Set-point regulation of an anaerobic digestion process with bounded output feedback

Published versio

Hybrid Control of a Bioreactor with Quantized Measurements: Extended Version

We consider the problem of global stabilization of an unstable bioreactor model (e.g. for anaerobic digestion), when the measurements are discrete and in finite number ("quantized"), with control of the dilution rate. The model is a differential system with two variables, and the output is the biomass growth. The measurements define regions in the state space, and they can be perfect or uncertain (i.e. without or with overlaps). We show that, under appropriate assumptions, a quantized control may lead to global stabilization: trajectories have to follow some transitions between the regions, until the final region where they converge toward the reference equilibrium. On the boundary between regions, the solutions are defined as a Filippov differential inclusion. If the assumptions are not fulfilled, sliding modes may appear, and the transition graphs are not deterministic

A method for the reconstruction of unknown non-monotonic growth functions in the chemostat

We propose an adaptive control law that allows one to identify unstable steady states of the open-loop system in the single-species chemostat model without the knowledge of the growth function. We then show how one can use this control law to trace out (reconstruct) the whole graph of the growth function. The process of tracing out the graph can be performed either continuously or step-wise. We present and compare both approaches. Even in the case of two species in competition, which is not directly accessible with our approach due to lack of controllability, feedback control improves identifiability of the non-dominant growth rate.Comment: expansion of ideas from proceedings paper (17 pages, 8 figures), proceedings paper is version v

Event-triggered control for rational and Lur’e type nonlinear systems

In the present work, the design of event-triggered controllers for two classes of nonlinear systems is addressed: rational systems and Lur’e type systems. Lyapunov theory techniques are used in both cases to derive asymptotic stability conditions in the form of linear matrix inequalities that are then used in convex optimization problems as means of computing the control system parameters aiming at a reduction of the number of events generated. In the context of rational systems, state-feedback control is considered and differentialalgebraic representations are used as means to obtain tractable stability conditions. An event-triggering strategy which uses weighting matrices to strive for less events is proposed and then it is proven that this strategy does not lead to Zeno behavior. In the case of Lur’e systems, observer-based state-feedback is addressed with event generators that have access only to the system output and observed state, but it imposes the need of a dwell-time, i.e. a time interval after each event where the trigger condition is not evaluated, to cope with Zeno behavior. Two distinct approaches, exact time-discretization and looped-functional techniques, are considered to ensure asymptotic stability in the presence of the dwell-time. For both system classes, emulation design and co-design are addressed. In the emulation design context, the control law (and the observer gains, when appropriate) are given and the task is to compute the event generator parameters. In the co-design context, the event generator and the control law or the observer can be simultaneously designed. Numerical examples are presented to illustrate the application of the proposed methods.Neste trabalho é abordado o projeto de controladores baseados em eventos para duas classes de sistemas não lineares: sistemas racionais e sistemas tipo Lur’e. Técnicas da teoria de Lyapunov são usadas em ambos os casos para derivar condições de estabilidade assintótica na forma de inequações matriciais lineares. Tais condições são então utilizadas em problemas de otimização convexa como meio de calcular os parâmetros do sistema de controle, visando uma redução no número de eventos gerados. No contexto de sistemas racionais, realimentação de estados é considerada e representações algébrico-diferenciais são usadas como meio de obter condições de estabilidade tratáveis computacionalmente. Uma estratégia de disparo de eventos que usa uma medida de erro ponderado através de matrizes definidas positivas é proposta e é demonstrado que tal estratégia não gera comportamento de Zenão. No caso de sistemas tipo Lur’e, considera-se o caso de controladores com restrições de informações, a saber, com acesso apenas às saídas do sistema. Um observador de estados é então utilizado para recuperar a informação faltante. Neste contexto, é necessária a introdução de um tempo de espera (dwell time, em inglês) para garantir a inexistência de comportamento de Zenão. Todavia, a introdução do tempo de espera apresenta um desafio adicional na garantia de estabilidade que é tratado neste trabalho considerando duas técnicas possíveis: a discretização exata do sistema e o uso de looped-functionals (funcionais em laço, em uma tradução livre). Para ambas classes de sistemas, são tratados os problemas de projeto por emulação e co-design (projeto simultâneo, em uma tradução livre). No projeto por emulação, a lei de controle (e os ganhos do observador, quando apropriado) são dados a priori e a tarefa é projetar os parâmetros do gerador de eventos. No caso do co-design, o gerador de eventos e a lei de controle ou o observador são projetados simultaneamente. Exemplos numéricos são usados para ilustrar a aplicação dos métodos propostos

