The phenomenon of vehicle rollover usually occurs when the driver suddenly steers at high speed. The centrifugal force will appear and cause the vehicle’s body to tilt. To overcome this situation, the solution of using the stabilizer bar is proposed. The passive stabilizer bar has a simple structure, low cost, and long service life. As a result, it is now a standard on most vehicles. This paper has established a dynamic model to describe a vehicle’s oscillation. As a result of the study, the maximum roll angle of the vehicle was reduced from 9.0° to 8.2° when the stabilizer bar was used. Besides, the minimum value of the vertical force at the wheel reached 485(N) and 1162(N), respectively, corresponding to the two survey cases. The movement trajectory of the vehicle when using the stabilizer bar does not have a big difference compared to the case when the vehicle does not use the stabilizer bar. So, the vehicle’s stability and safety can be effectively improved. This is the basis for further developing complex stable bar patterns in the future.

The suspension system plays a role in ensuring the stability of the vehicle when traveling on the road. On many modern vehicles, the active suspension system has been proposed to replace the conventional passive suspension system. The performance of the controller for the active suspension system depends on its control method. In this paper, a half dynamics model of the vehicle is established. Besides, the LQR control method is also used. The parameters of the control matrix are calculated through the triple in-loop optimization algorithm, which has been shown in the research. This is a completely novel algorithm. This algorithm helps to choose the most optimal parameters. Thus, it ensures the efficiency and stability of the controller. The calculation and comparison process are done automatically. When the loop ends, the optimal parameters are explicitly indicated. The simulation process is done in the MATLAB-Simulink environment. The results of the research showed that when the LQR controller, which was optimized through the triple in-loop algorithm used, the vehicle's oscillation was significantly reduced. In the three survey situations, the values of the roll angle and the angular acceleration of the sprung mass are guaranteed to be stable. Besides, when using this controller, the phenomenon of “chattering” after the excitation ends does not appear. This topic can be further developed in the future.

The roll angle of the vehicle φ is a characteristic parameter for the vehicle's instability. This value appears when the vehicle steers. If the vehicle’s body is tilted, the value of the vertical force at the wheels Fzij will also change. When the value of Fzij reaches zero, the wheel will be lifted off the road, the rollover phenomenon can occur. At this time, the roll angle of the vehicle will reach the maximum value φmax. Previous researches have often used only the vehicle dynamics model to determine the limits of this phenomenon. However, the calculation and simulation process are quite complicated. Therefore, this research has proposed a novel method that can calculate the limit of the rollover phenomenon more easily. In this research, the Rollover State Function (RSF) was established to calculate the limited roll angle of the vehicle. According to the content of the paper, this function depends only on the basic dimensions of the vehicle such as the height of center of the gravity, the track width, etc. Besides, it has relatively high accuracy, even when the vehicle's mass changes, its difference is not large. Therefore, the results of the paper can be applied to later studies to predict the rollover phenomenon.

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Centrifugal force is what causes the vehicle to roll over. This force is generated when the vehicle suddenly changes direction when moving at high speed. The solution of using a stabilizer bar is suggested to minimize this phenomenon. There are currently three types of stabilizer bars in use: mechanical stabilizer bars, hydraulic stabilizer bars, and electronic stabilizer bars. The content of this article is aimed at introducing and reviewing the characteristics of the stabilizer bar. Besides, two oscillation simulation models of vehicles equipped with stabilizer bars are also analysed in this article. Additionally, the characteristics of the control algorithms for the stabilizer bar are clearly analysed. The half-dynamics model is suitable for algorithms that need to use oscillatory state matrices such as SMC, LQR, and LQG. The spatial dynamics model is suitable for some algorithms such as PID, fuzzy, and neural. The roll angle of the vehicle has been significantly improved when the stabilizer bar is fitted. In general, the stability and safety of the vehicle can be guaranteed if the vehicle uses a stabilizer bar.