Development and research of the mathematical model of a vehicle with semitrailer planar motion

The movement of a road train, consisting of a biaxial tractor car and triaxial semitrailer, which are considered solid bodies, on a horizontal non-deformable ground has been considered. On the basis of the Lagrange’s equations of the second kind the nonlinear mathematical model of its plane motion, which uses as generalized coordinates the position of the fifth-wheel coupling and rotating angles of the tractor and semitrailer body, has been developed. The analysis and linearization of a formed system of equations has been held. The linear mathematical model, describing small lateral displacements and rotations of the road train elements while moving on a high longitudinal speed, with small jackknifing angle and small rotating angle of steer wheels, has been obtained. Through the equivalent conversions of an obtained system of equations the state-space linear model of a road train lateral motion has been formed. A comparative analysis of linear and nonlinear model usage has been delivered to describe a road train motion while passing standard maneuvers. It is shown that, if the limitations are complied, the results of nonlinear and linear model usage are quite close to each other and sufficiently good agree with the results of field tests. The developed model, unlike the already known ones, is fairly simple, linear. Further it could be used for an analytical synthesis of control laws for a road train lateral component of motion.