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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 predictorlike 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.

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 * Corresponding author. Tel.: +32 9 264 61 29; fax: +32 9 264 62 35Email addresses: eveline.volcke@ugent.be (E.I.P. Volcke), mihaela@autoctrl.ugent.be (M. Sbarciog), erik.noldus@ugent.be (E.J.L. Noldus), bernard.debaets@ugent.be (B. De Baets), mia.loccufier@ugent.be (M. Loccufier) Preprint submitted to Mathematical BiosciencesSeptember 21, 2010 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.

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.

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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.

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