Estimation of Intake Oxygen Concentration Using a Dynamic Correction State With Extended Kalman Filter for Light-Duty Diesel Engines

Abstract

An accurate estimation of the intake oxygen concentration (IOC) is a prerequisite to develop the optimal control strategy because it directly affects the combustion and emissions. Since the IOC is determined based on the mass conservation law in the intake manifold, estimating the mass flow rate of the exhaust gas recirculation (EGR) is most critical. However, to estimate the EGR mass flow rate, the conventional orifice valve model causes extrapolation error or inaccurate estimation results under transient operating conditions. In order to improve the estimation performance, this study proposes a correction algorithm for estimating IOC. A dynamic correction state is determined for the orifice valve model. In addition, the intake pressure dynamics is also derived based on the energy conservation law in the intake manifold. Using these dynamic models, a nonlinear parameter varying model is determined, and an extended Kalman filter (EKF) is applied to derive the value of correction state. Furthermore, unmeasurable physical states of the nonlinear parameter varying model are estimated from an air system model that only requires the engine-equipped sensors of mass production engines. The correction algorithm is validated through the engine experiments that clearly demonstrate high accuracy of the IOC estimation during transient conditions, which may apply for the vehicle application.

Calculation of Intake Oxygen Concentration through Intake CO2 Measurement and Evaluation of Its Effect on Nitrogen Oxide Prediction Accuracy in a Heavy-Duty Diesel Engine

“…In [14], the authors estimated the EGR rate considering the position of the EGR valve and the pressure drop across the valve and then obtained the intake O 2 concentration through the use of a similar correlation to that reported in [12,13]. Alternative methods to estimate the intake oxygen concentration are based on physics-based or artificial intelligence models [15][16][17][18][19][20][21]. In [15], the authors proposed a nonlinear output error model based on artificial neural networks and applied it to a turbocharged diesel engine.…”

“…In [18], the authors developed a supervisory model predictive control approach to manage the air path system of a diesel engine under multi-mode operating conditions, where the intake O 2 concentration is modeled and controlled together with the air mass flow rate, the O 2 concentration at the compressor inlet and the pressure drop across the air throttle valve. In [19], the authors proposed a dynamic correction state with extended Kalman filter to improve the performance of intake O 2 estimation methods based on EGR orifice valve modeling. In [20], the authors presented an estimation algorithm based on a first-order linear dynamic model with time varying coefficients in which the necessary input quantities are the boost pressure, the fueling rate, the engine speed and the EGR valve lift.…”

“…Although this correlation is very accurate, a precise estimation of the EGR rate, which may not be easily achievable, especially under transient conditions, is still needed. The EGR rate, in general, is estimated by means of orifice valve models [14], which may be affected by high uncertainties, especially under transient operating conditions [19]. An accurate estimation of the EGR rate requires the simultaneous measurement of the intake and exhaust CO 2 concentrations [22], but this would result in the need to use three input variables to evaluate the intake O 2 level (i.e., the intake/exhaust CO 2 concentrations and the relative air-to-fuel ratio), with the consequent arising of possible issues related to the time misalignment of the acquired signals, especially under transient operation conditions, as well as the combined uncertainty.…”

“…With reference to alternative methods based on physics-based or artificial intelligence models (i.e., [15][16][17][18][19][20][21]), they generally require a training procedure on a set of experimental data and may be thus subject to inaccuracies related to variances in the input variables since they generally require more than one input quantity.…”

Optimal Sensor Placement for High Pressure and Low Pressure EGR Estimation

“…Their model was validated both with dynamic and stationary measurements. Observer-based estimations were also used in [19] for estimation of the intake air mass for a SI engine using an Extended Kalman Filter, or in [20] where the authors also used an EKF applied to a light-duty diesel engine, creating 8 sub-models to estimate the air system states.…”