Filter
Top Products
42 CHAPTER 2. OVERVIEW OF THE UNDERLYING THEORY
Figure 2.8: Closed loop system, G(s), for performance analysis
initial choice of γ for the H
∞
design procedure. We will see later (Section 2.5) that it
can also be used to initialize the D-K iteration procedure when an open-loop H
∞
design
is poorly conditioned.
2.4 µ Analysis
2.4.1 Measures of Performance
Section 2.3 presented design performance objectives in terms of the norm (H
2
or H
∞
)of
a closed loop system. We will now expand on this idea of performance. Consider the
closed loop system illustrated in Figure 2.8. The interconnection structure, P(s), is
specified such that w represents unknown inputs; typically reference commands,
disturbances and noise. The outputs, e, represent signals that we would like to be small.
“Small” means in the sense of a selected norm. These signals might include actuator
effort, and tracking error. As Figure 2.8 suggests, this analysis is typically applied after
calculating a controller.
The inputs w are described only as members of a set. The performance question is then:
For all w in this set, are all possible outputs e also in some set? The following set