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Modelling of vehicle handling dynamics has received a renewed attention in recent years. Different from traditional vehicle modelling, a novel data-driven identification method for vehicle handling dynamics is proposed, which can avoid the problems of the under-modelling and parameter uncertainties in the first-principle modelling process. By first-order Taylor expansion, the nonlinear vehicle system can be linearised as a slowly linear time-varying system with fourth-order. In order to identify the derived identifiable model structure, a recursive subspace method is presented. Derived by optimal version of predictor-based subspace identification (PBSID opt ) and projection approximation subspace tracking (PAST), the identification method is numerical stability and gives an unbiased estimation for the closed-loop system. Based on standard road tests, the proposed modelling method is proven effective and the obtained model has good predictive ability. Additionally, it is noted that the model obtained from the initial phase of straight driving is just a mathematical model to describe the relationship between input and output. And when the vehicle is steering, the model can converge to a stable phase quickly and represent vehicle dynamic performance.

This paper presents two types of extended Kalman filter (EKF) and two types of unscented Kalman filter (UKF) based on vertical railway vehicle models for parameters estimation of secondary suspensions. Due to track irregularities, the random vertical velocity of the track can be approximated as a zero-mean Gaussian white noise and it is used to excite the dynamic model of the railway vehicle. Under this approximation, the variance of the vertical velocity of the track, which is affected by the track roughness level and vehicle velocity, can introduce uncertainty into the system. Based on the random track irregularity, two cases are proposed to determine how the track irregularities enter the system. One case uses the vertical velocity and displacement of the track as inputs of the system and assumes that the state variables are corrupted by the Gaussian noises. The other case assumes that the vertical velocity of the track is the process noise of the system. Based on these two cases, two types of EKF and UKF are developed to estimate the parameters of the secondary suspensions. In order to study the performances of the proposed EKFs and UKFs, several simulation experiments using linear and nonlinear model are carried out that consider the uncertainties of the random track.

Vehicle active control is an important technology for vehicle safety and performance. Most vehicle control systems are based on models, and the effects of model-based controllers are more dependent on the model parameters. In order to improve the adaptability and the veracity of a control system, a new vehicle predictive control method is proposed. Based on the recursive optimized version of the predictor-based subspace identification method, the vehicle model can be identified from input–output data. According to the predicted outputs and the optimal criterion, two predictive controllers are derived. One is called the recursive subspace predictive controller, and the other is called the recursive subspace predictive controller with integrator, which is an improved form to handle integrated white noise. Compared with the outputs from traditional predictive control, the predicted outputs in this paper are obtained directly from the subspace identification process at each step, which avoids the difficult process of solving Diophantine equations. In this paper, a simulation vehicle model, which is made up of a seven-degree-of-freedom vehicle model and a magic formula tyre model, is used to verify the effectiveness of the controllers. By numerical examples, it can be shown that the proposed methods not only are effective for vehicle control in the linear domain but also can track the desired values well and can improve the effect of vehicle control even when the lateral tyre forces reach saturation.

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