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The temperature control of the heterogeneous alkylation, where H2SO4 is used as catalyst, is discussed in this paper. The problem is to design a control function to stabilize temperature in face of uncertain kinetic model. The proposed controller, whose structure resembles a PI-controller, is based on energy balance. The resulting feedback controller is robust, leads to an acceptable performance, and computes the temperature of the coolant from the refrigeration section to the reactor. The effectiveness and robustness of the designed controller for computing the coolant temperature is tested by means of simulations in such a manner that we study the effects of: (i) load disturbances, (ii) model uncertainties and (iii) initial conditions for estimation values. [ABSTRACT FROM AUTHOR]

The oscillatory behavior in two controlled processes is presented in this chapter. The two study cases can permit further numerical or analytical research that, on the one hand, allows for an evaluation of new criteria on dynamics of controlled systems and, on the other, leads to new pictures featuring nonlinear (possibly chaotic) dynamics. The former is a feedback-controlled digester which is interconnected with heat exchanger via recycle stream. Oscillations in temperature bioreactor is studied in this case. The process is an anaerobic digestion for distillery vinasses and a heat exchanger. The heat exchanger is basically controlled by a Proportional-Integral-Derivative feedback (PID control) while the bioreactor is controlled by a feedback law with uncertainties compensation. In fact, the first case corresponds to the bioreactor discussed in Part II of this book. The latter is open-loop controlled, and concerns to gas-liquid tide column. Such a gas-liquid column can exhibit three classes of dynamical behavior: bubbling (disperse fluid-flow), vortical-spiral type, and turbulent (three-region) regime. Both processes have recycle streams, and their time series are analyzed exploiting Poincaré maps, maximum Lyapunov exponents and power spectrum density. [ABSTRACT FROM AUTHOR]

The Petlyuk distillation system has been considered with special interest in the field of separation processes because of the high energy savings that it can provide with respect to the operation of sequences based on conventional columns. The original design of the Petlyuk structure, however, shows two interconnections that seem to affect its operational and controllability properties. For one thing, the arrangement is more complex than the common structure of the conventional distillation systems of one feed and two products with no recycle streams. Furthermore, the interconnections show a bidirectional flow of the vapor streams between the two columns of the Petlyuk arrangement, posing a major control challenge for its operation. To overcome this problem, two new structures have been suggested that use unidirectional flows of the vapor or liquid interconnecting streams. The new options have been conceptually developed to improve the controllability properties of the Petlyuk system, but no formal analysis has been conducted on this matter. In this work, a comparative analysis of the control properties of the Petlyuk column and the new arrangements with unidirectional interconnecting flows is presented. Through a singular value decomposition analysis, it is shown that the new schemes provide better theoretical controllability properties than the Petlyuk system. Closed loop tests using proportional-integral controllers were also carried out, and the results showed that, in most of the cases considered, the new arrangements improved the dynamic responses of the Petlyuk column. Such arrangements, therefore, show promising perspectives for its practical consideration. [ABSTRACT FROM AUTHOR]

In this chapter, the non-linear dynamics of a nonisothermal CSTR where a simple first order reaction takes place is considered. From the mathematical model of the reactor without any control system, and by using dimensionless variables, it has been corroborated that an external periodic disturbance, either inlet stream temperature and coolant flow rate, can lead to chaotic dynamics. The chaotic behavior is analyzed from the sensitivity to initial conditions, the Lyapunov exponents and the power spectrum of reactant concentration. Another interesting case is the one researched from the self-oscillating regime, showing that a periodic variation of coolant flow rate can also produce chaotic behavior. Finally, steady-state, self-oscillating and chaotic behavior with two PI controllers have been investigated. From different parameters of the PI controllers, it has been verified that a new self-oscillating regime can appear. In this case, the saturation in a control valve gives a Shilnikov type homoclinic orbit, which implies chaotic dynamics. The existence of a new set of strange attractors with PI control has been analyzed from the initial conditions sensitivity. An Appendix to show a computationally simple form to implement the calculation of Lyapunov exponents is also presented. [ABSTRACT FROM AUTHOR]

