Specifications
In this chapter we consider specications that limit the dierential sensitivity
of the closed-loop transfer matrix with respect to changes in the plant. For
certain important cases, these specications are closed-loop convex. The most
general specication that limits dierential sensitivity of the closed-loop system
is, however,
closed-loop convex.
not
In the previous chapter we considered various speci cations that prescribe how the
closed-loop system should perform. This included such important considerations
as the response of the system to commands and disturbances that may a ect the
system. In this chapter and the next we focus on another extremely important
consideration: how the system would perform if the plant were to change.
Many control engineers believe that the primary bene ts of feedback are those
considered in this chapter and the next|robustness or insensitivity of the closed-
loop system to variations or perturbations in the plant. From another point of
view, the performance of a control system is often limited not by its ability to meet
the performance speci cations of the previous chapter, but rather by its ability to
meet the speci cations to be studied in this chapter and the next, which limit the
sensitivity or guarantee robustness of the system.
There are several general methods that measure how sensitive the closed-loop
system is to changes in the plant:
Dierential sensitivity: the size of the derivative of with respect to .
H
P
Worst case perturbation: the largest change in that can be caused by a
H
certain speci c set of plant perturbations.
Margin: the smallest change in the plant that can cause some speci cation to
be violated.
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