Dynamic Tube MPC for Hybrid Fault-Tolerant Torque Vectoring

Abstract

This thesis develops the groundwork for a hybrid fault-tolerant torque-vectoring controller for four-wheel independently driven electric vehicles. Actuator faults are modeled as loss-of-effectiveness gains on the applied wheel torques. An external estimator is assumed to provide both a nominal effectiveness estimate and a corresponding uncertainty description. The nominal estimate is used to update the prediction model, while the remaining uncertainty is handled through a robust tube nonlinear model predictive control formulation. Since classical tube model predictive control formulations are often too expensive for real-time use, this thesis builds on the zoRO framework, which preserves near-nominal computational complexity by propagating the uncertainty outside the optimal control problem.

A central difficulty in this setting is that the relevant uncertainty acts through the model parameters rather than through a standard additive disturbance channel. The first part of the thesis therefore studies how the zoRO framework can account for nonlinearly acting uncertainty represented through the model parameters. The resulting controller-side formulation covers both stage-wise parameter perturbations and constant parameter mismatch, and was implemented and validated in acados through numerical tests, generated-code verification, and closed-loop simulations on a differential-drive robot example with actuator uncertainty.

The second part of the thesis applies this framework to centralized torque vectoring under actuator-effectiveness uncertainty. The focus is placed on the fault direction in which the true actuator effectiveness is higher than assumed by the controller, so that the realized wheel torque is effectively amplified. A high-fidelity IPG CarMaker vehicle model is used for validation. First, it is shown that the nominal controller produces the intended change in handling behavior and extends the approximately linear operating region of the vehicle. The fault-related validation is then carried out in two representative maneuvers: hard-braking and Sine-with-Dwell.

The hard-braking results show that the robustified controller keeps the rear axle closer to the friction limit and prevents repeated excursions into deep slip, which leads to better braking performance than the nominal controller under mismatch. At the same time, introducing uncertainty in the healthy case increases conservatism and therefore reduces nominal braking performance. The Sine-with-Dwell results show that under combined longitudinal and lateral tire-force demand, the robustified controller can prevent the instability that arises in the nominal controller for sufficiently large mismatch. In a representative faulty case, the resulting yaw-rate response remains close to that of the healthy vehicle.

The final controller runs with average solver times around 10 ms in the main configuration, with lower times observed in reduced-iteration tests. The thesis therefore shows that uncertainty acting through the parameter channel can be incorporated in zoRO in a computationally practical way, and that this leads to a meaningful robustness benefit in fault-tolerant torque vectoring. The main limitations are the absence of an integrated fault estimator, the restricted uncertainty description used in the vehicle study, and the need for validation on real-time automotive hardware.

Merged acados contributions: https://github.com/acados/acados/pulls?q=is%3Apr+is%3Amerged+author%3Aivandoornen