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The rotational/translational proof-mass actuator (RTAC) system is a well-known benchmark for nonlinear control for which a number of controllers were designed. In this paper, we apply fuzzy Lyapunov synthesis, which is a computing with words version of classical Lyapunov synthesis, to design fuzzy controllers for the RTAC system. This allows us to systematically design state-feedback and output-feedback controllers using only a linguistic description of the RTAC system. The designed fuzzy controllers yield a globally asymptotically stable closed-loop system. We demonstrate their advantages in comparison with a previously designed linear controller for the RTAC system.