On stability-instability conditions of a simple robust adaptive servo controller

The paper studies the stability properties of a new adaptive servo controller possessing a robust servo structure and an error driven fixed regulation loop. This loop is designed to satisfy the disturbance rejection requirements and the reference tracking is ensured via an adaptive feedforward block. At both design stages a priori knowledge about the process dynamics may be easily incorporated. Global convergence of the scheme is established under the standard strictly positive real (SPR) condition. Two stability-instability boundaries for the adaptive system are derived, one based on the, now well known, low gain stability concept and a new (explicitly) gain-dependent boundary obtained for the single parameter adaptation case via Lyapunov techniques. In both cases the SPR assumption is obviated.