This document discusses the design of optimal and robust controllers for a quarter car active suspension system. It first introduces the mathematical model of a quarter car system and describes different types of road disturbances that are used as inputs. Then it presents the design of a μ-synthesis controller and LQR controller for the active suspension system. The μ-synthesis controller accounts for uncertainty in the hydraulic actuator dynamics. The LQR controller is designed to minimize a quadratic cost function and provide optimal control gains. Finally, the controllers are simulated and evaluated using MATLAB.