On the stability of adaptive pole-placement controllers with a saturating actuator

The authors examine how existing pole-placement algorithms work in the case of a saturating input. The stability of such algorithms and the modifications needed to make them work in the case of saturation are examined. The net result is that the analysis of G.C. Goodwin and K.S. Sin (1984) can be slightly modified to prove the stability of adaptive pole-placement, but only for the case where the plant is stable. It is shown that, for unstable plants, it is possible to push the plant into a state from which it cannot be returned to the origin (with a saturating input). Thus, it is fairly easy to generate examples of instability in the adaptive control system that would not exist with unbounded control authority. >