Modelling, Optimisation and Control of Anaerobic Co-digestion Processes

La digestión anaerobia es un proceso biológico que ocurre espontáneamente en la naturaleza. Sin embargo, el rendimiento de metanización varía mucho dependiendo del tipo de residuo y condiciones ambientales a las que los residuos están expuestos. La tesis “Modelling, Optimisation and Control of Anaerobic Co-digestion Processes” contribuye a la modelización, optimización y control de procesos de co-digestión con el objetivo de mejorar el rendimiento del proceso. Los fundamentos de la digestión anaerobia y co-digestión se presentan en el Capítulo 1, junto con una revisión bibliográfica sobre la modelización del proceso, centrándose principalmente en la descripción y aplicaciones del Anaerobic Digestion Model No. 1 (ADM1), y una revisión de las distintas estrategias de control que están disponibles en la actualidad. El Capítulo 2 describe detalladamente la planta piloto que se utilizó para realizar los ensayos experimentales del trabajo de investigación. En el Capítulo 3 se desarrolla y valida un método generalizado para incorporar diversos sustratos solubles fermentables en un modelo basado en ADM1. Las reacciones de fermentación de sustratos tales como el etanol, no incluidos originalmente en ADM1, se implementan como reacciones de fermentación equivalente de glucosa. Suponiendo que la acidogénesis es el paso más rápido en la digestión anaerobia, una descripción exacta de la estequiometría de la fermentación de sustratos solubles (etanol, glicerol...) y productos (acetato, butirato y propionato) no es necesaria siempre que se cumplan los balances de masa y de electrones, puesto que todos estos ácidos intermedios se convierten rápidamente en acetato, H2 y CO2 en sistemas metanogénicos. El tratamiento de residuos sólidos mediante digestión anaerobia es atractivo por su alto contenido en materia orgánica y al potencial de recuperación de energía. En el caso de sólidos, la etapa de desintegración-hidrólisis es el paso más lento del proceso. El Capítulo 4 presenta un nuevo enfoque para la modelización de las etapas de desintegración e hidrólisis de sustratos sólidos complejos. Éstos se suponen que están compuestos de una fracción fácilmente biodegradable y otra lentamente biodegradable. El modelo propuesto considera una desintegración desacoplada de estas dos fracciones para describir mejor la degradación de los residuos sólidos. La co-digestión puede mejorar el rendimiento de las plantas de biogás en términos de productividad de metano y estabilidad de la operación si se combinan adecuadamente los diferentes co-sustratos. El Capítulo 5 formula y valida un método de optimización basado en programación lineal que calcula la mejor mezcla de alimentación para sistemas de co-digestión, capaz de maximizar la producción de metano a cada velocidad de carga orgánica aplicada. La mezcla resultante está sujeta a un conjunto de restricciones fisicoquímicas, que se definen en base al conocimiento heurístico del proceso. Finalmente, el Capítulo 6 presenta una estrategia de control para co-digestión anaerobia. La mezcla óptima obtenida por programación lineal se alimenta a un digestor operando en continuo y un sistema de diagnosis evalúa el rendimiento del proceso. En función de los resultados de la diagnosis, la acción de control modifica las restricciones aplicadas en el cálculo de la alimentación. Esta acción de control permite calcular una nueva mezcla de sustratos y un nuevo TRH para el próximo período de operación. Como resultado, la estrategia funciona como un controlador en lazo cerrado que optimiza la mezcla de alimentación al digestor y posteriormente evalúa el rendimiento de operación con la mezcla alimentada

