: the prediction horizon, the control horizon, the weights of the error and the command. The predictive control structure has been tested in three functioning regimes, considered essential due to the frequency of their occurrence in current practice.

This paper presents a multivariable robust control structure for perfusion animal cell cultures. The control structure assumes a cascade form, where a linearizing feedback controller is used in the inner loop and linear controllers are used in the outer loops, to simultaneously control the cells concentration and the glucose concentration in the bioreactor. The growth rates needed by the linearizing controller are robustly estimated using sliding mode observers (SMO). Aside the effectiveness and the simplicity of the implementation and tuning, the proposed control scheme has the advantage that it does not require the knowledge of the process kinetics structure, which is generally difficult to identify.

This paper presents an optimizing start-up strategy for a bio-methanator. The goal of the control strategy is to maximize the outflow rate of methane in anaerobic digestion processes, which can be described by a two-population model. The methodology relies on a thorough analysis of the system dynamics and involves the solution of two optimization problems: steady-state optimization for determining the optimal operating point and transient optimization. The latter is a classical optimal control problem, which can be solved using the maximum principle of Pontryagin. The proposed control law is of the bang–bang type. The process is driven from an initial state to a small neighborhood of the optimal steady state by switching the manipulated variable (dilution rate) from the minimum to the maximum value at a certain time instant. Then the dilution rate is set to the optimal value and the system settles down in the optimal steady state. This control law ensures the convergence of the system to the optimal steady state and substantially increases its stability region. The region of attraction of the steady state corresponding to maximum production of methane is considerably enlarged. In some cases, which are related to the possibility of selecting the minimum dilution rate below a certain level, the stability region of the optimal steady state equals the interior of the state space. Aside its efficiency, which is evaluated not only in terms of biogas production but also from the perspective of treatment of the organic load, the strategy is also characterized by simplicity, being thus appropriate for implementation in real-life systems. Another important advantage is its generality: this technique may be applied to any anaerobic digestion process, for which the acidogenesis and methanogenesis are, respectively, characterized by Monod and Haldane kinetics.

This paper evaluates the number and stability of steady states of a two-population model, describing the anaerobic degradation of solid organic waste. Analytical conditions are provided, which define in the input space regions characterized either by a different number or change of stability of steady states. The qualitative results do not depend on the parameter values and allow the proper selection of inputs and initial conditions to achieve a good operation of the process.

This study analyses the steady state behaviour of biological conversion systems with general kinetics, in which two consecutive reactions are carried out by two groups of micro-organisms. The model considered is a realistic description of wastewater treatment processes. A step-wise procedure is followed to reveal the mechanisms affecting the occurrence of steady states in terms of the process input variables. It is clearly demonstrated how taking into account inhibition effects by simply including additional inhibition terms to the kinetic expressions, a common practice, influences the model’s long term behaviour. The overall steady state behaviour of the model has been summarized in easy-to-interpret operating diagrams, depicting the occurrence of steady states in terms of the reactor dilution rate and the influent substrate concentration, with well-defined boundaries between distinct operating regions. This knowledge is crucial for modelers as steady state multiplicity – in the sense that more than one steady state can be reached depending on the initial conditions – may remain undetected during simulation. The obtained results may also serve for experimental design and for model validation based on experimental findings.

Material or fluid transportation is a commonly encountered phenomenon in industrial applications, generating variable time delay that makes the design of feedback control loops more difficult. This paper investigates the applicability of MPC (Model Predictive Control) strategies to this type of processes. The experimental setup consists of a heated tank, of which the outlet temperature (measured at a certain distance from the tank) is controlled by manipulating the outlet flow. The nonlinear EPSAC (Extended Prediction Self-Adaptive Control) approach is used, which reduces the complexity of nonlinear optimization to iterative quadratic programming. It is shown that developing a process model in which dynamics are decoupled from the variable time delay leads to a Smith predictor-like control structure, that allows the proper operation of the control loop with fixed control parameters. The performance of the predictive controller is compared on the pilot plant to the performance of classic control approaches for systems with time delay.

The dynamics of biochemical reaction systems of rank one are studied. The global convergence of the set of equilibrium points is investigated and the local stability properties of the equilibria are analysed. The problem of stability boundary estimation is addressed and an algorithm for the visualization of the boundaries is proposed. The theoretical results and the effectiveness of the proposed algorithms are verified by two examples.