A thermodynamics-based homogeneous charge compression ignition engine model for adaptive nonlinear controller development

Abstract

Low-temperature combustion modes, such as homogeneous charge compression ignition, represent a promising means to increase the efficiency and to reduce significantly the emissions of internal combustion engines. Implementation and control are difficult, however, owing to the dependence of the combustion event on the chemical kinetics rather than an external trigger. This work describes a nonlinear control-oriented model developed for a single-cylinder homogeneous charge compression ignition engine, which is physically based on a five-state thermodynamic cycle. This model is aimed at capturing the behavior of an engine which utilizes fully vaporized gasoline-type fuels, exhaust gas recirculation, and intake air heating in order to achieve homogeneous charge compression ignition operation. The onset of combustion, which is vital for control, is modeled using an Arrhenius reaction rate expression which relates the combustion timing to both the charge dilution and the temperature. Despite the fact that homogeneous charge compression ignition combustion is indeed fast, it is not perfectly instantaneous and therefore requires some finite amount of time to occur. To account for this phenomenon within the model, a Δθ term is added which shifts the point of instantaneous combustion from the start of combustion to a point of very-high-energy release based on experimental heat release data. The model is validated against experimental data from a single-cylinder compression ignition engine operating under homogeneous charge compression ignition conditions at two different fueling rates. Parameters relevant to control such as the combustion timing, peak in-cylinder pressure, and pressure rise rates from the simulation agree very well with the experiment in both operating conditions. The extension of the model to other fuels is also investigated via the octane index of several different gasoline-type fuels. Since this nonlinear model is developed from a controls perspective, both the output and the state update equations are formulated such that they are functions of only the control inputs and the state variables, therefore making them directly applicable to state-space methods for control. The result is a discrete-time nonlinear control model which provides a platform for developing and validating various nonlinear control strategies.

Extremum-seeking for nonlinear discrete-time systems with application to HCCI engines

“…This model generated the numerical results used to validate the extremum-seeking method proposed in the paper. The reader is referred to [14] for details about implementing HCCI engines.…”

“…Controlling such engines is difficult because the combustion event depends on chemical kinetics rather than an external trigger. In [14], the author outlined a nonlinear, control-oriented model of a single-cylinder HCCI engine, which is physically based on a five-state thermodynamic cycle.…”

“…The results from this paper are used to design an outer control loop via extremumseeking in order to identify the best set point that maximizes the performance function. In contrast to [18] where the engine dynamics along with the PID inner loop dynamics was assumed to be a static nonlinear map, as previously mentioned, the HCCI engine dynamics [14] studied in this paper is nonlinear and uncertain for which a PID controller may not be suitable. In the next section, the extremumseeking method for a nonlinear, discrete-time system and the stability of the proposed scheme are introduced.…”

“…From the perspective of application, low temperature combustion (LTC) mode engines, such as Homogeneous Charge Compression Ignition (HCCI) engines, show promise in increasing the efficiency and reducing the emissions significantly of internal combustion engines [14]. In [15], the authors considered the problem of optimally controlling the engine in a forward-in-time manner when the system dynamics were completely unknown, although the best operating point that maximized the performance was determined a priori.…”

“…In the recent years, due to the advent of embedded digital processors and discrete modeling of physical systems [14], digital control of nonlinear systems has received a lot of attention [1] [15]. This paper considers the problem of extremum-seeking for nonlinear nonaffine, discrete-time systems whose output performance function is uncertain.…”