Saturation is a very common nonlinearity in control systems and may produce serious performance deterioration or even loss of stability. To cope with saturation, several anti-windup (AW) schemes have been developed over a long time. Unfortunately, they are based on the assumption that there is a static nonlinearity between the input and output of the saturating element, which, in very many situations, is not the case. Against this background we give sufficient conditions for stability of the observer based anti-windup to face unmodeled actuator dynamics and propose a method with an unknown input observer (UIO) to improve the performance of the robust AW in the case where the output of the actuator is not available. The effectiveness of the presented algorithm is demonstrated on the simple roll-yaw dynamics of a bank to turn missile and compared to another robust anti-windup approach.