This thesis compares three control methods for a quarter-vehicle active suspension system: state-space control, model predictive control, and sliding mode control. Dynamic models of the system are established using the Newton-Euler method, key-graph method, and Lagrange method, and the corresponding state-space equations are derived. The controllability and observability of the system are analyzed, including special cases such as chassis spring failure and tire stiffness failure. Then, three controllers are designed under the same physical parameters and tested under step and impulsive road disturbances. The study also considers variations in vehicle load to evaluate the robustness of the controllers. The performance of various methods is compared by rise time, overshoot, settling time, and steady-state error.