Katalin M. Hangos

Local dissipative Hamiltonian description of reversible reaction networks

In this letter we show that closed reversible chemical reaction networks with independent elementary reactions admit a global pseudo-Hamiltonian structure which is at least locally dissipative around any equilibrium point. The structure matrix of the Hamiltonian description reflects the graph topology of the reaction network and it is a smooth function of the concentrations of the chemical species in the positive orthant. The physical interpretation of the description is briefly explained and two illustrative examples are presented for global and local dissipative Hamiltonian description, respectively.

Grey box fault detection of heat exchangers

Abstract A grey-box model-based method for fault diagnosis is proposed in this paper. The method is based on a first principle model of the process unit, i.e. a heat exchanger, and on a grey-box model of the fault, i.e. the deterioration of the heat transfer surface by aging. During normal operating conditions the heat transfer coefficient is constant or slowly decreasing due to material settling on the heat transfer surface. In old heat exchangers big pieces of settled material can break off causing damage. When this happens, the heat transfer coefficients will rise sharply. In the proposed method a recursive least-squares estimator with forgetting factor is used to track the heat transfer coefficients. The settled material breakage fault is detected via detection of abrupt positive jump in the estimated heat transfer coefficients using a cumulative sum (CUSUM) test. The capability to detect faults in any industrial equipment is heavily dependent on the availability of suitable measurements. For heat exchangers the variables related to the in- and outflows of the equipment (flowrates and temperatures) are usually measured, but measurements along the equipment length are rarely available. Therefore, the possibilities of fault location in space are rather limited. However, simplified models can be used for fault detection in this case. Moreover, a fault detection method is proposed with the possibility of spatial fault location when measurements along the cold side are available. The proposed method is illustrated on simulated examples with different measurement situations.

Finding complex balanced and detailed balanced realizations of chemical reaction networks

Reversibility, weak reversibility and deficiency, detailed and complex balancing are generally not “encoded” in the kinetic differential equations but they are realization properties that may imply local or even global asymptotic stability of the underlying reaction kinetic system when further conditions are also fulfilled. In this paper, efficient numerical procedures are given for finding complex balanced or detailed balanced realizations of mass action type chemical reaction networks or kinetic dynamical systems in the framework of linear programming. The procedures are illustrated on numerical examples.

Nonlinear analysis and control of a continuous fermentation process

Abstract Different types of nonlinear controllers are designed and compared for a simple continuous bioreactor operating near optimal productivity. This operating point is located close to a fold bifurcation point. Nonlinear analysis of stability, controllability and zero dynamics is used to investigate open-loop system properties, to explore the possible control difficulties and to select the system output to be used in the control structure. A wide range of controllers are tested including pole placement and LQ controllers, feedback and input–output linearization controllers and a nonlinear controller based on direct passivation. The comparison is based on time-domain performance and on investigating the stability region, robustness and tuning possibilities of the controllers. Controllers using partial state feedback of the substrate concentration and not directly depending on the reaction rate are recommended for the simple fermenter. Passivity based controllers have been found to be globally stable, not very sensitive to the uncertainties in the reaction rate and controller parameter but they require full nonlinear state feedback.

Controllability and observability of heat exchanger networks in the time-varying parameter case

Abstract In this paper the structural controllability and observability of heat exchanger networks are determined from qualitative information about the heat exchangers and their network topology. The heat exchanger network is modelled as a time-varying linear system based on first engineering principles where the effect of the flowrate variations is described by unknown time-varying parameters, inlet temperature variations are regarded as disturbances and external heaters/coolers are considered as input variables. Necessary and sufficient conditions for structural controllability and observability of heat exchanger networks are derived, based on an extended Kalman-type rank criterion for linear systems with time-varying parameters. Determining the structural controllability and observability of heat exchanger networks needs only checks for the input and output connectability of the network in both constant and time-varying parameter cases. The results are extended to the more-practical case where bypass ratios are also used as control variables and where more than one time-varying parameter enters into the state-space matrices.

