The problem of robust in the large anti-windup compensation (in the “weakened” anti-windup sense) is revisited with an adaptive approach in order to reduce the conservativeness of previous robust (worst case) approaches just to what is needed to preserve stability with respect to the uncertainty actually present on the plant during operation. Compared to a recent paper having the same goal, the proposed approach adopts a completely different architecture and a new switching strategy, leading to reduced computational effort and stronger stability properties.