D. Vonwissel et al., THE EFFECTS OF COMPUTATIONAL DELAY IN DESCRIPTOR-BASED TRAJECTORY TRACKING CONTROL, International Journal of Control, 67(2), 1997, pp. 251-273
Citations number
23
Categorie Soggetti
Controlo Theory & Cybernetics","Robotics & Automatic Control
Descriptor Predictive Control (DPC) has been shown to be a useful meth
od for solving nonlinear tracking problems. A rigorous analysis of loc
al stability and performance characteristics of this method has been a
chieved previously by studying the linear plant under the assumption t
hat the delay introduced in the control due to numerical computation c
an be neglected. It was shown that, if the plant is controllable and m
inimum phase, stability is guaranteed and tracking is achieved exponen
tially with any desired rate of convergence. It was also shown that so
metimes DPC must include a specially designed preliminary feedback. In
this paper, we carry out a similar analysis by taking into account co
mputational delay, which is unavoidable in actual implementation of DP
C. We show, in particular, that under the same assumptions, and provid
ed the special preliminary feedback is used, that the closed loop syst
em remains stable as long as the delay is smaller than a threshold and
that exponential tracking is achieved. However, the rate of convergen
ce of the tracking error cannot be chosen arbitrarily because it is co
nstrained by the plant zeros. The delay analysis is used to explain ex
perimental observations in the literature about the occasional failure
of previous implementations of the DPC approach at small sampling per
iods. A nonlinear robotics problem is worked in detail.