No abstract

To describe the disturbed movement of a car with a tank, a discrete mathematical model has been compiled, which allows one to take into account the oscillations of the free surface of the liquid and determine their effect on the directional stability of the car during uniform movement and during emergency braking. Linearization is carried out and an equation is obtained for the natural frequencies of oscillations of the electrohydromechanical system, which combines dynamic changes in the parameters of the movement of a car with a tank, partial layers of liquid in a tank and the operation of an electromagnetic drive of the control valve and an electronic PID controller for a two-circuit scheme to ensure directional stability. It is shown that low-frequency oscillations of the free surface of liquid lead to a significant reduction in the stability region, which indicates the need to take such oscillations into account when solving problems of analysis and synthesis of this system. It has been established that for a car with a tank, where low-frequency transverse oscillations of the liquid occur, which are accompanied by redistribution of mass and disturb the movement, an increase in the speed unambiguously leads to a deterioration in road-holding ability. This made it possible to exclude the speed from the variable parameters and significantly simplify the task. It was found that the liquid level in the tank, taking into account its connection with the maximum speed, has an ambiguous effect on the road-holding ability of the vehicle, and it is unacceptable to limit the research to calculations for 50 % of the load. Instead of this traditional simplification, it is necessary to find a line that bends from above those stability boundaries that correspond to many liquid levels from the entire range of their variation. It is shown that the dynamics of emergency braking weakly depends on the viscosity of the liquid in the tank, but with long-term continuous operation of the brake control system, self-oscillations appear in it. A method for tuning the parameters of an electronic regulator for low-amplitude self-oscillations is proposed.

The existing publications that investigate vehicle course stability optimization were analyzed. A mathematical model, which describes the disturbed movement of a car with a tank, was compiled. This model allows to consider the liquid free surface oscillations and determine their effect on the car course stability during constant motion or emergency braking. There was described the main information regarding the car that was used to perform mathematical calculations. An algorithm was developed for deriving the characteristic equation for a complex system of differential equations describing dynamic changes in the movement parameters of a car, oscillations of partial layers of liquid in a tank and the operation of an electromagnetic drive of the control valve and an electronic PID controller for a two-circuit system for ensuring course stability. Based on the developed mathematical model, the influence of forced oscillations of the fluid on the stability area of the system built in the plane of variable parameters of the controller is investigated. It is shown that low-frequency oscillations of the free surface of a liquid lead to a significant reduction in the stability area, which indicates the need to consider such oscillations when solving problems of analysis and synthesis of this system. It was found that for a car with a tank, where low-frequency transverse oscillations of the liquid occur, which are accompanied by a redistribution of mass and disturb the movement, an increase of the speed unambiguously leads to a deterioration in directional stability. That enables exclusion of speed from the number of variable parameters and significantly simplify the problem being solved. The calculations for cases with different loading levels were performed. It was found out that the level of liquid in the tank, considering its relationship with the speed, has an ambiguous effect on the car course stability, and it is unacceptable to limit the research calculations to the case with 50 % load. Instead of this, it is necessary to find a line that bends from above the stability boundaries that correspond to many liquid levels. Keywords: fluid vibrations; exchange rate stability system; area of stability; tank; PID-controller; parameters.

The problem of choosing the variable parameters of a stabilizer of an object which minimize an additive quadratic integral functional reflecting the complex of requirements for a closed stabilization system is considered. To solve the problem a combined method of parametric synthesis of the stabilizer, which is a sequential combination of the Sobol grid method and the Nelder-Mead method, is proposed. At the first stage of the method by applying the Sobolev grid method a working point of the closed system in the pace of its variable parameters is transferred into a neighborhood of the quality functional global minimum point. Then at the second stage the Nelder-Mead method is used to relocated the working point into a small neighborhood of the global minimum. The method proposed comprises a particular algorithm for choosing the weight coefficient of the additive quality functional as well as makes use of the stabilization object state vector main coordinates, which provide the most adequate description of its dynamic features. The properties of a mathematical model of controlled system with discontinuous stabilization process control are studied numerically. The analysis of the plots in the dynamical system state phase space indicates non-spiral approach of the system to its equilibrium state. The synthesized control is realized in the form of a sequence of switchovers.