Passivity-based nonlinear control of CSTR via asymptotic observers.

International audienceThis work makes use of a passivity-based approach (PBA) and tools from Lyapunov theory to design a nonlinear controller for the asymptotic stabilization of a class of non isothermal Continuous Stirred Tank Reactors (CSTR) around any desired stationary point. The convergence and stability proofs are derived in the port Hamiltonian framework. Asymptotic observers that do not require knowledge of reaction kinetics are also proposed for a system with incomplete state measurement. Numerical simulations are given to illustrate the application of the theoretical results to a CSTR with multiple steady states

Lyapunov-based control of non isothermal continuous stirred tank reactors using irreversible thermodynamics.

International audienceIn this paper, the thermodynamic availability function is used as a Lyapunov function for the practical derivation of non linear control laws for the stabilization of a large class of CSTRs far from the equilibrium. The strict convexity of the availability function is guaranteed as long as one of the extensive variables is fixed. In this study, we consider liquid mixture with constant volume, the constraint on the volume being insured by perfect regulation of the outlet flow of the CSTR. Several control laws are then derived which insure global asymptotic stability, exponential stability or simple asymptotic stability. These control laws are discussed regarding the magnitude and the dynamic variations of the control variable. It is shown that the availability function can be split into two parts: one corresponds to the mixing term and depends on mole numbers only and the other depends on both temperature and mole numbers. The two parts are positive and the second one is chosen as a new Lyapunov function. The use of this new Lyapunov function insures smooth variations of the control variable. An exothermal, first order chemical reaction leading to multiple steady-state operating points of the CSTR illustrates the proposed theory

Control of Reaction Systems via Rate Estimation and Feedback Linearization

Abstract of the conference paper The kinetic identification of chemical reaction systems often represents a time-consuming and complex task. This contribution presents an approach that uses rate estimation and feedback linearization to implement effective control without a kinetic model. The reaction rates are estimated by numerical differentiation of reaction variants. The approach is illustrated in simulation through the temperature control of a continuous stirred-tank reactor. Extended abstract Model identification and controller design are often seen as closely related tasks, since the control law is calculated using the plant model. Previous control approaches based on extensive variables or inventories are examples of this strong dependence on the model [1, 2]. Since the identification of chemical reaction systems can be a time-consuming and complex task, one would ideally like to avoid it as much as possible. The concept of variant and invariant states allows isolating the different rates in chemical reaction systems, thereby facilitating analysis, monitoring and control [3-5]. Using this concept, one can estimate dynamic effects without the need of identifying the corresponding kinetic models. This contribution presents a feedback linearization approach that is based on the estimation of unknown rates, such as the rates of reaction and mass transfer, thus allowing efficient control without the use of kinetic models. Rate estimation uses the numerical differentiation of appropriately transformed extensive variables called rate variants that are invariant with respect to the manipulated variables. A rate variant contains all the information about the corresponding rate and, as such, is decoupled from the other unknown rates. Since it is possible to estimate the unknown rates this way, the controller does not require kinetic information. However, because of the differentiation step, the controller is most effective with frequent and precise measurements of several output variables. Feedback linearization sets a rate of variation for the controlled variables, thereby guaranteeing quick convergence of these variables to their set points. For open chemical reactors, the parameters of the feedback linearization controller are determined by readily available information, such as the reaction stoichiometry, the heats of reaction, the inlet composition or the inlet and outlet flow rates. This novel control strategy is illustrated in simulation for the control of both concentration and temperature in a continuous stirred-tank reactor. [1] Georgakis, Chem. Eng. Sci., 1986, 41, 1471 [2] Farschman et al., AIChE J., 1998, 44, 1841 [3] Asbjørnsen and Fjeld, Chem. Eng. Sci., 1970, 25, 1627 [4] Bhatt et al., Ind. Eng. Chem. Res., 2011, 50, 12960 [5] Srinivasan et al., IFAC Workshop on Thermodynamic Foundations of Mathematical Systems Theory, Lyon, 2013.<br

Variant and Invariant States for Reaction Systems

Models of chemical reactors can be quite complex as they include information regarding the reactions, the transfer of species between phases, the transfer of energy, and the inlet and outlet flows. Furthermore, the effects of the various phenomena are quite intertwined and thus difficult to quantify from measured data. This paper proposes a mathematical transformation of the balance equations that allows viewing a complex reaction system via decoupled dynamic variables, each one associated with a particular phenomenon such as a single chemical reaction, a specific mass transfer or heat transfer between the reactor and the jacket. Three aspects are investigated, namely, (i) the decoupling of mole balance equations, (ii) the decoupling of mole and heat balance equations, and (iii) the applicability of the decoupling transformation for model reduction, static state reconstruction and incremental kinetic identification

