Periodic Input Observer Design: Application for Imbalance Diagnosis

Abstract

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 o 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.

Six Degrees Crankshaft Individual Air Fuel Ratio Estimation of Diesel Engines for Cylinder Balancing Purpose

“…The sensor dynamics can be approximated by a second order filter. In order to robustly invert dynamics of the sensor, we apply an observer based on an adaptive Fourier decomposition as described in [30] (Block (D) in Figure 4).…”