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2.12 Summary and Notes 101

EXAMPLE 2.11-5: SPR Design

Consider the double integrator system

where c 2≠0 and c 1, c 2 are of the same sign. The open-loop transfer function is
then

which has relative degree 1 and is minimum phase. Note that CB=c 2 which is
invertible. The gain K is chosen to be

where p>0. The closed-loop system is then

which is stable for any choice of γ>0 and is SPR if γ>c 1 /(pc 2 (check!).

2.12 Summary and Notes

This chapter is meant to be a review of various control theory concepts that
will be used in the remainder of the book. The emphasis has been to include
enough material so that readers with little or no background in control theory
are able to follow the design of robot controllers. Simplifications were often
made to concentrate on the systems studied in this book, namely, mechanical
systems and systems described by the Lagrange-Euler equations. In particular,
the double integrator system was illustrated in detail, since it will result from
applying a preliminary nonlinear feedback on mechanical manipulators. In
Chapter 3, we introduce the dynamical description of rigid robot

Copyright © 2004 by Marcel Dekker, Inc.