The problem of constructing the invariant stabilizer of the ESP (Electronic Stability Program) car course stability system is considered by implementing two control principles by the electronic brake force distribution unit EBD (Electronic Brakeforce Distribution) – the principle of control by deviation and the principle of control by external disturbance. The values of the variable parameters of the stabilization algorithm are selected from the conditions for minimizing both the static and dynamic errors of the system. Two brake fluid pressure sensors are introduced into the EBD structural-functional scheme in the brake lines of the right and left sides of the car. It is proven that the pressure difference of the brake fluid, which is measured by pressure sensors, is proportional to the external disturbance acting on the car body from the side of the road surface. Therefore, in order to give the ESP system the property of invariance to external disturbances, the control signal generated by the EBD electronic unit contains current information not only about the parameters of the disturbed movement of the car, namely, about the angle of deviation of the longitudinal axis of the car relative to the given direction of movement, about the angular velocity of rotation of the body relative to its vertical axis and about lateral displacement of the center of mass of the body, but also the current information about the external disturbance acting on the car body. Recommendations for choosing the values of variable parameters of the ESP system stabilizer are given, which ensure the minimization of both static and dynamic errors of the closed system in the emergency braking mode.

Problem. Usually, complex dynamic systems are characterized by a high order of equations in their mathematical models and intricate interconnections among subsystems that constitute the complex dynamic system. Naturally, the analysis and synthesis of complex dynamic systems require the use of powerful computational systems with vast memory and high processing speed. Goal. The aim is quantitative assessment of the influence of the continuum part of a dynamic system on the behavior of its discrete part and the possibility to perform decomposition of the mathematical model of perturbed motion of a discrete-continuum system based on this assessment. Methodology. The measures are aimed at addressing issues that are based on the discrete-continuum capabilities and their decomposition. Results. For three types of complex dynamic systems described by infinite-dimensional systems of ordinary differential equations, quantitative assessments of the influence of the continuum part on the discrete part of the system have been proposed. These assessments determine the decomposition of the mathematical models of perturbed motion for such systems. Originality. Simplified mathematical models for three types of discrete-continuous dynamic systems were obtained. Practical value. The obtained results can be recommended for the study of the specialized course on the motion characteristics of cargo trucks during the transportation of liquids in tanks. Through optimization using the MATLAB software package, it is possible to simulate various parameters of both the cargo truck and the cargo being transported.

The paper reviews the scientific and technical literature on the development of electronic stability systems with brake force distribution, which led to the conclusion that for all-terrain wheeled vehicles such systems should be built using inertial navigation sensors - gyroscopes and accelerators. The proposed functional scheme of the stability system with brake force distribution is built using the principles of platformless inertial systems, in which the orientation of the car body relative to the axes of the inertial coordinate system is carried out by calculating in the onboard digital computer quaternion in contrast to Euler angles can be calculated with the required degree of accuracy using a fairly simple algorithm. Algorithms for estimating the current parameters of perturbed motion of the wheel body in the process of its urgent braking, namely, the angle of deviation of the elongated axis of the body from a given direction, angular velocity and lateral displacement of the center of gravity relative to a given trajectory. On the basis of the current estimation of the listed parameters the algorithm of stabilization of the case of the wheeled car in the mode of its urgent braking is formed.

Problem. When driving a vehicle with comfortable suspension settings, there is a high probability that such adjustments may, firstly, cause discomfort to the driver and passengers, and secondly, when cornering, there is a high probability that the vehicle will overturn. A stiffer suspension leads to discomfort when driving on bumps. To choose the optimal parameters of the car's suspension, it is necessary to take into account the various parameters of the car's suspension, its settings and the features of the road surface. Goal. Solving the problem of choosing the values of the varied parameters of the car suspension - the coefficients of stiffness of the elastic elements and the average values of the damping coefficients of the shock absorbers, which provide a comfortable state of the driver and passengers while driving. Methodology. The approaches adopted in the work to solve the problems are based on the algorithmic method of parametric synthesis of dynamic systems. Results. The obtained maximum values of generalized coordinates, speeds and accelerations of the sprung part of the car body, as well as the minimum values of functionalities, with the help of ratios are possible to estimate the values of weights of additive functionality based on MathCAD software package. With the help of the algorithmic method of solving the problem of parametric synthesis of a dynamic system it is possible to it automate. Analysis of the process with the specified coefficients allows to detect high efficiency of damping of vertical oscillations of the under-sprung part of the car body. The amplitude of the linear displacement of the center of mass of the body does not exceed 0,02 m, and the amplitude of the generalized veloc-ity of the centre of mass of the sprung part of the housing does not exceed 0,08 m/s-1. Originality. The obtained parameters allow to minimize the time for selection of average values when designing the vehicle suspension. Practical value. The results can be recommended when studying the design features of vehicle suspensions. Thanks to the optimization of the MATLAB software package, modeling with different suspension parameters is possible.