Describing and compensating gas transport dynamics for accurate instantaneous emission measurement

Abstract

Instantaneous emission measurements on chassis dynamometers and engine test benches are becoming increasingly usual for car-makers and for environmental emission factor measurement and calculation, since much more information about the formation conditions can be extracted than from the regulated bag measurements (integral values). The common exhaust gas analysers for the “regulated pollutants” (carbon monoxide, total hydrocarbons, nitrogen oxide, carbon dioxide) allow measurement at a rate of one to ten samples per second. This gives the impression of having after-the-catalyst emission information with that chronological precision. It has been shown in recent years, however, that beside the reaction time of the analysers, the dynamics of gas transport in both the exhaust system of the car and the measurement system last significantly longer than 1 s. This paper focuses on the compensation of all these dynamics convoluting the emission signals. Most analysers show linear and time-invariant reaction dynamics. Transport dynamics can basically be split into two phenomena: a pure time delay accounting for the transport of the gas downstream and a dynamic signal deformation since the gas is mixed by turbulence along the way. This causes emission peaks to occur which are smaller in height and longer in time at the sensors than they are after the catalyst. These dynamics can be modelled using differential equations. Both mixing dynamics and time delay are constant for modelling a raw gas analyser system, since the flow in that system is constant. In the exhaust system of the car, however, the parameters depend on the exhaust volume flow. For gasoline cars, the variation in overall transport time may be more than 6 s. It is shown in this paper how all these processes can be described by invertible mathematical models with the focus on the more complex case of the car's exhaust system. Inversion means that the sharp emission signal at the catalyst out location can be reconstructed from a flattened emission signal at the sensor. In this modelling, special focus is put on finding an easy parameterisation for different cars. The process of finding these compensators consists of first describing the process by differential equations of appropriate order and parameterising them, resulting in low pass systems. The following step of inverting these systems results automatically in high pass systems. These kinds of systems, however, amplify measurement noise, thus they need signal filters to smooth their output.