Time-optimal velocity control of a motor-vehicle with CVT
by Aurel P. Stoicescu
International Journal of Vehicle Design (IJVD), Vol. 30, No. 4, 2002

Abstract: By taking into account the case of motor-vehicle with continuously variable transmission (CVT), the paper presents the motor vehicle velocity control that ensures the minimisation of the following criteria: (1) acceleration time; (2) accelerating time for a given travelled distance; (3) accelerating index. As a preliminary the analysis of the motion equation of a motor vehicle with CVT and of the phase trajectories emphasises certain peculiarities of motion regimes. The optimal control problem is appropriately formulated for the three criteria and solved by applying Pontryagin's maximum principle. It is shown that for the three criteria there are singular solutions of the optimal control problem. In the case of the criterion (1), for usual values of the CVT ratios, the numerical computations prove that the singular phase trajectory almost coincides with the trajectory corresponding to the CVT ratio which provides the ideal traction hyperbole. In the case of the criterion (2), depending on the final conditions, there are two singular solutions. The first of them is nearly enough to the solution of the criterion (1) when the given travelled distance is, in general, more than 500 m. The latter solution is very close to the singular solution of the criterion (1). In the case of the criterion (3), the singular trajectory is similar to the first solution of the criterion (2). The paper analyses different variants of optimal trajectories pointing out control switching points.

Online publication date: Fri, 15-Aug-2003

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