The enhancement of rollover stability in vehicles, particularly in liquid tank trucks, is imperative for reducing the risk of vehicular rollovers and consequent threats to human life and property. The dynamic behavior of the liquid within the tank during maneuvers such as turning or lane-changing plays a significant role in the vehicle's stability. It has been demonstrated that the implementation of a Proportional Integral Derivative (PID) controller within the stabilizer bar of an active suspension system can substantially mitigate the vehicle's propensity to roll. This mitigation is quantitatively evidenced by reductions in the lateral load transfer ratio (LTR) and the roll angle (TRA) of the suspension system. Specifically, during steady turning maneuvers, a decrease of 5.6% in LTR and 12.9% in TRA was observed for liquid levels deemed most hazardous at heights of 1.2m and 1.6m, respectively. Similarly, during lane-changing maneuvers, LTR was reduced by 6.2%, and TRA was decreased by 9.1% at critical liquid levels of 0.8m and 1.6m. These analytical outcomes were derived through the application of the Lagrange method and the quasi-static method for establishing the fluid vibration equation within the tank, supplemented by D'Alembert's principle in constructing a four Degrees of Freedom (DOFs) roll model for the differential equation system of vehicle motion. This research underpins the foundational principles for the design, manufacture, and enhancement of suspension systems, and elucidates the direction for future investigations into tank trucks transporting various liquid types.