F. Benamara et al., ADAPTIVE BAND-LIMITED DISTURBANCE REJECTION IN LINEAR DISCRETE-TIME-SYSTEMS, Mathematical problems in engineering, 1(2), 1995, pp. 139-177
The problem of adaptively rejecting a disturbance consisting of a line
ar combination of sinusoids with unknown and/or time varying frequenci
es for SISO LTI discrete-time systems is considered. The rejection of
the disturbance input is achieved by constructing the set of stabilizi
ng controllers using the Youla parametrization and adjusting the Youla
parameter to achieve asymptotic disturbance rejection. The first main
result in this paper concerns off-line controller design where a cont
roller that achieves regulation is numerically designed off-line based
on the assumption that only the sequence of discrete disturbance inpu
t values (as opposed to a model of the disturbance) is available. A le
ast squares based optimization algorithm is used in the controller des
ign. As expected, it is shown, under some mild assumptions, that if th
e off-line designed controller achieves regulation, then it must inclu
de a model of the disturbance input. The second main result concerns o
n-line controller design where recursive versions of the off-line algo
rithm used above for controller design are presented and their converg
ence properties analyzed. Conditions under which the on-line algorithm
s yield an asymptotic controller that achieves regulation are presente
d. Conditions both for the case where the disturbance input properties
are constant but unknown and for the case where they are unknown and
time-varying are given. The on-line controller construction amounts to
an adaptive implementation of the Internal Model Principle. The perfo
rmance robustness of the off-line designed controller in the face of p
lant model uncertainties is investigated. It is shown, under some mild
assumptions, that performance robustness is realized provided interna
l stability is maintained. The performance of the adaptation algorithm
s is illustrated through a simulation example.