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284 Robust Control of Robotic Manipulators

(3)

Then all the stabilizing controllers are given by

(4)

where Q(s) is a stable rational function which is otherwise arbitrary. One
choice, of course, is to let Q(s)=0, which leads to the “central solution”
[Vidyasagar 1985]

(5)

One can also choose Q(s) to satisfy the required performance. In particular,
the following choice of Q(s) is presented in [Spong and Vidyasagar
1987]:

(6)

which leads to the following controller:

where

and

(7)

As k increases, the disturbance rejection property of the controller is enhanced
at the expense of higher gains as seen from the expression of C(s). A simulation

Copyright © 2004 by Marcel Dekker, Inc.