Soft sensor development and process control of anaerobic digestion

This thesis focuses on soft sensor development based on fuzzy logic used for real time online monitoring of anaerobic digestion to improve methane output and for robust fermentation. Important process parameter indicators such as pH, biogas production, daily difference in pH and daily difference in biogas production were used to infer alkalinity, a reliable indicator of process stability. Additionally, a fuzzy logic and a rule-based controller were developed and tested with single stage anaerobic digesters operating with cow slurry and cellulose. Alkalinity predictions from the fuzzy logic algorithm were used by both controllers to regulate the organic loading rate that aimed to optimise the biogas process. The predictive performance of a software sensor determining alkalinity that was designed using fuzzy logic and subtractive clustering and was validated against multiple linear regression models that were developed (Partner N° 2, Rothamsted Research 2010) for the same purpose. More accurate alkalinity predictions were achieved by utilizing a fuzzy software sensor designed with less amount of data compared to a multiple linear regression model whose design was based on a larger database. Those models were utilised to control the organic loading rate of a twostage, semi-continuously fed stirred reactor system. Three 5l reactors without support media and three 5l reactors with different support media (burst cell reticulated polyurethane foam coarse, burst cell reticulated polyurethane foam medium and sponge) were operated with cow slurry for a period of seven weeks and twenty weeks respectively. Reactors with support media were proven to be more stable than the reactors without support media but did not exhibit higher gas productivity. Biomass support media were found to influence digester recovery positively by reducing the recovery period. Optimum process parameter ranges were identified for reactors with and without support media. Increased biogas production was found to occur when the loading rates were 3-3.5g VS/l/d and 4-5g VS/l/d respectively. Optimum pH ranges were identified between 7.1-7.3 and 6.9-7.2 for reactors with and without support media respectively, whereas all reactors became unstable at ph<6.9. Alkalinity levels for system stability appeared to be above 3500 mg/l of HCO3 - for reactors without media and 3480 mg/l of HCO3 - for reactors with support media. Biogas production was maximized when alkalinity was 3 between 3500-4500 mg/l of HCO3 - for reactors without support media and 3480- 4300 mg/l of HCO3 - for reactors with support media. Two fuzzy logic models predicting alkalinity based on the operation of the three 5l reactors with support media were developed (FIS I, FIS II). The FIS II design was based on a larger database than FIS I. FIS II performance when applied to the reactor where sponge was used as the support media was characterized by quite good MAE and bias values of 466.53 mg/l of HCO3- and an acceptable value for R2= 0.498. The NMSE was close to 0 with a value of 0.03 and a slightly higher FB= 0.154 than desired. The fuzzy system robustness was tested by adding NaHCO3 to the reactor with the burst cell reticulated polyurethane foam medium and by diluting the reactor where sponge was used as the support media with water. FIS I and FIS II were able to follow the system output closely in the first case, but not in the second. FIS II functionality as an alkalinity predictor was tested through the application on a 28l cylindrical reactor with sponge as the biomass support media treating cow manure. If data that was recorded when severe temperature fluctuations occurred (that highly impact digester performance), are excluded, FIS II performance can be characterized as good by having R2= 0.54 and MAE=Bias= 587 mg/l of HCO3-. Predicted alkalinity values followed observed alkalinity values closely during the days that followed NaHCO3 addition and water dilution. In a second experiment a rulebased and a Mamdani fuzzy logic controller were developed to regulate the organic loading rate based on alkalinity predictions from FIS II. They were tested through the operation of five 6.5l reactors with biomass support media treating cellulose. The performance indices of MAE=763.57 mg/l of HCO3-, Bias= 398.39 mg/l of HCO3-, R2= 0.38 and IA= 0.73 indicate a pretty good correlation between predicted and observed values. However, although both controllers managed to keep alkalinity within the desired levels suggested for stability (>3480 mg/l of HCO3-), the reactors did not reach a stable state suggesting that different loading rates should be applied for biogas systems treating cellulose.New Generation Biogas (NGB

Sewage Treatment Plants

Sewage Treatment Plants: Economic Evaluation of Innovative Technologies for Energy Efficiency aims to show how cost saving can be achieved in sewage treatment plants through implementation of novel, energy efficient technologies or modification of the conventional, energy demanding treatment facilities towards the concept of energy streamlining. The book brings together knowledge from Engineering, Economics, Utility Management and Practice and helps to provide a better understanding of the real economic value with methodologies and practices about innovative energy technologies and policies in sewage treatment plants

Real-Time Substrate Feed Optimization of Anaerobic Co-Digestion Plants

In anaerobic co-digestion plants a mix of organic materials is converted to biogas using the anaerobic digestion process. These organic materials, called substrates, can be crops, sludge, manure, organic wastes and many more. They are fed on a daily basis and significantly affect the biogas production process. In this thesis dynamic real-time optimization of the substrate feed for anaerobic co-digestion plants is developed. In dynamic real-time optimization a dynamic simulation model is used to predict the future performance of the controlled plant. Therefore, a complex simulation model for biogas plants is developed, which uses the famous Anaerobic Digestion Model No. 1 (ADM1). With this model the future economics as well as stability can be calculated resulting in a multi-objective performance criterion. Using multi-objective nonlinear model predictive control (NMPC) the model predictions are used to find the optimal substrate feed for the biogas plant. Therefore, NMPC solves an optimization problem over a moving horizon and applies the optimal substrate feed to the plant for a short while before recalculating the new optimal solution. The multi-objective optimization problem is solved using state-of-the-art methods such as SMS-EMOA and SMS-EGO. The performance of the proposed approach is validated in a detailed simulation studyAlgorithms and the Foundations of Software technolog