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

This paper discusses and simulates an apparently fatal flaw in the behavior of the reduced-order application 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 than twice the order of the plant, which arises from underestimating the plant order.