Parametric synthesis of the digital system of the course stability of a car

Abstract

The problem of choosing the variable parameters of a control algorithm, implemented by a digital electronic unit of the system of the course stability of a car and providing the maximum stability margin and the maximum speed of the stabilized process during car braking is considered. It is believed that the angular velocity sensors of the car body are used as the sensitive elements of the system, whose sensitivity axes coincide in direction with the main central axes of the body inertia, and the angular deviation of the longitudinal axis of the body from a given direction is calculated by a digital electronic unit using algorithms of platformless inertial systems (PINS) in the form of a lattice function. Information about the angular velocity of a body rotation is a lattice function at the output of the Lanczos digital low-pass filter, whose input is supplied with the lattice function of the angular deviation of the body from a given direction of the car movement. The lattice control function is a weighted sum of these functions, the weight coefficients of which are variable digital parameters of the Vehicle Stability Controls that are to be selected. The perturbed motion of the continuous part of the closed system is described by ordinary differential equations, the work of the discrete part is described by relations in finite differences. By means of special transformations, the mathematical model of the perturbed motion of the closed-loop control system is represented in the form of a system of difference equations, using which the characteristic equation of the closed discrete system of the course stability of the car is constructed. Using the bilinear W-transformation, the characteristic equation is reduced to a form convenient for constructing the lines of equal degree of stability in the plane of the variable parameters of the digital electronic control unit, followed by determining the optimal values of its variable parameters, as well as assessing the effect of the selected value of the quantization period of the digital electronic unit on the area of stability of the closed digital system of the course stability of a car. Key words: system of the course stability of a car, Rodrigue Hamilton parameters, lattice function, low-frequency digital filters, variable system parameters.