Recently, anaerobic digestion (AD) has shown potential applicability to reduce organic matter from wastewater. However, AD processes are not widely applied at industrial scale. One of the main factors that explain this phenomenon is related to the lack of control schemes that guarantee a suitable operation of the process. As well, AD control is a non trivial task, because the control schemes must operate under an uncertain environment because of the difficult to monitoring AD processes (on-line measurements are limited and expensive). Particularly, this chapter is devoted to the development and the experimental validation of a robust nonlinear approach to regulate (i) the total amount of decomposable organic pollutant agents measured as total organic carbon (TOC) and, (ii) the concentration of volatile fatty acids (VFA); by using in both cases the input flow rate as manipulated variable. The proposed approach is a model-based controller obtained from geometric control tools and the definition of an uncertain but observable function that lumps the uncertain terms associated to the dynamics of the controlled variables TOC and VFA (e.g., feeding composition, kinetic growth functions and parameters). The robust scheme is composed of a feedback linearizing control law and a high-gain Luenberger observer which adapts the linearizing control law from estimates of the uncertain function. The robust approach is experimentally validated in a fixed-bed AD process used in the wastewater treatment of industrial distillery vinasses. Several experiments are performed to evaluate the controller performance and robustness under different set-points, feeding concentrations and sampling times (2 and 30min). Results show that both, the regulation of COT and VFA can be addressed in spite of the full ignorance of the kinetic growth functions, noisy measurements and unknown feeding composition. [ABSTRACT FROM AUTHOR]

The on-line diagnosis is a key requirement of industrial processes. This is particularly true in the case of biological process due to the composition of media, the requirements of operating conditions and the wide variety of possible disturbances that necessitate careful and constant monitoring of the processes. Moreover, because only partial information is available in an on-line context and because of the technical and biological complexities of the involved processes, specific characteristics are required for diagnosis purposes. Several approaches like quantitative model based, qualitative model based and process history based methods were applied over the years. This chapter presents a methodological framework based on Evidence theory to manage the fault signals generated by conventional approaches (i.e., residuals from hardware and software redundancies, fuzzy logic based modules for process state assessment) and to account for uncertainty. The advantages of using evidence theory like modularity, detection of conflict and doubt in the information sources are illustrated with experimental results from a 1m3 fixed bed anaerobic digestion process used for the treatment of industrial distillery wastewater. [ABSTRACT FROM AUTHOR]

In this chapter, some state estimation schemes used in bioprocesses engineering are firstly reviewed with particular emphasis on the so-called nonlinear observers. Second, two simple robust nonlinear observers are proposed and applied in a number of bioprocesses. The first estimation scheme is a generalized asymptotic observer which has demonstrated to be robust in the face of a complete lack of knowledge of the process nonlinearities whereas the second one has shown to be robust in the face of both, the system nonlinearities and the input uncertainty and yields guaranteed intervals for the non-measured variables from the available measurements. The design of both observer schemes are detailed for a general dynamical system which may be applied in a number of bioprocesses. The interval observer is further developed for fault detection and diagnosis purposes. In addition, detailed stability analysis are developed for both observers. Finally, these observers are tested in an actual experimental pilot plant used for the anaerobic digestion of wine vinasses. Key results are presented and discussed. [ABSTRACT FROM AUTHOR]

In this chapter the control problem of output tracking with disturbance rejection of chemical reactors operating under forced oscillations subjected to load disturbances and parameter uncertainty is addressed. An error feedback nonlinear control law which relies on the existence of an internal model of the exosystem that generates all the possible steady state inputs for all the admissible values of the system parameters is proposed, to guarantee that the output tracking error is maintained within predefined bounds and ensures at the same time the stability of the closed-loop system. Key theoretical concepts and results are first reviewed with particular emphasis on the development of continuous and discrete control structures for the proposed robust regulator. The role of disturbances and model uncertainty is also discussed. Several numerical examples are presented to illustrate the results. [ABSTRACT FROM AUTHOR]

In this chapter, the nonlinear and linear mathematical model of a CSTR where an irreversible exothermic reaction takes place is considered. From the analysis of the steady states, the curves of removed and generated heat are deduced in order to determine the equilibrium point and the transfer function of the reactor. Considering a set of reactors ranging from small to high volume, it is shown that the open-loop transfer function can be conditionally stable, and the effect of the scaling-up is investigated by means of the root locus. Reactor and jacket equilibrium temperatures vs. reactor volume are deduced in order to obtain an intuitive notion of the reactor controllability. The problem of the local control of a single loop concentration and cascade temperature control from the linearized model previously considered is analyzed by using PI controllers. Several examples considering step responses to changes in the concentration and temperature references are considered. Finally, the decoupling and the feedback control of the reactor by using the pole-placement technique have been also considered. [ABSTRACT FROM AUTHOR]