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On Compensating Long Actuator Delays in Nonlinear Control

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1 Author(s)
Miroslav Krstic ; Dept. of Mech. & Aerosp. Eng., Univ. of California, La Jolla, CA

We are interested in finite-escape open-loop unstable plants that are globally stabilizable in the absence of actuator delay but require controller redesign in the presence of delay. The simplest such plant is Z(t) = Z(t)2 + U(t - D), where D is actuator delay of arbitrary length. For this system we present a control law that compensates the delay and achieves feedback linearization (of the entire ODE+delay infinite-dimensional cascade). However, even though exponential stability is achieved, the result is not global because the plant can have a finite escape with an initial condition Z(0) ges 1/D before the feedback control "reaches" it at t = D. We prove a stability result whose region of attraction is essentially Z(0) < 1/ D and for which we derive an asymptotic stability bound in terms of the system norm Z(t)2 + intt t-D U(thetas)2dthetas.

Published in:

IEEE Transactions on Automatic Control  (Volume:53 ,  Issue: 7 )