The problem of optimal suppression of spurious vibrations by an antilock braking system (ABS) installed on cars with deformable wheels is considered. The vibrations are caused by sharp variations in the braking moment during operation of the ABS due to peculiarities of rolling of a deformable wheel. This problem is formulated as a problem of finding the control that takes the system (in the shortest possible time) from a point in the state space to the variety characterized by the following: the angular velocity of the rotating wheel and the contact force are constant. When such a control is constructed, the dynamics of a pneumatic braking actuator is modeled. The sensitivity of the solution to errors in the model is studied.
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