Robust sliding mode‐based extremum‐seeking controller for reaction systems via uncertainty estimation approach

"This paper deals with the design of a robust sliding mode‐based extremum‐seeking controller aimed at the online optimization of a class of uncertain reaction systems. The design methodology is based on an input–output linearizing method with variable‐structure feedback, such that the closed‐loop system converges to a neighborhood of the optimal set point with sliding mode motion. In contrast with previous extremum‐seeking control algorithms, the control scheme includes a dynamic modelling‐error estimator to compensate for unknown terms related with model uncertainties and unmeasured disturbances. The proposed online optimization scheme does not make use of a dither signal or a gradient‐based optimization algorithm. Practical stabilizability for the closed‐loop system around to the unknown optimal set point is analyzed. Numerical experiments for two nonlinear processes illustrate the effectiveness of the proposed robust control scheme.

Reaction rate reconstruction from biomass concentration measurement in bioreactors using modified second-order sliding mode algorithms

This paper deals with the estimation of unknown signals in bioreactors using sliding observers. Particular attention is drawn to estimate the specific growth rate of microorganisms from measurement of biomass concentration. In a recent article, notions of high-order sliding modes have been used to derive a growth rate observer for batch processes. In this paper we generalize and refine these preliminary results. We develop a new observer with a different error structure to cope with other types of processes. Furthermore, we show that these observers are equivalent, under coordinate transformations and time scaling, to the classical super-twisting differentiator algorithm, thus inheriting all its distinctive features. The new observers’ family achieves convergence to timevarying unknown signals in finite time, and presents the best attainable estimation error order in the presence of noise. In addition, the observers are robust to modeling and parameter uncertainties since they are based on minimal assumptions on bioprocess dynamics. In addition, they have interesting applications in fault detection and monitoring. The observers performance in batch, fed-batch and continuous bioreactors is assessed by experimental data obtained from the fermentation of Saccharomyces Cerevisiae on glucose.This work was supported by the National University of La Plata (Project 2012-2015), the Agency for the Promotion of Science and Technology ANPCyT (PICT2007-00535) and the National Research Council CONICET (PIP112-200801-01052) of Argentina; the Technical University of Valencia (PAID-02-09), the CICYT (DPI2005-01180) and AECID (A/024186/09) of Spain; and by the project FEDER of the European Union.De Battista, H.; Picó Marco, JA.; Garelli, F.; Navarro Herrero, JL. (2012). Reaction rate reconstruction from biomass concentration measurement in bioreactors using modified second-order sliding mode algorithms. Bioprocess and Biosystems Engineering. 35(9):1-11. https://doi.org/10.1007/s00449-012-0752-yS111359Aborhey S, Williamson D (1978) State amd parameter estimation of microbial growth process. Automatica 14:493–498Bastin G, Dochain D (1986) On-line estimation of microbial specific growth rates. Automatica 22:705–709Bastin G, Dochain D (1990) On-line estimation and adaptive control of bioreactors. Elsevier, AmsterdamBejarano F, Fridman L (2009) Unbounded unknown inputs estimation based on high-order sliding mode differentiator. In: Proceedings of the 48th IEEE conference on decision and control, pp 8393–8398Corless M, Tu J (1998) State and input estimation for a class of uncertain systems. 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Development of monitoring and control systems for biotechnological processes

The field of biotechnology represents an important research area that has gained increasing success in recent times. Characterized by the involvement of biological organisms in manufacturing processes, its areas of application are broad and include the pharmaceuticals, agri-food, energy, and even waste treatment. The implication of living microorganisms represents the common element in all bioprocesses. Cell cultivations is undoubtedly the key step that requires maintaining environmental conditions in precise and defined ranges, having a significant impact on the process yield and thus on the desired product quality. The apparatus in which this process occurs is the bioreactor. Unfortunately, monitoring and controlling these processes can be a challenging task because of the complexity of the cell growth phenomenon and the limited number of variables can be monitored in real-time. The thesis presented here focuses on the monitoring and control of biotechnological processes, more specifically in the production of bioethanol by fermentation of sugars using yeasts. The study conducted addresses several issues related to the monitoring and control of the bioreactor, in which the fermentation takes place. First, the topic concerning the lack of proper sensors capable of providing online measurements of key variables (biomass, substrate, product) is investigated. For this purpose, nonlinear estimation techniques are analyzed to reconstruct unmeasurable states. In particular, the geometric observer approach is applied to select the best estimation structure and then a comparison with the extended Kalman filter is reported. Both estimators proposed demonstrate good estimation capabilities as input model parameters vary. Guaranteeing the achievement of the desired ethanol composition is the main goal of bioreactor control. To this end, different control strategies, evaluated for three different scenarios, are analzyed. The results show that the MIMO system, together with an estimator for ethanol composition, ensure the compliance with product quality. After analyzing these difficulties through numeric simulations, this research work shifts to testing a specific biotechnological process such as manufacturing bioethanol from brewery’s spent grain (BSG) as renewable waste biomass. Both acid pre-treatment, which is necessary to release sugars, and fermentation are optimized. Results show that a glucose yield of 18.12 per 100 g of dried biomass is obtained when the pre-treatment step is performed under optimized conditions (0.37 M H2SO4, 10% S-L ratio). Regarding the fermentation, T=25°C, pH=4.5, and inoculum volume equal to 12.25% v/v are selected as the best condition, at which an ethanol yield of 82.67% evaluated with respect to theoretical one is obtained. As a final step, the use of Raman spectroscopy combined with chemometric techniques such as Partial Least Square (PLS) analysis is evaluated to develop an online sensor for fermentation process monitoring. The results show that the biomass type involved significantly affects the acquired spectra, making them noisy and difficult to interpret. This represents a nontrivial limitation of the applied methodology, for which more experimental data and more robust statistical techniques could be helpful

