Linear system identification of longitudinal vehicle dynamics versus nonlinear physical modelling

Mathematical modelling of vehicle dynamics is essential for the development of autonomous cars. Many of the vehicle models that are used for control design in cars are based on nonlinear physical models. However, it is not clear, especially for the case of longitudinal dynamics, whether such nonlinear models are necessary or simpler models can be used. In this paper, we identify a linear data-driven model of longitudinal vehicle dynamics and compare it to a nonlinear physically derived model. The linear model was identified in continuous-time state-space form using a prediction error method. The identification data were obtained from a Lancia Delta car, over 53 km of normal driving on public roads. The selected linear model was first order with requested torque, brake and road gradient as inputs and car velocity as output. The key results were that 1. the linear model was accurate, with a variance accounted for (VAF) metric of VAF=96.5%, and 2. the identified linear model was also superior in accuracy to the nonlinear physical model, VAF=77.4%. The implication of these results, therefore, is that for longitudinal dynamics, in normal driving conditions, a first order linear model is sufficient to describe the vehicle dynamics. This is advantageous for control design, state estimation and real-time implementation, e.g. in predictive control.