A data-driven controller design procedure is proposed in this paper. The controller is based on both an estimated plant model and its estimated uncertainty described by an ellipsoid in parameter space. Desired performance is specified by the speed and the damping of the modeled response. The unmodeled response is rejected by requiring robust performance with respect to a generalized stability region. Moreover, estimation of a disturbance model enables further rejection of the unmodeled response. The methodology is applied to a nonlinear and unstable magnetic suspension system. High performance is achieved for various specifications over a large operational range.