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This research focuses on the development and analysis of a mathematical model for a half vehicle suspension system. The model incorporates a six degree of freedom system, including the heave motion of wheels, car body, and seats with a seated passenger, as well as the pitch motion of the car body. The effect of road disturbances on the seat and the resulting impact on the passenger are also considered. Using Newton's second law of motion, the characteristic equation of the system is derived, and a Simulink model is constructed based on the derived equations. The model is then tested under two different scenarios: a low residential speed limit of 20 km/hr and a highway speed limit of 80 km/hr. Various characteristics such as settling time, rise time, and percent overshoot are observed and compared. It is found that when the speed of the vehicle increases, such as when passing over speed bumps or encountering road disturbances, the settling time and percent overshoot for all components of the vehicle (wheels, chassis, and seat) also increase. This can lead to riding discomfort, road accidents, and adverse effects on the vehicle's health, including permanent damage and deformation of the shock absorber system. To address these issues, an analysis of both active and passive suspension systems is conducted. The research demonstrates significant improvements when an active system is controlled with a PID controller. By optimizing the system parameters, such as decreasing the proportional gain for higher speeds, the settling time and percent overshoot can be effectively reduced, mitigating riding discomfort and enhancing overall system performance.

Keywords: Half Car Model, Active Suspension System, PID Controller, Ziegler Nichols Method.