Matthias Bitzer

Flatness-based feedforward control of a two-stage turbocharged diesel air system with EGR

In this work, a nonlinear inversion-based feed-forward controller for a two-stage turbocharged diesel air system with exhaust-gas recirculation is developed. A nonlinear mathematical model is derived for the controller design on the basis of a high-order reference model by applying the singular perturbation theory. In this context, simplified models of different air system components are formulated in such a way that the resulting reduced-order model is differentially flat. Thereafter, the differential flatness property of the design model is exploited to derive the feedforward controller. The approximation performance of the reduced-order model as well as the suitability of the developed feedforward control scheme are finally evaluated by means of simulation studies.

Mathematical modelling of a domestic heating system with stratified storage tank

A hybrid distributed parameter model of a heating system for domestic hot water is presented in this paper. This heating system comprises a condensing boiler (burner), a counter current heat exchanger, and a so-called stratified storage tank which is the state of the art domestic hot water storage unit. The paper presents the model for the different operational modes of the plant which are described by a finite state automaton representing the discrete-event dynamics and driving the underlying continuous-time dynamics of the storage tank, the heat exchanger, and the burner. These interconnected components are modelled by a system of six coupled, quasi-linear partial differential equations (PDEs) comprising diffusion-, convection-, and source terms. In order to perform numerical simulations, the set of PDEs is spatially discretized using the method of lines. Thereby, the influence of various discretization schemes on the temporal evolution of the traveling temperature profiles in the single components is investigated. A high resolution slope limiter scheme for the stratified storage tank and a higher order up–/downwind scheme for the heat exchanger and the burner are found to be an appropriate choice for the spatial discretization of the model equations in order to adequately cover the plant dynamics. Simulation results fortify the effectiveness of the chosen discretization schemes and show the excellent performance of the suggested model representing the measurement data.

Lumped Parameter Modeling of Electrochemical and Thermal Dynamics in Lithium-Ion Batteries

Abstract This paper presents a novel electrochemical lithium-ion cell model which can be used in battery control units. Based on classical single-particle approaches, a lumped-parameter nonlinear model is developed that is able to predict accurately the terminal voltages for arbitrary loads, and even for potentiostatic operation. The key features of the extended model are: (1) an incorporation of the electrolyte potential, (2) a modal decomposition of the partial differential equation for the lithium-ion concentration in the liquid phase, (3) a functional handling of the SOC-dependent diffusivity in the insertion materials of both electrodes, and (4) a consideration of temperature-dependent kinetic processes. The prediction quality of the model is verified by means of various experimental load cases applied to the investigated high-power 18650 cell.

Design of a combined quasi-linear distributed state and online parameter estimator for a stratified storage tank

This contribution presents the late lumping design of a combined distributed state and online parameter estimator for a state of the art domestic hot water storage system, a so called stratified storage tank. The discrete- and continuous-time dynamics of the storage tank are described by a hybrid, quasi-linear distributed parameter system, namely a finite state automaton interacting with an underlying diffusion-convection system (DCS), characterized by heat exchange to the ambiance and change of the flow direction. For the development of an advanced process control, the reconstruction of the temperature profile in the storage tank is compulsory. Therefore, a quasi-linear distributed parameter observer with a simultaneously running online estimation algorithm for the determination of the flow velocity are derived. Hereby, the injected correction terms and their tuning parameters are designed based on physical and heuristical considerations. In view of observer convergence, a discussion on the choice of appropriate sensor locations as well as the approximation of the initial temperature profile for the state observer are given. The performance of the distributed state observer and parameter estimator is illustrated by simulation studies and compared to measurement data

FEEDFORWARD BOUNDARY CONTROL OF LINEAR DISTRIBUTED PARAMETER SYSTEMS USING A NUMERICAL INVERSE LAPLACE TRANSFORM

Abstract The feedforward boundary control design and disturbance compensation for a class of linear distributed parameter systems with fiat and non-fiat outputs is presented based on the analytical derivation of a control law in the Laplace domain and the use of a numerical inverse Laplace transformation. Control laws are derived for a conduction system, a conduction-convection system with source term, and two different types of counter-current heat exchanger systems. For the calculation of the inverse Laplace transform, a variant of the Weeks algorithm with automatic parameter tuning is employed. Simulation results show that the algorithm converges for different desired output trajectories and a wide range of parameter configurations.

