COMPRESSION RATIO ESTIMATION BASED ON CYLINDER PRESSURE DATA Marcus Klein, Lars Eriksson and Jan ˚ Aslund Vehicular Systems, Dept of EE Link¨ opings Universitet, SWEDEN email:klein@isy.liu.se, larer@isy.liu.se, jaasl@isy.liu.se Abstract: Four methods for compression ratio estimation of an engine from cylinder pressure traces are described and evaluated for both motored and fired cycles. The first three methods rely upon a model of polytropic compression for the cylinder pressure, and it is shown that they give a good estimate of the compression ratio for simulated cycles at low compression ratios. For high compression ratios, this simple model lack the information about heat transfer and the model error causes the estimates to become biased. Therefore a fourth method is introduced where heat transfer and crevice effects are modeled, together with a commonly used heat release model for firing cycles. This method is able to estimate the compression ratio more accurately at low as well as high compression ratios. Copyright c 2004 IFAC Keywords: Polytropic pressure model, nonlinear least squares, variable projection, compression ratio estimation, weighted least squares, parameter estimation, SI engine, variable compression 1. INTRODUCTION A newly developed engine, which can continously change the compression ratio between 8 and 14 by tilting the mono-head, has been developed at SAAB Automobile AB. This ability to change the compression ratio opens up new opportunities to increase the efficiency of SI engines by down sizing and super charging. But if the compression ratio gets stuck at too high ratios, the risk of engine destruction by heavy knock increases rapidly. If the compression ratio gets stuck at too low ratios, we get an unnecessary low efficiency, and therefore an unnecessary high fuel consumption. It is there- fore vital to monitor and diagnose the continuously changing compression ratio. Due to geometrical un- certainties, a spread of the compression ratio among the different cylinders is inherent [Amann, 1985], and since it is hard to measure the compression ratio directly, estimation is required. The questions asked here are related to: 1) accuracy, 2) conver- gence speed and 3) over all convergence. The ap- proach investigated is to use cylinder pressure to estimate the compression ratio. A desirable prop- erty of the estimator is that it must be able to cope with the unknown offset introduced by the charge amplifier, changing thermodynamic conditions, and possibly also the unknown phasing of the pressure trace in relation to the crank angle revolution. Two models of cylinder pressure with different com- plexity levels, a polytropic model and a single- zone zero-dimensional heat release model [Gatowski et al., 1984] are used. To estimate the parameters in the cylinder pressure models, three different opti- mization algorithms minimizing the prediction error are utilized, namely: (1) A linear subproblem approach, where groups of the parameters are estimated one at a time and the predictor function is rewritten to be linear for the group of estimated parameters. Thus we can use linear regression at every substep for estimating the particular group of parameters. (2) A variable projection method [Bj¨ orck, 1996], where one iteration consists of two substeps: The first substep estimates the parameters that are linear in the predictor function, hold-