Biomedical Engineering Reference
In-Depth Information
r ( nT ) +
e p ( nT )
K i
_
∆ u PI ( nT )
u PI ( nT )
+
u PID ( nT )
+
+
y ( nT )
fuzzy PI
controller
z -1
K u PI
Process
_
_
+
e v ( nT )
u D ( nT )
z -1
1/ T
K p
_
u D ( nT )
+
fuzzy D
controller
z -1
K u D
K d
1/ T
_
+
∆ y ( nT )
∆ u D ( nT )
z -1
y d ( nT )
-1
Figure 5.5
Fuzzy.PID.controller.system..(From.Tang,.K..S.,.Man,.K..F.,.Chen,.G.,.Kwong,.S.,.An.optimal.
fuzzy.PID.controller,. IEEETransactionsonIndustrialElectronics ,.48(4),.757-765,.2001.)
The. problem. is. to. design. a. discrete-time. fuzzy. proportional-integral-
derivative.(PID).controller.design;.its.block.diagram.is.depicted.in. Figure 5.5 ..
Fuzzy.PID.controllers,.evolving.from.conventional.PID.controllers,.are.gen-
erally.designed.for.nonlinear.systems,.higher-order.and.time-delayed.linear.
systems,. and. particularly. complex. and. vague. systems. that. cannot. be. rep-
resented.by.precise.mathematical.models..The.framework.of.the.fuzzy.PID.
control.was.given.in.Carvajal,.Chen,.and.Ogmen.[3].and.Chen.[5],.and.a.brief.
summary.is.also.given.in.Appendix.D..Further.details.of.the.design.can.be.
found.in.Misir,.Malki,.and.Chen.[12].and.Tang,.Man,.Chen,.and.Kwong.[17].
Although.the.structure.of.the.fuzzy.PID.controller.given.in. Figure 5.5 . is.
standard,.it.remains.a.difficult.task.to.determine.its.optimal.parameters;.this.
was.addressed.based.on.a.MOGA.[17]..As.stated.in.Fonseca.and.Fleming [10],.
instead. of. having. a. single. solution,. a. Pareto-optimal. solution. set. can. be.
obtained.based.on.various.control.performance.criteria.
5.7.3.1  Optimization of Controller Design
For.the.design.problem,.the.following.time-delayed.nonlinear.process.is.assumed:
=
y t
( )
| ( )|
y t
+
y t
(
2)
+
u
( )
t
.
(5.20)
PID
.
As.shown.in . Figure 5.5 . and.explained.in.Appendix.D,.there.are.six.control.
parameters.to.be.determined.in.this.design.problem..Therefore,.the.chromo-
some.can.be.constructed.as
{
}
I
=
K K K R K
,
,
,
,
,
K
p
i
d
uD
uPI
.
where.each.parameter.is.coded.in.a.16-bit.binary.number.
 
 
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