Extents of Reaction and Mass Transfer in the Analysis of Chemical Reaction Systems

Monitoring, control and optimization of chemical reaction systems often requires in-depth analysis of the underlying reaction mechanisms. This dissertation investigates appropriate tools that facilitate the analysis of homogeneous and gas-liquid reaction systems. The main contribution is a novel procedure for computing the extents of reaction and the extents of mass transfer for reaction systems with inlet and outlet streams. These concepts can help reduce the dimension of reaction models and are useful in the identification of reaction kinetics based on concentrations and spectral data. Extents of reaction, mass transfer and flow The concept of extents of reaction is well established for single-phase closed systems such as batch homogeneous reactors. However, it is difficult to compute the extent of reaction for open and heterogeneous reactors due to material exchange with the surroundings via inlet and outlet streams and between phases via mass transfer. For open homogeneous reaction systems involving S species, R independent reactions, p independent inlet streams and one outlet stream, this dissertation proposes a linear transformation of the number of moles vector (S states) into four distinct parts, namely, the extents of reaction, the extents of inlet, the extent of outlet and the invariants, using only the stoichiometry, the inlet composition and the initial conditions. The open gas-liquid reaction systems considered in this thesis involve Sg species, pg independent inlets and one outlet in the gas phase, Sl species, R independent reactions, pl independent inlets and one outlet in the liquid phase. In addition, there are pm mass-transfer fluxes between the two phases. For these systems, various extents are developed successively for the liquid and gas phases. Using only the stoichiometry, the inlet composition, the initial conditions, and knowledge of the species transferring between phases, a linear transformation of the numbers of moles (Sl states) in the liquid into five distinct parts is proposed, namely, the extents of reaction, the extents of mass transfer, the extents of liquid inlet, the extent of liquid outlet and the invariants. Similarly, a transformation of the numbers of moles (Sg states) in the gas phase into four distinct parts is proposed to generate the extents of mass transfer, the extents of gas inlet, the extent of gas outlet and the invariants. Minimal state representation and state reconstruction A state representation is minimal if (i) it can be transformed into variant states that evolve with time and invariants that are constant with time (representation condition), and (ii) the transformed model is minimal (minimality condition). Since the linear transformation transforms the numbers of moles into variant states (the extents) and invariant states, it satisfies the representation condition. For homogeneous reaction systems, the linearly transformed model is of the order (R + p + 1), while the order of the linearly transformed model for open gas-liquid reaction systems is (R + pl + pg + 2pm + 2). Using the concept of accessibility of nonlinear systems, the conditions under which the transformed models are minimal state representations are derived for both types of reaction systems. Since it is often not possible in practice to measure the concentrations of all the species, the unmeasured concentrations have to be reconstructed from available measurements. Using the measured flowrates and the proposed transformations, it is possible to reconstruct the unmeasured concentrations without knowledge of the reaction and mass-transfer rate expressions. Furthermore, it is shown that the minimal number of measured concentrations is R for homogeneous reactors and (R + pm) for gas-liquid reactors. Use of concentrations and spectral data The identification of reaction kinetics can be done incrementally or globally from experimental data. Using measured concentrations and spectral data with knowledge of pure-component spectra, incremental identification proceeds in two steps: (i) computation of the extents of reaction and mass transfer from measured data, and (ii) estimation of the parameters of the individual reaction and mass-transfer rates from the computed extents. In the first step, the linear transformation is applied to compute the extents of reaction, mass transfer and flow directly from measured concentrations without knowledge of the reaction and mass-transfer rate expressions. The transformation can be extended to measured spectral data, provided the pure-component spectra are known. An approach is developed for the case where concentrations are only available for a subset of the reacting species. In the second step, the unknown rates can be identified individually for each reaction or each mass transfer from the corresponding individual extent using the integral method. For the case of measured concentrations corrupted with zero-mean Gaussian noise, it is shown that the transformation gives unbiased estimates of the extents. For the case of spectral data with unknown pure-component spectra, the contributions of the reactions and mass transfers can be computed by removing the contributions of the inlet flows and the initial conditions. This leads to the reaction- and mass-transfer-variant (RMV) form of spectral data, from which the reaction and mass-transfer rate parameters can be estimated simultaneously. However, if the RMV-form is rank deficient, the rank must be augmented before applying factor-analytical methods. In such cases, it is shown that, for example, gas consumption data can be used for rank augmentation. The concepts and tools are illustrated using simulated data. Several special reactors such as batch, semi-batch and continuous stirred-tank reactors are considered

