Nonlinear Control Sy.. - Free

Chapter 10
Feedback Linearization
In this chapter we look at a class of control design problems broadly described as feedback
linearization. The main problem to be studied is: Given a nonlinear dynamical system,
find a transformation that renders a new dynamical system that is linear time-invariant.
Here, by transformation we mean a control law plus possibly a change of variables. Once
a linear system is obtained, a secondary control law can be designed to ensure that the
overall closed-loop system performs according to the specifications. This time, however,
the design is carried out using the new linear model and any of the well-established linear
control design techniques.
Feedback linearization was a topic of much research during the 1970s and 1980s.
Although many successful applications have been reported over the years, feedback linearization
has a number of limitations that hinder its use, as we shall see. Even with these
shortcomings, feedback linearization is a concept of paramount importance in nonlinear
control theory. The intention of this chapter is to provide a brief introduction to the subject.
For simplicity, we will limit our attention to single-input-single-output systems and
consider only local results. See the references listed at the end of this chapter for a more
complete coverage.
10.1 Mathematical Tools
Before proceeding, we need to review a few basic concepts from differential geometry.
Throughout this chapter, whenever we write D C R", we assume that D is an open and
connected subset of R'.
We have already encountered the notion of vector field in Chapter 1. A vector field
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