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280 Robust Control of Robotic Manipulators

Table 5.2.2: Static Controller, Input-Output Design

which did not used dynamical feedback, and with the two-degree-of-freedom
controllers considered next.
In [Spong and Vidyasagar 1987] the factorization approach was used to
design a class of dynamic linear compensators C(s), parameterized by a stable
transfer matrix Q(s), which guarantee that the solution e(t) to the linear
system (5.2.9) is bounded. The actual factorization approach design is beyond
the scope of this book, but fairly general representative of the methodology
as it applies to robotics is given in Example 5.2.3. In [Spong and Vidyasagar
1987] it was actually assumed that the bound on is linear [i.e., 2=0 in
5.2.10)] before the family of all ∞ stabilizing compensators of the nominal
plant was found. Although the case of noisy measurements was treated in
[Spong and Vidyasagar 1987], we limit ourselves to the noiseless case for
simplicity. Let us first recall the system (5.2.16), while suppressing the s
dependence,

(5.2.30)

and define

Copyright © 2004 by Marcel Dekker, Inc.