This article presents a robust nonlinear model predictive control (NMPC) strategy for constrained systems with piecewise constant references and bounded disturbances based on nominal predictions. An artificial target is employed to avoid feasibility loss due to target change and to provide a potentially enlarged domain of attraction. Recursive feasibility and input‐to‐state stability are ensured. Recursive feasibility is guaranteed due to the tighter constraints that are recursively computed offline based on the disturbance reachable sets. The zonotopic approach from the mean‐value theorem extension is applied to compute these tighter constraints. In the presence of stochastic disturbances with known distribution, individual chance constraints can be considered in the proposed NMPC algorithm. Furthermore, simplified stabilizing ingredients are proposed in order that the robust assumptions hold based on standard algorithms. Case studies based on the continuous stirred tank reactor and buck‐boost control benchmarks are presented to illustrate the main properties of the proposed approach.