In this paper, a three-degree-of-freedom cabin model for a commercial truck is derived to study ride motions of the cabin under random road excitations. First, an active suspension system is designed using the linear-Nquadratic-Gaussian (LQG) design methodology. Then, the LQG design is reduced by the method of balanced truncation. The simulation results show that both the LQG design and the truncated controller effectively suppress the cabin vibrations induced by road unevenness. Next, the control design problem is re-formulated as a non-convex and non-smooth optimisation problem with fixed-order controllers and solved by the recently developed H-infinity fixed-order optimisation (HIFOO) toolbox.