A.C.P.M. Backx

Modeling of an Automotive Exhaust Gas Converter at Low Temperatures Aiming at Control Application

The LEV/ULEV emission standards pose challenging problems on automotive exhaust gas treatment. This increases the need for good catalytic converter models, which can be applied for control. A dynamic converter model was made on the basis of first principles, accounting for the accumulation of mass in the bulk gas phase, in pores of the washcoat and on the catalytic surface, as well as for the energy accumulation in the gas and solid phase. The basis for the model is the elementary step kinetics of the individual global reactions. The main purpose of the model is to describe the low temperature behavior of the converter, when the majority of the emissions occur. The light-off process is analyzed in detail with different inputs. The biggest improvement occurs when secondary air is injected in front of the converter. The converter model is also coupled with a simple SI engine model to investigate the dynamic behavior of the whole system.

LOW TEMPERATURE DYNAMIC CHARACTERISTICS OF A THREE-WAY CATALYTIC CONVERTER

Abstract A mathematical model of a three-way catalytic converter based on a detailed chemical kinetic model has been created mainly to analyze the converters dynamic behavior at low temperatures. The light-off process of the converter is analyzed in detail. Competition of species for empty noble metal surface determines the light-off characteristic, as inhibition processes increase light-off temperatures of some exhaust gas components in the complete exhaust mixture. Perturbations of the exhaust gas mixture around stoichiometry can in certain conditions decreasethe effect of inhibition and lower the light-off temperature for some exhaust components.

Nonlinear transition controller design using neural networks tested on a polymerization reactor

We propose a complete scheme for a nonlinear controller design to steer the process between different operating points. The main features of the controller are that it includes a state observer and dynamic state feedback. The process disturbances are considered in the design as well. The controller is designed for a wide range of nonlinear process dynamics where the performance of a linear controller dramatically deteriorates. The state observer includes a nonlinear state space simulation model of the process being estimated from measured input/output data. The state vector is partitioned into two parts which reflect our a priori knowledge about the process dynamics. The design algorithm is verified using a simulation model of a fluidized bed polymerization reactor. No assumptions are made in the design that would be violated in application of the controller for a real process.

Asymptotic Characteristics of Toeplitz Matrix in SISO Model Predictive Control

The singular value decomposition (SVD) of the Toeplitz matrix in the quadratic performance index of Model Predictive Control (MPC) is studied. It was shown in Rojas et al. (2003, 2004) that for sufficiently long prediction horizons, the eigenvalues of the Hessian matrix converge to the energy density spectrum of the associated system seen by the performance index. In this paper, we extend that work and show that the left and right singular vectors of the Toeplitz matrix provide the phase information of the associated system for sufficiently long prediction and control horizons. A SISO system is used to illustrate the method.

State-tracking control of non-linear systems with unknown dynamics in the presence of disturbances

This paper deals with the design of a state tracking controller for a non-linear dynamical system where the dynamics are only partly known and where only part of the state vector components are directly measured. The design procedure takes the influence of state disturbances and measurement noise into account, which are naturally present in practical designs of control systems. The design of a non-linear controller is based on the estimation of a simulation model of the process in state space form. A non-linear filter gain is estimated to build up a state observer to be used for the optimization of a non-linear static state feedback controller. All non-linear maps are approximated by neural networks trained by a mixed stochastic deterministic optimization procedure. The performance of the proposed design procedure is demonstrated by means of at simulation example.

Model reduction of systems with traveling waves using projection methods

Proper Orthogonal Decomposition (POD) based projection methods are an impor- tant tool for the reduction of complex nonlinear models. Large reductions in model order can be frequently be obtained due to the exploitation of correlations between model states that exist for representative behavior of the model. However, when this model behavior includes traveling waves or shock fronts these methods perform less well as a large number of modes is required to capture this type of behavior. This paper investigates the use of correlation to pre-process simulation data such that bi-orthogonal projection can subsequently be applied to obtain a reduced model that is of low order.

Reduction of kinetic mechanisms in reactive flow models for dynamic optimization

In this contribution kinetic mechanism reduction techniques are developed and applied to a 1-D plug-flow reactor (PFR) model. The proposed method yields different reduced mechanisms at each spatial position in the reactor. Local sensitivity analysis and flux analysis are combined with species lumping to obtain an automated reduction method. The criteria for the reduction method were modified to account for the spatial distribution of the reactor concentrations. The method generates reduced models with the same spatial structure as the original model that approximate reactor outflow concentrations. These models are used for dynamic optimization with an integral cost criterion applied to the reactor outflows.

APPROXIMATION OF FAST SPECIES IN KINETIC NETWORKS USING NON-NEGATIVE POLYNOMIALS

Abstract Kinetic models of reaction networks often feature sets of fast-reacting species. If the slow timescale is of interest these species can be assumed to be in equilibrium and using a lumping method a system of lower order is obtained. However, to obtain a reduction in the number of equations that represent the dynamics of the reaction network, an explicit representation of the equilibrium species is required. In many cases algebraic manipulations required to obtain an explicit form are prohibitive. This paper examines the use of constrained polynomial fitting techniques to obtain an approximation of the explicit form that is consistent with the physical constraints of the reaction network.