Prioritization-based constrained trajectory planning for a nonlinear turbocharged air system with EGR

The problem of generating sufficiently smooth reference trajectories for the flatness-based feedforward control of a Diesel engine air system with input constraints is addressed in this work. The proposed trajectory planning can handle arbitrary command inputs and provides the reference signals required by the flatness-based controller. Thereby, the desired tracking behavior for the controlled variables is defined by a linear target system. The input constraints are taken into account by limiting the target system dynamics to the realizable air system dynamics as determined by the flat design model and the limits of the control input. Furthermore, a prioritization of the controlled variables is included in this limitation. The differentially flat reduced-order design model used in this work is deduced from a high-order reference model by applying the singular perturbation theory. The suitability of the proposed trajectory planning in combination with the feedforward controller is shown by means of simulation studies relying on the high-order reference air system model.

Fault Tolerant Oxygen Control of a Diesel Engine Air System

Abstract This paper is devoted to the fault tolerant control problem of a Diesel engine air system having a jammed Exhaust Gas Recirculation (EGR) valve. The fault tolerant control is based on replaning the trajectory in order to track a new controlled variable which is the oxygen concentration in the intake manifold instead of the fresh air mass flow. The trajectory planning is based on an inverse model approach, utilizing the fundamental thermodynamic relations of the air system.

Beladungsregelung einer Brennwerttherme mit Schichtladespeicher (Control of a Heating System with Stratified Storage Tank)

In dem Beitrag wird ein Regelkonzept für die Beladung eines Schichtladespeichers zur Warmwasserversorgung vorgestellt. Die Beladung erfolgt über die dem Speicher vorgeschalteten Komponenten Wärmetauscher und Brenner des betrachteten Heizungssystems. Dem Reglerentwurf liegt ein dynamisches Modell zugrunde, das aus fünf partiellen Differentialgleichungen für Brenner und Wärmetauscher besteht. Für den modellbasierten Reglerentwurf wird ein modularisierter Ansatz verfolgt, bei dem Brenner und Wärmetauscher separat betrachtet werden. Für den Brenner wird auf Basis eines reduzierten, nichtlinearen Galerkin-Modells mit Hilfe der Ein-/Ausgangslinearisierung ein entsprechendes Regelgesetz hergeleitet. Die Trajektorienfolge für die Austrittstemperatur des Wärmetauschers wird durch eine Vorsteuerung mit unterlagerter PI-Regelung realisiert. Dabei wird die Vorsteuerung durch Inversion der transzendenten Übertragungsfunktion des linearen verteilt-parametrischen Modells des Wärmetauschers sowie mit Hilfe einer numerischen Laplace-Rücktransformation auf Basis des Weeks-Algorithmus berechnet. A control scheme for the loading of a stratified storage tank is presented. The loading is realized by means of a burner and a heat exchanger of the considered heating system. The control design is based on a dynamical model consisting of five partial differential equations for the burner and the heat exchanger. A modularized set-up of the control scheme is proposed, burner and heat exchanger are therefore considered separately. For the burner, a feedback control is designed by means of a reduced-order, nonlinear Galerkin model using input/output linearization. The output temperature of the heat exchanger is controlled by means of a feedforward and an underlying PI-control. The feedforward control is calculated by inverting the transcendent transfer function of the linear distributed parameter model of the heat exchanger and by using a numerical inverse Laplace transform based on the Weeks algorithm.