In this paper for the design of a Steer-by-Wire (SbW) system a generic controller structure is proposed with bidirectional position feedback. The design goal for SbW here is to match the dynamics of an (electric or hydraulic power) steering system which may notionally be subdivided into a manual and an assistance steering part. For matching the manual steering part a generic linear controller structure and for matching the assistance steering part a nonlinear unilateral controller structure are suggested. The controller design problem is formulated as a system dynamics equivalence problem, either based on a physical or an identified model, and is solved exactly. This result is then adapted according to practical considerations. For robustness and stability analysis of the linear part of the steer-by-wire system passivity theory is applied and performance is evaluated by Bode magnitude plots and a H_∞-performance criterion. Nonlinear simulations at various operating conditions (vehicle speed, road-tire contact) with a high fidelity vehicle dynamics model demonstrate the robustness of the whole system.