Biomedical Engineering Reference
In-Depth Information
r
0
e
(
t
)
u
(
t
)
r
(
t
)
System
Controller
+
FIGURE 3.23
A general closed loop control system.
r
(
t
)
r
0
FIGURE 3.24
A desired output response of a good control system.
They can also be extended and generalized to cover a variety of subconditions.
A collection of rules such as “if-then” rules can be used to form a rule-based
system and in particular act as mappings for fuzzy sets. These are better
known as “fuzzy rules” and are used in many applications such as fuzzy con-
trollers, fuzzy schedulers, and fuzzy optimizations. We will describe the fuzzy
controller briefly to illustrate how fuzzy rule-based systems are implemented.
The standard control problem can be stated as follows. Given a reference
signal
r
(
t
), which may be static for all time, design a controller that maps an
input
r
0
using some control action
u
(
t
) so that
r
0
achieves
r
(
t
) as smoothly
and as quickly as possible. The standard controller with feedback is depicted
in Figure 3.23 and an example of a desired system response is shown in
Figure 3.24. One way to achieve this control is by considering the errors at the
system output, which are defined as the difference between the initial signal
and the current output signal
e
(
t
)=
x
0
−
x
(
t
)
The change in the error can be defined as successive values of the error
e
=
e
(
t
+1)
−
e
(
t
)
Search WWH ::
Custom Search