The suspension system has the role of regulating and extinguishing oscillations in the vehicle. To improve stability and comfort, the active suspension system is proposed to replace the passive suspension system. There are many algorithms used for active suspension system control, such as PID, LQR, Fuzzy, etc. Among them, the nonlinear control method which uses the SMC algorithm gives a stable performance. This research proposes the use of the SMC algorithm to control the operation of the active suspension system equipped with a quarter dynamics model. The process of linearization of the hydraulic actuator is presented in the paper. As a result of the simulation, the values of displacement and acceleration of the sprung mass were significantly reduced when the vehicle used the active suspension system controlled by the SMC algorithm. The SMC controller established in this paper provides stability in many situations. Therefore, the vehicle's smoothness and comfort have been significantly improved. In the future, intelligent algorithms can be combined with SMC algorithms to improve the efficiency of the controller.

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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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