A reconfigurable feedback controller based on a digital twin is illustrated using simulations of a system with a time-varying nonlinear backlash. The control system consists of a motor driving the position of a flexible structure through a lead screw subject to backlash, whose gap angle changes over time. An internal model control (IMC) approach is utilised as the feedback path to increase the linear controller robustness. When a backlash is considered in the model, it is shown that although the linear IMC remain asymptotically stable, its performance deteriorates. A nonlinear IMC (NIMC) approach improves the closed-loop system’s transient behaviour. When the backlash model used in the NIMC is exact, the NIMC can follow the reference model. However, residual vibrations are observed if the backlash model is not estimated precisely. A digital twin of the system is used to estimate the backlash gap angle and to re-design the backlash model for the NIMC via asynchronous communication, thus ensuring the stability of the feedback system.