Automatic Adaptive Control of the Vehicle Trailer when Reversing

The paper considers the problem of constructing a driver assistance system for a car with a trailer when reversing, functioning under apriori uncertainty of parameters of the controlled object car-trailer and uncontrollable disturbances. The mathematical model of the controlled object car-trailer and the basic relations, necessary for the synthesis of the control law are substantiated. Stability conditions of motion taking into account the notions of short and long trailer and the influence of disturbances are evaluated. The relative angular speed of the trailer, i.e., the angular speed of the trailer divided by the speed of the vehicle, is used as the controlled variable. An adaptive control law on the deviation of the the vehicle steered wheels to achieve the value of the controlled variable set by the driver using an implicit reference model is formed. Apriori uncertainty is eliminated by approximate estimates of trailer length and current parametric identification of the control object mathematical model. The current estimates delivered by the identifier are immediately used to synthesize the control law. The rationale for the operation of the adaptive control system is based on simplified adaptability conditions. The synthesized control law is aimed at preventing from reaching the folding angle with a short trailer and limiting the coupling angle with a long trailer. Automatic formation of warning signals, in particular about trailer folding, is proposed, and model examples showing efficiency of the proposed control system are given

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