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Abstract



System Identification of Nonlinear Thermochemical Systems with Dynamical Instabilities


Thermochemical systems appear in applications as widespread as in combustion engines, in industrial chemical plants and inside biological cells. Science in all these areas is going towards a more model based thinking, and it is therefore important to develop good methods for system identification, especially fit for these kind of systems. The presented systems are described as nonlinear differential equations, and the common feature of the models is the presence of a boundary between an oscillating and a non-oscillating region, i.e. the presence of a bifurcation. If it is known that a certain input signal brings the system to a bifurcation manifold, and this is the case for many thermochemical systems, this knowledge can be included as an extra constraint in the parameter estimation. Except for special cases, however, this constraint can not be obtained analytically. For the general case a reformulation, adding variables and equally many constraints, have been done. This formulation allows for efficient use of standard techniques from constrained optimization theory. For systems with large state spaces the parameter vector describing the initial state becomes big (sometimes > 1000), and special treatment is required. New theory for such treatment have been shown, and the results are valid for systems operating close to a Hopf bifurcation. Through a combined center manifold and normal form reduction, the initial state is described in minimal degrees of freedom. Experiment designs are presented that force the minimal degrees of freedom two be 2 or 3, independently of the dimension of the state space. The initial state is determined by solving a sub-problem for each step in the ordinary estimation process. For systems starting in stationary oscillations the normal form reduction reveals the special structure of this sub-problem. Therefore it can be solved in a straight-forward manner, that does not have the problem of local minima, and that does not require any integration of the differential equations. It is also shown how the knowledge, coming from the presence of a bifurcation, can be used for model validation. The validation is formulated as a test quantity, and it has the benefit that it can work also with uncalibrated sensors, i.e. with sensors whose exact relation to the state variables is not known. Two new models are presented. The first is a multi-zonal model for cylinder pressure, temperature and ionization currents. It is a physically based model with the main objectives of understanding the correlation between the ionization curve and the pressure peak location. It is shown that heat transfer has a significant effect on this relation. It is further shown that the combination of a geometrically based heat transfer model and a dynamical NO-model predicts the correct relationship between the pressure and ionization peak location within one crank angel degree. The second developed model is for the mitogenic response to insulin in fat cells. It is the first developed model for this specific pathway and the model has been compared and estimated to experimental data. Finally, a 16-dimensional model for activated neutrophils has been used to generate virtual data, on which the presented methods have been applied, and on which the performance of the methods were demonstrated.

Gunnar Cedersund

2004

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