Abstract
Since the numerator polynomial of the plant is adaptively canceled in model reference adaptive control, it can be applied only to minimum phase plants. If model reference adaptive control would be unjustly applied to a nonminimum phase plant, the closed loop system will always be led into instability. While nonminimum phase plants are found more often in discrete time systems, the plant should be regarded as nonminimum phase from the general point of view. Unless the plant is certainly of minimum plase, in order to obtain a closed loop system with satisfactory dynamics, we need adaptive pole assignment where only the denominator polynomial is changed to a desired stable polynomial, leaving the numerator unchanged. There have been many research works on adaptive pole assignment, but most of them are concerned with indirect method. The unallowable defect of indirect method is that stability is not guaranteed unless the outer reference input contains sufficiently many frequency components. Elliott presented a direct method for constructing adaptive pole assignment systems, but he did not demonstrate the motivation of introducing Bezout identity. Moreover, stability was not discussed at all. This paper is also concerned with direct method. Not only the motivation of introducing Bezout identity is clearly demonstrated, but stability is also discussed in detail. The important result is that stability is guranteed even if the outer reference input is not sufficiently rich. Of course, otherwise pole assignment is adaptively achieved. The key concept in the discussionof stability is comparison of orders of two divergent time functions.
