Abstract Individual pitch control (IPC) is an effective and widely used strategy to mitigate blade loads in wind turbines. However, conventional IPC fails to cope with blade and actuator faults, and this situation may lead to an emergency shutdown and increased maintenance costs. In this paper, a fault‐tolerant individual pitch control (FTIPC) scheme is developed to accommodate these faults in floating offshore wind turbines (FOWTs), based on a Subspace Predictive Repetitive Control (SPRC) approach. To fulfill this goal, an online subspace identification paradigm is implemented to derive a linear approximation of the FOWT system dynamics. Then, a repetitive control law is formulated to attain load mitigation under operating conditions, both in healthy and faulty conditions. Since the excitation noise used for the online subspace identification may interfere with the nominal power generation of the wind turbine, a novel excitation technique is developed to restrict excitation at specific frequencies. Results show that significant load reductions are achieved by FTIPC, while effectively accommodating blade and actuator faults and while restricting the energy of the persistently exciting control action.