• To derive the mathematical model for the passive and active suspension systems for different models. • Creating random rough road inputs for both passive and active suspension system. • To implement linear quadratic regulation controller to the active suspension system for different models. • The different mathematical models are made to run on a random rough road and the ride response is predicted for different velocities using MATLAB. • Analyzing and comparing the performance of active suspension system with LQR controller against the passive suspension system in all the vehicle velocity ranges. Tools: MATLAB, MS Excel