Adaptive Tracking of the Relative Angular Velocity of a Car Trailer when Reversing

The article considers the task of generating the assist system for the driver of a passenger car with trailer during reversing, operating with a very rough initial estimate of the trailer length and the effect of uncontrolled external disturbances. The mathematical model of the “passenger car - trailer” controlled object is substantiated. The conditions for the stability of movement are evaluated taking into account the concepts of “short”, “long” trailer and the influence of disturbances. The relative angular velocity of the trailer - the angular velocity of the trailer, related to the speed of the car- is used as a controlled variable. An adaptive control law is formed according to the deviation of the car steered wheels to achieve a predetermined value of adjustable variable using an implicit reference model. A priori uncertainty is eliminated by the current parametric identification of the mathematical model of the controlled object, while the current estimates are immediately used to synthesize the control law. The substantiation of the functioning of the adaptive control system is based on “simplified conditions of adaptability” The paper substantiates signal generation on the approach to the trailer jackknifing angle. A modelling example is given.