We present a linear, one-parameter model for rigid displacement of a toroidally symmetric plasma. When the feedback control is feasible, plasma inertia can be neglected, and the instability growth rate is proportional to wall resistivity. We benchmark the linear model against non-linear, hybrid simulations of an axially unstable, beam-driven field-reversed configuration to fix the free parameter of the model. The resulting parameter-free model is validated using linear and non-linear closed-loop simulations with active feedback control by voltage-controlled coils. In closed loop simulations, the predictions of the parameter-free linear model agree satisfactory with the non-linear results. Implications for the feedback control of the positional instability in experiments are discussed. The presented model has been used to guide the design of the feedback control hardware in the C-2W experiment.