Periodic Input Observer Design: Application for Imbalance Diagnosis

Observation problems have been garnering increasing attention in recent years. They can be seen as the estimation of a periodic output dynamics driven by periodic inputs. At various level of modelling, automotive engine dynamics can be considered as a linear periodic system mechanically coordinated through the revolution of the crankshaft. In this paper, two practical examples are addressed. The first example is the inversion of sensor dynamics. A classical way of modelling such a sensor is a first order dynamics with periodic excitations which can be, depending on the application, the intake pressure, the intake temperature, the exhaust pressure, the Air Fuel Ratio, or the Mass Air Flow. The second example is the estimation of the engine speed next to the cylinder using as only sensor the easily available instantaneous crankshaft angle speed at the end of the connecting rod. The contribution of this paper is the design of a real-time observer of the periodic excitation of a linear periodic systems by the estimation of the Fourier decomposition of the signal. The estimation of the coefficients of the Fourier basis decomposition of the input periodic excitation is a handy tool for engineering purposes. Indeed, the energy levels of the signal allow another interpretation of the signal and can lead to detect the balance of the engine. This high frequency (6 crankshaft estimation) information can be used for imbalance diagnosis and torque balance control. Real application observation problems are exposed in their practical context and illustrated by experimental results on a 4 cylinder HCCI engine. INTRODUCTION Performance and environmental requirements impose advanced control strategies for automotive applications. Ideally, pressures, temperatures, and flows would be measured at numerous places in the engine, allowing accurate control. Unfortunately, their cost and reliability can prevent these sensors from reaching commercial products (e.g. in-cylinder pressure sensors). As a result, observer design has been garnering increasing attention in recent years. While each of the sensing technology poses its own challenges, several common threads can be found. In particular, many of these observation problems can be seen as the estimation of periodic dynamics driven by periodic inputs. At various level of modelling, automotive engine dynamics can be considered as a linear periodic system mechanically coordinated through the revolution of the crankshaft. A prime example is the inversion of sensor dynamics (Zone 1 on Figure 1) (see [1] and [2] for more details). A classical model of such a sensor is a first order dynamics with periodic excitation which can be, depending on the application, the intake pressure, the intake temperature, the exhaust pressure, the Air Fuel Ratio, or the Mass Air Flow. A second example is the inversion of the transmission dynamics using as only sensor the instantaneous crankshaft angle speed (Zone 2 on Figure 1) which can lead to the estimation of the combustion torque (see [3, 4], [5], [6, 7, 8] for more details). Imbalance is mostly produced by the injection system. Due to the high pressure in the common rail injection system, it is very difficult to estimate the fuel mass injected in the cylinder accurately. Moreover, aging of this system can create lag in the injection which leads to lag in the injection timing. Both problems imply the imbalance of the cylinder, i.e. with the same injection setpoint (injected masses and timing), the cylinder do not produce the same torque. A diagnosis based on commercial engine sensors is a great tool to solve this problem.