Engineering Model Reduction and Entropy-based Lyapunov Functions in Chemical Reaction Kinetics

In this paper, the structural properties of chemical reaction systems obeying the mass action law are investigated and related to the physical and chemical properties of the system. An entropy-based Lyapunov function candidate serves as a tool for proving structural stability, the existence of which is guaranteed by the second law of thermodynamics. The commonly used engineering model reduction methods, the so-called quasi equilibrium and quasi steady state assumption based reductions, together with the variable lumping are formally defined as model transformations acting on the reaction graph. These model reduction transformations are analysed to find conditions when (a) the reduced model remains in the same reaction kinetic system class, (b) the reduced model retains the most important properties of the original one including structural stability. It is shown that both variable lumping and quasi equilibrium based reduction preserve both the reaction kinetic form and the structural stability of reaction kinetic models of closed systems with mass action law kinetics, but this is not always the case for the reduction based on quasi steady state assumption.

Structure simplification of dynamic process models

Abstract Lumped process models derived from first engineering principles are usually too detailed for control purposes where only the major dynamic characteristics of the system should be captured. Two common steps of simplifying dynamic process models, the steady-state variable removal and the variable lumping simplification steps are investigated in this paper, in order to show if they preserve the key properties: the structural controllability, observability and stability of the models. In order to enable the formal analysis, these simplification steps are represented as context sensitive graph transformations acting on the structure graphs of the dynamic process models. It is shown that the simplification transformations above preserve the structural controllability and observability of process models. But only the steady-state variable removal transformation has been found not to destroy their structural stability. The variable lumping structure simplification transformation is further specialized to the case of cascade process models. It is shown that the inverse of this transformation does exist in this case, and both transformations preserve structural controllability and observability.

Structural solvability analysis of dynamic process models

Abstract The variable structure of dynamic process models is represented by a directed graph termed as the representation graph for the purpose of solvability analysis in this paper. Structural solvability analysis, the determination of the structural differential index and the structural decomposition of the differential–algebraic equations (DAE) model set can be performed using the representation graph. The characteristic features of the representation graph for both index 1 and high index semi-explicit DAE models are presented. Based on the above a novel index reduction procedure for high index models is proposed. The notions and methods are illustrated on simple process examples.

Verification of a primary-to-secondary leaking safety procedure in a nuclear power plant using coloured Petri nets

This paper deals with formal and simulation-based verification methods of a PRImary-to-SEcondary leaking (abbreviated as PRISE) safety procedure. The PRISE safety procedure controls the draining of the contaminated water in a faulty steam generator when a non-compensable leaking from the primary to the secondary circuit occurs. Because of the discrete nature of the verification, a Coloured Petri Net (CPN) representation is proposed for both the procedure and the plant model. We have proved by using a non-model-based strategy that the PRISE safety procedure is safe, there are no dead markings in the state space, and all transitions are live; being either impartial or fair. Further analysis results have been obtained using a model-based verification approach. We created a simple, low dimensional, nonlinear dynamic model of the primary circuit in a VVER-type pressurized water nuclear power plant for the purpose of the model-based verification. This is in contrast to the widely used safety analysis that requires an accurate detailed model. Our model also describes the relevant safety procedures, as well as all of the major leaking-type faults. We propose a novel method to transform this model to a CPN form by discretization. The composed plant and PRISE safety procedure system has also been analysed by simulation using CPN analysis tools. We found by the model-based analysis-using both single and multiple faults-that the PRISE safety procedure initiates the draining when the PRISE event occurs, and no false alarm will be initiated.

Modeling and model identification of a pressurizer at the Paks Nuclear Power Plant

Abstract The modeling and identification of a pressure controlling tank located in the primary circuit of the Paks Nuclear Power Plant in Hungary is presented in this paper. The main goal of the identification procedure is to produce a physically meaningful process model which is simple enough but still applicable for controller design. Based on first engineering principles a second order dynamic model has been constructed the structure of which has been validated by using the ESS structure estimation algorithm. The estimated model forms the basis of an already implemented controller in Paks NPP.