Controller Design of Quarter Car Suspension System and Stability Analysis of the Linear System

The suspension system plays a pivotal role in ensuring the safety, stability, and comfort of passengers in a vehicle by absorbing shocks and vibrations caused by road irregularities. The primary purpose of the suspension system is to improve passenger comfort and facilitate safe handling by maintaining tire contact with the road surface. This paper proposes a linear model of a quarter-car suspension system, focusing on its dynamic behavior under typical driving conditions. The suspension system operates to counteract disturbances from road irregularities, such as bumps, potholes, and uneven surfaces, which can impact vehicle stability. Though the system’s dynamics are generally nonlinear due to the complexity of real-world road conditions and mechanical components, this study simplifies the model to a linear approximation. Controller design comparison using a traditional PID controller and a State Feedback Controller is done for the system, and the result from MATLAB can be used for further analysis. Lyapunov stability analysis is employed in this paper to evaluate the system’s stability, ensuring that the suspension system remains within a stable operating range and does not lead to uncontrolled oscillations or instability. The linear model, though an approximation, allows for identifying critical parameters that affect system performance and the development of design strategies that enhance vehicle safety and ride quality.