Admittance based time-delay control of a steer-by-wire system using stochastic MPC

Time-delays are a common issue in control tasks and must be considered when analysing both stability and performance. To address this, the proposed approach models time-delays as stochastic variables with known probability distributions and embeds them directly into a stochastic model predictive control framework. A nominal delay compensation is first performed to estimate the optimisation initial state, while the remaining delay uncertainty is propagated as a state uncertainty over the prediction horizon and incorporated into an SMPC formulation, which follows established approaches from the literature but considers uncertainty induced by the stochastic delay model. This permits the implementation of robust and chance constraints on the control problem compared to for example the Smith predictor. The stochastic model predictive time-delay control method is then applied to a Steer-by-Wire system. A state-space model for the steering wheel and the front wheel system is formulated and augmented with an admittance model to allow a straightforward modification of the steering feel for the driver. This structure allows the independent shaping of perceived inertia and damping characteristics, enabling a physically interpretable and tunable steering feel decoupled from the force feedback design. Multiple driving manoeuvres were simulated to evaluate the performance of this control strategy. The results show that, in a double lane change manoeuvre, the proposed method improves the tracking accuracy of the reference state compared to conventional model predictive control, reducing the tracking error by up to one order of magnitude while effectively suppressing oscillatory behaviour in the tracking response. However, the performance is constrained by the inherent lack of information regarding future uncertainties and the model quality.