Nonlinear Control Sy.. - Free

10.8. EXERCISES 289
(10.8) Consider the following system:
(a) Find the relative order.
.t1 =21+22
±2=2g+U
X3 = X2 - (X23
y = 21
(b) Determine whether it is minimum phase.
(c) Using feedback linearization, design a control law to track a desired signal y =
yref-
Notes and References
The exact input-state linearization problem was solved by Brockett [12] for single-input
systems. The multi-input case was developed by Jakubczyk and Respondek, [39], Su, [77]
and Hunt et al. [34]. The notion of zero dynamics was introduced by Byrnes and Isidori
[14].
For a complete coverage of the material in this chapter, see the outstanding books of
Isidori [36], Nijmeijer and van der Schaft [57], and Marino and Tomei, [52]. Our presentation
follows Isidory [36] with help from References [68], [88] and [41]. Section 10.1 follows closely
References [36] and [11]. The linear time-invariant example of Section 6, used to introduce
the notion of zero dynamics follows Slotine and Li [68].