Liquid Transport Pipeline Monitoring Architecture Based on State Estimators for Leak Detection and Location

This research presents the implementation of optimization algorithms to build auxiliary signals that can be injected as inputs into a pipeline in order to estimate —by using state observers—physical parameters such as the friction or the velocity of sound in the fluid. For the state estimator design, the parameters to be estimated are incorporated into the state vector of a Liénard-type model of a pipeline such that the observer is constructed from the augmented model. A prescribed observability degree of the augmented model is guaranteed by optimization algorithms by building an optimal input for the identification. The minimization of the input energy is used to define the optimality of the input, whereas the observability Gramian is used to verify the observability. Besides optimization algorithms, a novel method, based on a Liénard-type model, to diagnose single and sequential leaks in pipelines is proposed. In this case, the Liénard-type model that describes the fluid behavior in a pipeline is given only in terms of the flow rate. This method was conceived to be applied in pipelines solely instrumented with flowmeters or in conjunction with pressure sensors that are temporarily out of service. The design approach starts with the discretization of the Liénard-type model spatial domain into a prescribed number of sections. Such discretization is performed to obtain a lumped model capable of providing a solution (an internal flow rate) for every section. From this lumped model, a set of algebraic equations (known as residuals) are deduced as the difference between the internal discrete flows and the nominal flow (the mean of the flow rate calculated prior to the leak). The residual closest to zero will indicate the section where a leak is occurring. The main contribution of our method is that it only requires flow measurements at the pipeline ends, which leads to cost reductions. Some simulation-based tes

DYNAMICS AND CONTROL OF FORCED UNSTEADY-STATE CATALYTIC REACTORS

This research deals with the dynamics and control of forced unsteady-state catalytic reactors and it is focused on two topics: 1. auto-thermal after-treatment of lean VOC mixtures. Two reactor configurations have been taken into consideration: the reverse-flow reactor (RFR), where the flow direction is periodically changed, and the network of two or three reactors (RN), where the flow direction remains the same, but the feeding position is periodically changed, thus simulating a moving bed. This study (§3) has been organised as follows: - modelling of the two reactor configurations and study of the influence of the main operating parameters (§3.1 and §3.2). As the RFR shows higher stability with respect to disturbances in the feed a deeper investigation has been carried out on this device; - optimisation of the RFR. A simplified model has been used for this analysis in order to strongly reduce the computational effort which is required by detailed models. It has been pointed out that both heat capacity and thermal conductivity of the catalyst play a role, not less important than kinetic activity, strongly influencing the minimum inlet VOC concentration required for autothermal operation (§3.3); - experimental validation of the modelling results in a bench-scale RFR with reduced influence of the wall effects. This activity has been carried at the Departamento de Ingeniería Química y Tecnología del Medio Ambiente-Universidad de Oviedo (Spain) in the framework of the Research Project "Azioni Integrate Italia-Spagna", granted by the Italian Ministry of Research (MIUR). In addition to the intrinsecally dynamic behaviour of the RFR, one must deal with unexpected external perturbations (feed concentration, composition and temperature) which may lead to reactor extinction or catalyst overheating. In order to avoid these problems it is necessary to implement some closed-loop control strategy based on the measurement of the inlet concentration (and composition) and the outlet conversion. This study has been organised as follows: - a model-based soft-sensor (observer) has been developed, in order to quickly and reliably estimate the feed composition from some temperature measurements in the reactor, thus avoiding expensive hardware sensors and time consuming on-line measurements. As deriving an observer from a detailed model is an overwhelming task, a simplified model has been developed and validated in a medium size RFR. This research has been carried out in cooperation with prof. H. Hammoury and D. Schweich of the CPE-Lyon, France (§4.1); - a Model Based control strategy has been proposed and tested to prevent reaction extinction and catalyst overheating (§4.2); 2. enhancement of conversion and selectivity in exothermic, equilibriumlimited reactions. Methanol synthesis and syngas prouction by partial oxidation of methane have been considered as test reactions. This section has been organised as follows: - modelling of the two processes in the two reactor configurations previously described. The influence of the main operating conditions has been addressed with the aim to optimise the two processes. As the RN has shown higher conversion and selectivity with respect to the RFR, in the following the research will be focused on this device (§5); - a simple open loop control policy, which can be useful for a safe startup, has been also tested to study the response of the RN to disturbances on the input parameters, showing that a more robust control strategy is needed for this application; - if a tight control on the outlet product conversion is needed, a Model Predictive Control scheme (MPC) should be used, varying the switching time to maximise the conversion and the selectivity of the reactor. The on-line optimisation requires a simplified model and a Neural Network based model has been developed (§6