Abstract
This study discusses vehicle stability control based on explicit nonlinear model predictive control (NMPC) and investigates the influence of prediction model fidelity on controller performance. The explicit solutions are generated through an algorithm using multiparametric quadratic programming (mp-QP) approximations of the multiparametric nonlinear programming (mp-NLP) problems. Controllers with different prediction models are assessed through objective indicators in sine-with-dwell tests. The analysis considers the following prediction model features: 1) nonlinear lateral tire forces as functions of slip angles, which are essential for the operation of the stability controller at the limit of handling. Moreover, a simple nonlinear tire force model with saturation is shown to be an effective alternative to a more complex model based on a simplified version of the Magic Formula; 2) longitudinal and lateral load transfers, playing a crucial role in the accurate prediction of the lateral tire forces and their yaw moment contributions; 3) coupling between longitudinal and lateral tire forces, which has a significant influence on the front-to-rear distribution of the braking forces generated by the controller; and 4) nonlinear peak and stiffness factors of the tire model, with visible yet negligible effects on the results.
Highlights
T HE primary objective of vehicle stability control is to reduce the deviations of the actual yaw rate from the one intended by the driver through the individual actuation of the friction brakes while limiting the sideslip angle to prevent vehicle spin and preserve some yaw moment gain [1].Conventional vehicle stability controllers have a hierarchical structure, usually including: 1) a reference generation layer; 2) a motion control layer, generating the reference direct yaw moment and corrected total wheel torque demand; and 3) a control allocation layer, specifying the reference torque or slip ratio for each wheel
This section compares the two cases with constant vertical tire load, i.e., (b) and (c), with three cases with variable vertical tire load, i.e., (d), in which the lateral load transfer only depends on yaw rate, and (g) and (f), in which the lateral load transfer depends on both yaw and sideslip rates. (b) and (g) adopt a nonlinear lateral tire force model without tire force coupling, whereas (c), (f), and (d) use a nonlinear lateral tire force model with linear force coupling
Accurate vertical tire load estimation is important for predicting the yaw moment contributions, with significant influence of the yaw rate, steering angle, and sideslip rate, where the latter is beneficial in extreme transient conditions
Summary
T HE primary objective of vehicle stability control is to reduce the deviations of the actual yaw rate from the one intended by the driver through the individual actuation of the friction brakes while limiting the sideslip angle to prevent vehicle spin and preserve some yaw moment gain [1]. The inclusion of the nonlinear vehicle and tire dynamics in the optimal control problem increases the computational complexity of MPC implementations. In [9], the required computational time limits the entry speeds in an autonomous double-lane-change maneuver, in an MPC implementation based on a single-track model neglecting load transfer effects. An explicit NMPC method using multiparametric quadratic programming (mp-QP) approximations of the multiparametric NLP (mp-NLP) problem is proposed in [22] for vehicle stability control and in [23] for control allocation, with a model neglecting load transfers. 1) An explicit NMPC approach to vehicle stability control based on a flexible and practical formulation of the optimal control problem, combining motion control and control allocation aspects. The analysis covers nonlinear tire characteristics, including the coupling between lateral and longitudinal tire forces, and load transfers
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