Modeling and Research of the Controllability of Wheeled Tractors

Abstract

In this paper we considered the issues of controllability and stability of wheeled tractors on the slopes with the help of mathematical modeling and optimal control. The well-known methods of modeling and research for improving the stability of the tractor do not allow solving the problem of stable motion of the tractor on the slopes, as they do not provide sufficient correction of the moving direction, which depends on the character of external disturbances. The application of modern optimal control methods allows to investigate this problem at the design phase of the machine with using mathematical models. To solve the problem, we created the equations of motion of a wheeled tractor using the Lagrange equations of the second kind. On the basis of the equations of motion we developed models and algorithms for optimal control of a wheeled tractor. The necessary conditions for optimal control of the motion using the Pontryagin maximum principle were investigated. With the help of auxiliary functions of Hamilton-Pontryagin, we have determined the coefficients of stiffness and viscous resistance of wheel tractor tires. The boundary value problem of the maximum principle to determine the transient process motion of the tractor is formulated and on its basis the equations of horizontal and vertical oscillations of the tractor were solved at an uneven distribution of mass between the front and rear driven wheels and the coefficient of adhesion of the wheels and the lateral slip of the tractor in turning were calculated.

Mathematical modeling of the movement of the guide wheel of the cotton MX harvesting machine

“…Mathematical modeling of MX-1.8 type CHM turning process at the edge of the field was considered for the first time in [11], and later, the issue of mathematical modeling of the movement of guide wheels and selection of criteria for optimal control of its parameters was considered in [15].In these studies, the specific characteristics of the CHM of the MX (XM) type (proneness to two-arm arm-shaped vibrations along the length of the unit due to the lack of a support wheel under the front part of the engine, the variability of the load falling on the rear steering wheels, etc.) and the parameters of the rear steering wheel bridge were not sufficiently taken into account and Gyroscopic oscillations generated in the wheels have not been studied.…”

Mathematical modeling of truck movement in rough road conditions of agricultural area

“…Below we will use the example of small truck LABO movement in solving this problem (Fig 1 .). Based on the scheme of the dynamic model of the small truck LABO shown in Figures 1 and 2, we construct a mathematical model of car motion using the second type of Lagrange equation [1][2][3][4][5][6][7][8][9][10].…”

“…By means of the wheel, a force transmitted to the car that connects it with the road and causes the car to move, stop, and change directions. Although it may seem simple, the wheel is a complex part that described and interpreted using different models of performance activities based on the specified direction and degree of accuracy [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”

Mathematical modeling of small soil channel laboratory stand drive and evaluation of its energy state

“…Mathematical modeling is a universal method of abstract modeling, which is used in scientific research and in the design of technical objects. The use of mathematical modeling makes it possible to reduce the amount of testing and design work and contributes to the creation of highly efficient and high-quality agricultural machines [3,4].…”