Mathematical Modeling of Tractor Movement on the Slope

Researching issues of the controllability and stability of wheeled tractors on slopes with road irregularities using mathematical modeling and optimal control are considered in the paper. The static transverse stability at the limiting angle of the slope is pre-determined. In accordance with the calculation scheme, generalized mathematical models in the form of Lagrange equations of the second kind for horizontal and vertical oscillations of a four-wheeled tractor in the process of moving along the road-irregularities on the turning strip of the cotton field are developed. The theory of optimal systems is used to control the movement of the tractor, control purpose and functional in the form of performance evaluation are formulated. The Pontryagin maximum principle was used to study the necessary conditions for optimal control. The conjugate system with variation of design parameters and generalized models under different conditions of tractor movement are investigated by numerical method. The functioning conditions of the tractor and the main parameters arising from vibrations of the tractor in obstacle negotiation on the slopes with ensuring of the stabilization.