An adaptive controller based on some compensation methods that preserve stability for fast time-varying plants in the presence of bounded output disturbances and unmodelled dynamics is presented. No minimum phase assumption is required by the adaptive scheme to guarantee closed-loop stability, although the unstable plant zeros must be transmitted to the closed-loop system to avoid unstable cancellations. The unknown plant parameters are estimated by a normalized algorithm with dead zone. The design is completed with a modified control law which adds an internal impulse to the system whenever the controllability of the estimated model is lost. This strategy confers a self-excitation capability to the system, so that it makes unnecessary the presence of external persistently exciting signals. As a result, the estimated models are sufficiently controllable by the underlying control law based on the special compensation methods, and global stability is ensured. The performance of the given scheme is evaluated by simulations.