Stability of Adaptive Servo Systems with Partial Reference Model

Abstract

Stability of a model reference adaptive positioning servo system which have adaptive velocity loop and nonadaptive position loop is discussed. Such structure of model reference adaptive controller has been applied to real systems and some successful results have been reported.
Although asymptotic stability of the system with gradient type adaptation law can be proved under the ideal conditions, the system become unstable when a disturbance exists inside the position loop. In this paper, stability of the system is analyzed by singular perturbation method, supposing that the speed of the adaptation is small enough. Further, the system with two different adaptation laws proposed to improve the stability of the system is analyzed similarly.