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Sliding mode control with a disturbance observer (SMC-DO) is proposed for suppressing the sprung mass vibration in a quarter-car with double-wishbone active suspension system (ASS), which contains the geometry structure of the upper and lower control arms. The governing equations of double-wishbone ASS are obtained by the balance-force analysis of the sprung mass in ASS. Considering uncertainties in damping, stiffness, and external disturbance acting on the sprung mass, we design a disturbance observer based on a sliding mode control (SMC) to estimate these uncertainties under the unknown road excitation. By the Lyapunov minimax approach, the uniform boundedness and the uniform ultimate boundedness of ASS with the proposed control are rigorously proved. Through co-simulation of ADAMS software and MATLAB/Simulink software, the sprung mass acceleration of ASS can be obtained with and without the proposed control.