Development of software sensors for on-line monitoring of bakers yeast fermentation process

Software sensors and bioprocess are well-established research areas which have much to offer each other. Under the perspective of the software sensors area, bioprocess can be considered as a broad application area with a growing number of complex and challenging tasks to be dealt with, whose solutions can contribute to achieving high productivity and high-quality products. Although throughout the past years in the field of software sensors and bioprocess, progress has been quick and with a high degree of success, there is still a lack of inexpensive and reliable sensors for on-line state and parameter estimation. Therefore, the primary objective of this research was to design an inexpensive measurement system for on-line monitoring of ethanol production during the backers yeast cultivation process. The measurement system is based on commercially available metal oxide semiconductor gas sensors. From the bioreactor headspace, samples are pumped past the gas sensors array for 10 s every five minutes and the voltage changes of the sensors are measured. The signals from the gas sensor array showed a high correlation with ethanol concentration during cultivation process. In order to predict ethanol concentrations from the data of the gas sensor array, a principal component regression (PCR) model was developed. For the calibration procedure no off-line sampling was used. Instead, a theoretical model of the process is applied to simulate the ethanol production at any given time. The simulated ethanol concentrations were used as reference data for calibrating the response of the gas sensor array. The obtained results indicate that the model-based calibrated gas sensor array is able to predict ethanol concentrations during the cultivation process with a high accuracy (root mean square error of calibration as well as the percentage error for the validation sets were below 0.2 gL-1 and 7 %, respectively). However the predicted values are only available every five minutes. Therefore, the following plan of the research goal was to implement an estimation method for continues prediction of ethanol as well as glucose, biomass and the growth rates. For this reason, two nonlinear extensions of the Kalman filter namely the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) were implemented separately for state and parameter estimation. Both prediction methods were validated on three different cultivation with variability of the substrate concentrations. The obtained results showed that both estimation algorithms show satisfactory results with respect to estimation of concentrations of substrates 6 and biomass as well as the growth rate parameters during the cultivation. However, despite the easier implementation producer of the UKF, this method shows more accurate prediction results compared to the EKF prediction method. Another focus of this study was to design and implement an on-line monitoring and control system for the volume evaluation of dough pieces during the proofing process of bread making. For this reason, a software sensor based on image processing was designed and implemented for measuring the dough volume. The control system consists of a fuzzy logic controller which takes into account the estimated volume. The controller is designed to maintain the volume of the dough pieces similar to the volume expansion of a dough piece in standard conditions during the proofing process by manipulating the temperature of the proofing chamber. Dough pieces with different amounts of backers yeast added in the ingredients and in different temperature starting states were prepared and proofed with the supervision of the software sensor and the fuzzy controller. The controller was evaluated by means of performance criteria and the final volume of the dough samples. The obtained results indicate that the performance of the system is very satisfactory with respect to volume control and set point deviation of the dough pieces.Softwaresensoren und Bioprozese sind gut etablierte Forschungsgebiete, die sich gegenseitig viel befruchten können. Unter dem Blickwinkel der