NON-LINEAR SYSTEMS REPRESENTATION USING ARMAX MODELS WITH TIME-DEPENDENT COEFFICIENTS

Abstract

An approach that models a non-linear process operating over a large dynamic range is developed and validated. This approach is based on stochastic Time-varying AutoRegressive Moving Average with eXogeneous inputs (TARMAX) models. The TARMAX model coefficients are explicit functions of time and vary in a deterministically organised fashion. A novel model parameter estimation method fully based on linear operations is presented. The estimation approach is characterised by a low computational complexity and requires no initial guess of the parameter values. The ability of the approach to model non-linear processes is validated by addressing problems dealing with improving the estimation of mass air flow going into an automobile engine. First, a TARMAX model is used to capture the dynamics of the engine process relating air flow provided by a laboratory grade sensor and three input signals available in the engine electronic controller. The TARMAX model is used to simulate the complex relationship between the output and the three input signals. Second, TARMAX models are used to anticipate the future response of a hot-wire-based mass air flow sensor (MAF) in order to obtain an accurate estimate of the cylinders air charge. The estimated TARMAX models prove to have good simulation and prediction capabilities. All models are estimated using actual production vehicle data.