Mathematical Models and Structures of the Vehicle Lateral Stability Stabilization System

Abstract

Currently, intensive research is being carried out to improve the operational characteristics of the car: vibration protection, smoothness, stability, and controllability. These properties are largely determined by the characteristics of the vehicle suspension, which provides a connection between the carrier system and the wheels of the vehicle. Significant attention is paid to the development of active suspensions, in which additional actuators are used to form the necessary characteristics, in particular, linear dc motors. The use of active actuators permits to control the position of the car body, including its lateral roll. In the article, relations are obtained that establish the dependence of additional elastic deformations in the suspension and the car roll angle on the centrifugal force in a stationary mode. When developing a linearized mathematical model of the control object for the study of nonstationary modes, a two-mass design scheme is used and operator equations are obtained that take into account the elastic–dissipative properties of the sprung and unsprung parts of the car, as well as an additional control action created by the actuator. It is shown that the dynamic properties of the studied control object can be approximately described by the transfer functions of a second-order aperiodic link or an oscillatory link. For the former case, a single-loop system was developed, which was closed in terms of the roll angle with a proportional-integral-derivative (PID) controller. In the latter situation, it is advisable to use a two-loop system with an internal flexible feedback loop for suspension deformation and an external loop closed for the roll angle using a PID controller. The possibility of forming a feedback signal in the strain rate of the suspension in the internal loop with the help of an EMF sensor of a linear dc motor is demonstrated. On the basis of the block diagram, a computer model of the system is developed, and for typical parameters of the control object, a study is made of transient processes of working off a disturbance in the form of a change in centrifugal force. Based on the simulation results, it was found that the use of the developed automatic control system (ACS) provides high accuracy in stabilizing the vehicle roll angle.