Application of linear optimal preview control theory to severe braking of a car

Linear optimal preview control theory is applied to severe braking of a car, providing an extension of work already reported. A new technique is developed to prepare equilibrium running states for a braking vehicle, from which linearized, small-perturbation models can be constructed, with sets of optimal preview controls following. Simulations of straight-line manoeuvres with near-limit decelerations demanded are conducted, first, with linear interpolation of trim states and control gains according to car speed and, second, with bilinear interpolation according to car speed and deceleration. A special procedure is required to compute the preview controls in the latter case. Bilinear gain scheduling over speed and deceleration is shown to give excellent tracking and tyre-force utilization in very challenging circumstances, giving substantial advantage with respect to the alternative simpler scheme.