Softwaresensorik kann der Bioprozess als ein breites Anwendungsgebiet mit einer wachsenden Zahl komplexer und anspruchsvoller Aufgabenstellungen betrachtet werden, deren Lösung zur Erzielung hoher Produktivität und qualitativ hochwertiger Produkte beitragen kann. Obwohl in den letzten Jahren auf dem Gebiet der Softwaresensoren und des Bioprozesses rasch und mit großem Erfolg Untersuchung erzielt wurden, fehlt es immer noch an kostengünstigen und zuverlässigen Sensoren für die Online-Zustands- und Parameterschätzung. Daher war das primäre Ziel dieser Forschung die Entwicklung eines kostengünstigen Messsystems für die Online-Überwachung der Ethanolproduktion während des Kultivierungsprozesses von Backhefe. Das Messsystem basiert auf kommerziell erhältlichen Metalloxid-Halbleiter-Gassensoren. Die Headspace-Proben des Bioreaktors werden alle fünf Minuten für 10 s an der Gassensor-Anordnung vorbeigepumpt und die Spannungsänderungen der Sensoren werden gemessen. Die Signale des Gassensorarrays zeigten eine hohe Korrelation mit der Ethanolkonzentration während des Kultivierungsprozesses. Um die Ethanolkonzentrationen aus den Daten des Gassensorarrays vorherzusagen, wurde ein Hauptkomponenten-Regressionsmodell (PCR) verwendet. Für das Kalibrierungsverfahren ist keine Offline-Probenahme notwendig. Stattdessen wird ein theoretisches Modell des Prozesses genutzt, um die Ethanolproduktion zu jedem beliebigen Zeitpunkt zu simulieren. Die kinetischen Parameter des Modells werden im Rahmen der Kalibration bestimmt. Die simulierten Ethanolkonzentrationen wurden als Referenzdaten für die Kalibrierung des Ansprechverhaltens des Gassensorarrays verwendet. Die erhaltenen Ergebnisse zeigen, dass das modellbasierte kalibrierte Gassensorarray in der Lage ist, die Ethanolkonzentrationen während des Kultivierungsprozesses mit hoher Genauigkeit vorherzusagen (der mittlere quadratische Fehler der Kalibrierung sowie der prozentuale Fehler für die Validierungssätze lagen unter 0,2 gL-1 bzw. 7 %). Die vorhergesagten Werte sind jedoch nur alle fünf Minuten verfügbar. Daher war der folgende Plan der Untersuchung die Implementierung einer Schätzmethode zur kontinuierlichen Vorhersage von Ethanol sowie von Glukose, Biomasse und der Wachstumsrate. Aus diesem Grund wurden zwei nichtlineare Erweiterungen des Kalman Filters, nämlich der erweiterte Kalman Filter (EKF) und der unscented Kalman Filter (UKF), getrennt für die Zustands und Parameterschätzung implementiert. Beide 8 Vorhersagemethoden wurden an drei verschiedenen Kultivierungen mit Variabilität der Start substratkonzentrationen validiert. Die erhaltenen Ergebnisse zeigen, dass beide Schätzungsalgorithmen zufriedenstellende Ergebnisse hinsichtlich der Schätzung der Konzentrationen von Substraten und Biomasse sowie der Parameter der Wachstumsrate während der Kultivierung ermitteln. Trotz der einfacheren Implementierung des UKF zeigt diese Methode jedoch genauere Vorhersageergebnisse im Vergleich zur EKF-Vorhersagemethode. Ein weiterer Schwerpunkt dieser Untersuchung war der Entwurf und die Implementierung eines Online-Überwachungs- und Regelungssystems für die Volumenauswertung von Teigstücken während des Gärprozesses bei der Brotherstellung. Aus diesem Grund wurde ein auf Bildverarbeitung basierendes Überwachungssystem zur Messung der Teigvolumenauswertung entworfen und implementiert. Das Regelsystem besteht aus einem Fuzzy-Logic-Controller, der das gemessene Volumen für die Regelung nutzt. Die Regelung ist so ausgelegt, dass das Volumen der Teiglinge mit Werten des Volumens eines Teiglings unter Standardbedingungen während des Gärprozesses vergleicht und die Temperatur der Gärkammer entsprechend anpasst. Teiglinge mit unterschiedlichen Hefemengen in den Zutaten und verschiedenen Temperaturstartwerten wurden vorbereitet und unter Anwendung des Fuzzy-Reglers gegärt. Der Regler wurde anhand von Leistungskriterien und dem Endvolumen der Teigproben bewertet. Die erhaltenen Ergebnisse zeigen, dass die Leistung des Systems in Bezug auf die Volumenregelung und die Sollwertabweichung der Teigstücke sehr zufriedenstellend ist

Specific growth rate estimation in (fed-)batch bioreactors using second-order sliding observers

