Gábor Szederkényi

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.

A linear programming approach to weak reversibility and linear conjugacy of chemical reaction networks

A numerically effective procedure for determining weakly reversible chemical reaction networks that are linearly conjugate to a known reaction network is proposed in this paper. The method is based on translating the structural and algebraic characteristics of weak reversibility to logical statements and solving the obtained set of linear (in)equalities in the framework of mixed integer linear programming. The unknowns in the problem are the reaction rate coefficients and the parameters of the linear conjugacy transformation. The efficacy of the approach is shown through numerical examples.

Computing weakly reversible linearly conjugate chemical reaction networks with minimal deficiency

Mass-action kinetics is frequently used in systems biology to model the behavior of interacting chemical species. Many important dynamical properties are known to hold for such systems if their underlying networks are weakly reversible and have a low deficiency. In particular, the Deficiency Zero and Deficiency One Theorems guarantee strong regularity with regards to the number and stability of positive equilibrium states. It is also known that chemical reaction networks with distinct reaction structure can admit mass-action systems with the same qualitative dynamics. The theory of linear conjugacy encapsulates the cases where this relationship is captured by a linear transformation. In this paper, we propose a mixed-integer linear programming algorithm capable of determining the minimal deficiency weakly reversible reaction network which admits a mass-action system which is linearly conjugate to a given reaction network.

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.

Parameter Estimation of a Simple Primary Circuit Model of a VVER Plant

A simple dynamic model in physical coordinates (an improved version of our model reported in ) and the corresponding parameter estimation procedure for the primary circuit dynamics of VVER-type pressurized water reactors is presented in this paper. The primary uses of the model are control oriented dynamic model analysis and high level controller design. The most important requirements of the simple physical model are that it should contain the possible minimal number of differential equations and it should be capable of describing important dynamic phenomena such as load change transients between day and night periods. Furthermore, the estimated parameter values should fall into physically meaningful ranges. The parameter estimation method is based on the decomposition of the overall system model into separably identifiable subsystems. The identification of the subsystems is followed by the fine-tuning of the model parameters with the parameter estimation of the entire system model. The constructed model satisfies the predefined requirements and its response shows good fit to the measurement data that were obtained from three units of the Paks Nuclear Power Plant in Hungary.

Dynamic analysis and control of biochemical reaction networks

In the present work, we combine the concepts and tools from Irreversible Thermodynamics and Control Theory in a contribution to unravel the origin of complex nonlinear behaviour in biochemical networks. Regarding cells as thermodynamic systems, we can consider dynamic evolution of intracellular processes in terms of the combined action of an endogenous entropy production and the entropy flux associated to chemicals passing through the control volume. Based on a generalized description of biochemical systems, a physically motivated storage function is constructed and used for stability analysis. In this way, the entropy flux of open systems can be meaningfully modified by efficient nonlinear control schemes capable of network stabilization, and irreversible thermodynamics provide us with the physical insight to further interpret the controlled response.

Throwing motion generation using nonlinear optimization on a 6-degree-of-freedom robot manipulator

A 6-degree-of-freedom rigid robot arm and its throwing motion generation is described in this paper. The trajectories for the joint variables are generated off-line as a cubic spline obtained using general constrained nonlinear optimization, taking into consideration limitations (position, speed, acceleration and jerk) of the joint actuators, and the current limit of the whole structure. The obtained trajectories are previously checked to avoid collisions using oriented bounding boxes and their separating axis theorem tests. The trajectory tracking of the individual joint is done using a discrete-time constrained optimal control technique.