A flaw in the reduced-order behavior of a direct adaptive pole placer

This paper discusses and simulates an apparently fatal flaw in the reduced-order behavior of a recently proposed direct adaptive pole placer. The algorithm can exhibit instability in the output and input of the controlled plant despite the stability of the prediction error driving the parameter adaption equations. This occurs when the order of each of the directly adjusted compensator elements is less than that of the plant and correspondingly the number of prespecified, desired (nonzero) pole locations is less that twice the order of the plant, which arises from underestimating the plant order.