[EN] This paper addresses the estimation of specific growth rate of microorganisms in bioreactors using sliding observers. In particular, a second-order sliding observer based on biomass concentration measurement is proposed. Differing from other proposals that only guarantee bounded errors, the proposed observer provides a smooth estimate that converges in finite time to the time-varying parameter. Stability is proved using a Lyapunov approach. The observer exhibits also robustness to process uncertainties since no model of the reaction is used for its design. In addition, the off-surface coordinate of the sliding observer is useful to determine the convergence time as well as to identify sensor faults and unexpected behaviors. Because of the structure of the output error injection, chattering phenomena of conventional sliding mode algorithms are substantially reduced. The features of the proposed observer are assessed by numerical and experimental data. (C) 2011 Elsevier Ltd. All rights reserved.This work was supported by the National University of La Plata (Project 11-1127), ANPCyT (PICT2007-00535) and CONICET (PIP112-200801-01052) of Argentina; the Technical University of Valencia (PAID-02-09 program and FPI-2009/21 grant), the CICYT (DPI2005-01180) and AECID (A/024186/09) of Spain: and by FEDER funds of the European Union.De Battista, H.; Picó, J.; Garelli, F.; Vignoni, A. (2011). Specific growth rate estimation in (fed-)batch bioreactors using second-order sliding observers. Journal of Process Control. 21(7):1049-1055. https://doi.org/10.1016/j.jprocont.2011.05.008S1049105521

Fermentation: Metabolism, Kinetic Models, and Bioprocessing

Biochemical and metabolic interpretation of microbial growth is an important topic in bioreactor design. We intend to address valuable information about the relation of critical operation variables and the simulation of bioprocesses with unstructured and structured kinetic models. Process parameters such as nutrient supply, pH, dissolved oxygen, and metabolic end-products directly impact the physiology and metabolism of microorganisms. Changes in the membrane as well as cell viability are of interest since protein expression and maturation in prokaryota are directly related to membrane integrity. This chapter intends to deliver an insight of different alternatives in kinetic modeling

An Equivalent Control Based Observer for Biomass in a Batch Process

In this paper a sliding-mode observer for a batch bioprocess, the d-endotoxins production of bacillus thuringiensis (BT), is presented. The proposed observer is based on the equivalent control method and a class of second-order sliding mode operators. The use of these operators in the observer design allows the fixed-time convergence of the measured variables, while the unmeasured variables converge exponentially. This structure allows to estimate the biomass in the d-endotoxins production of BT, even, under noisy measurement conditions. Simulations show the feasibility of the proposed observer. Convergence proofs are also presented

Enzymatic Synthesis of Ampicillin: Nonlinear Modeling, Kinetics Estimation, and Adaptive Control

Nowadays, the use of advanced control strategies in biotechnology is quite low. A main reason is the lack of quality of the data, and the fact that more sophisticated control strategies must be based on a model of the dynamics of bioprocesses. The nonlinearity of the bioprocesses and the absence of cheap and reliable instrumentation require an enhanced modeling effort and identification strategies for the kinetics. The present work approaches modeling and control strategies for the enzymatic synthesis of ampicillin that is carried out inside a fed-batch bioreactor. First, a nonlinear dynamical model of this bioprocess is obtained by using a novel modeling procedure for biotechnology: the bond graph methodology. Second, a high gain observer is designed for the estimation of the imprecisely known kinetics of the synthesis process. Third, by combining an exact linearizing control law with the on-line estimation kinetics algorithm, a nonlinear adaptive control law is designed. The case study discussed shows that a nonlinear feedback control strategy applied to the ampicillin synthesis bioprocess can cope with disturbances, noisy measurements, and parametric uncertainties. Numerical simulations performed with MATLAB environment are included in order to test the behavior and the performances of the proposed estimation and control strategies

Applications of Mathematical Models in Engineering

The most influential research topic in the twenty-first century seems to be mathematics, as it generates innovation in a wide range of research fields. It supports all engineering fields, but also areas such as medicine, healthcare, business, etc. Therefore, the intention of this Special Issue is to deal with mathematical works related to engineering and multidisciplinary problems. Modern developments in theoretical and applied science have widely depended our knowledge of the derivatives and integrals of the fractional order appearing in engineering practices. Therefore, one goal of this Special Issue is to focus on recent achievements and future challenges in the theory and applications of fractional calculus in engineering sciences. The special issue included some original research articles that address significant issues and contribute towards the development of new concepts, methodologies, applications, trends and knowledge in mathematics. Potential topics include, but are not limited to, the following: Fractional mathematical models; Computational methods for the fractional PDEs in engineering; New mathematical approaches, innovations and challenges in biotechnologies and biomedicine; Applied mathematics; Engineering research based on advanced mathematical tools