Chapitre 5. —
Estimation de la richesse cylindre à cylindre
Dans ce chapitre, nous considérons le problème de l’estimation et du contrôle de la richesse cylindre à cylindre. La richesse désigne la composition des gaz dans le cylindre à la fin de la combustion. Les déséquilibres de richesse cylindre à cylindre reflètent les différences entre la combustion de chacun des cylindres. Ces différences peuvent être mesurées par le capteur placé derrière la turbine. La dynamique du système fait intervenir un terme non linéaire, provenant de la non linéarité de la turbine, et est excitée par les débits sortant de chacun des cylindres. Nous présentons deux stratégies dont nous comparons les efficacités. D’abord, nous proposons un observateur non linéaire dont les termes correctifs sont également non linéaires. Les termes correctifs dépendent des débits à la sortie de chacun des cylindres ce qui permet de conclure à la convergence de l’observateur par des arguments de type Lyapunov. Ensuite, nous comparons les performances en terme de précision et de temps de calcul avec un filtre de Kalman étendu. Ces observateurs sont validés et comparés expérimentalement sur une large zone opératoire (Régime moteur de 1250 tr/min à 3500 tr/min et IMEP de 3 à 9 bar). Nous présentons aussi des résultats en boucle fermée.
5.1. Introduction
Another important step toward accurate combustion control is individual Air Fuel Ratio
(AFR) control. AFR= mair˙
P CO ˙mf uel [58, chap. 3] employs various inputs such as injected quan- tities, Exhaust Gas Recirculation (EGR) rate and intake manifold pressure. Classically, in
98 CHAPTER 5. CYLINDER INDIVIDUAL AFR ESTIMATION
spark ignition engines, overall AFR is directly controlled with the injection system. By this control strategy, all cylinders share the same closed-loop input signal based on the single
equivalent ratio sensor φ (an oxygen sensor in the exhaust manifold φ , 1
AF R , 1−
Mexh,air Mexh ). Ideally, all the cylinders should have the same AFR as they have the same injection set- point. Unfortunately, due to inherent flaws of the injection system (such as pressure waves and mechanical tolerances), the total mass of fuel injected in each cylinder is very difficult to predict with a relative precision below 7%. Most of the source of unbalance comes from this difficulty. Consider now a class of planned Homogeneous Charge Compression Ignition (HCCI) engines (see [72, 60, 4, 111] for an overview of the technology, see [74, 78, 39] for more control oriented models, and [108, 66, 71, 3, 11] for control techniques). For
these engines and regeneration filters (Particulate filters, DeNOx [92, 8, 81], even slight
unbalance between the cylinders can in particular induce malicious noise, possible stall and increased emissions. Cylinder-individual control is needed to address the potential draw- backs in these planned technologies. In this context, cylinder-individual AFR estimation may provide crucial information to assist the HCCI engine controller.
The contribution of this chapter is the design and experimental testing of two real- time observers for the cylinder-individual AFR, using only a equivalent ratio sensor placed downstream from the turbine as the source of measurement. In previous work, cylinder- individual control has been addressed using cylinder-individual equivalent ratio sensors in [12]. In practice, cost and reliability of multiple equivalent ratio sensors prevents this technology from reaching commercial products lines. Other approaches use a single equiv- alent ratio sensor. In [52, 19, 50], a method is proposed to reconstruct the AFR of each cylinder based on the permutation dynamics at the TDC (Top-Dead Center) time- scale. This method is well suited for SI engines where the normalized AFR is closely controlled to 1. However, for a HCCI engine, a wider operating region needs to be consid- ered (0.3 < φ < 1) and the available sensor measurements are noisy. To address this, we propose a high frequency model-based observer that considers the system as a gas mixing dynamic process fed with pulsative flows. In supportive detail, we claim it is possible to derive key information from the equivalent ratio sensor high frequency variations. Indeed, over an engine cycle time period, the measured signal is significantly varying, and typically a 5% fluctuation is often observed. Rather than considering average or downsampled val- ues, as implicitly suggested by the previous approaches relying on the TDC dynamics, we
notice that the AFR signal is correlated to output flows at the 6o resolution. By inverting
the mixing dynamics, two high frequency filters (Extended Kalman Filter and Luenberger type) are synthesized. We demonstrate that the individual equivalent ratios are robustly
5.2. MODELLING 99
and efficiently reconstructed by using high frequency information, whereas the equivalent ratios are generally only poorly observable when relying on lower frequencies.
The chapter is organized as follows. In subsection 5.2, we state the AFR estimation
problem under consideration. We propose a high frequency approach, using a 6ocrankshaft
angle model and update instead of a TDC-based model (180o for a 4-cylinder engine). The
use of the various measurements and the mass balance model of the exhaust manifold dynamics is presented. In subsection 5.3, we define a nonlinear observer whose dynamics involve nonlinear tracking terms. In subsection 5.4, we present a Kalman filter. The same code and tuning parameters are kept and implemented in the control system in order to be tested on the true platform. Experimental results are reported in subsection 5.5, with test speed ranging from 1250 rpm to 3500 rpm and pressure from 3 to 9 bar of IMEP (Indicated Mean Effective Pressure). Accuracy of 10% or less of error is demonstrated. CPU power requirements are given and show that the nonlinear observer outperforms the Kalman filter. Robustness issues are studied in subsection 5.7. Conclusions and extensions of the proposed technique are then given in subsection 5.8.
5.2. Modelling
Figure 5.1 shows the flow sheet of individual FAR from the cylinders outlet down to the turbine. From the cylinders to the FAR sensor (located downstream the turbine), the gas travel through the exhaust pipes, the exhaust manifold, and the turbocharger. The EGR acts as a flow discharge for the turbocharger. Composition is preserved though. All these components have an influence on the gas pressure, the temperature, and the composition in the exhaust manifold. In a very naive model, the gas move at constant speed, without mixing. In practice, diffusion and mixing effects are present. We propose a nonlinear model to take these into account. Our approach focuses on macroscopic balances involving experimentally derived nonlinear functions.
5.2.1. Mass balance in the exhaust manifold. — Notations are given in Table 5.1. Mass balance in the exhaust manifold lead to
100 CHAPTER 5. CYLINDER INDIVIDUAL AFR ESTIMATION
Turbocharger
0 100 200 300 400 500 600 700 0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Crankshaft Angle [˚]Gas Flow from the Cylinders [kg/s]
0 100 200 300 400 500 600 700 0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Crankshaft Angle [˚]
Gas Flow from the Cylinders [kg/s]
0 100 200 300 400 500 600 700 0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Crankshaft Angle [˚]
Gas Flow from the Cylinders [kg/s]
0 100 200 300 400 500 600 700 0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Crankshaft Angle [˚]
Gas Flow from the Cylinders [kg/s]