Journal
of
Process
Control
22 (2012) 194–
206
Contents
lists
available
at
SciVerse
ScienceDirect
Journal
of
Process
Control
j
ourna
l
ho
me
pag
e:
www.elsevier.com/locate/jprocont
Adaptive
neural
network
predictive
control
for
nonlinear
pure
feedback
systems
with
input
delay
夽
Jing
Na
a,∗
,
Xuemei
Ren
b
,
Cong
Shang
b
,
Yu
Guo
a
a
Faculty
of
Mechanical
&
Electrical
Engineering,
Kunming
University
of
Science
and
Technology,
Kunming
650093,
China
b
School
of
Automation,
Beijing
Institute
of
Technology,
Beijing
100081,
China
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
27
November
2010
Received
in
revised
form
7
September
2011
Accepted
16
September
2011
Available online 15 October 2011
Keywords:
Process
control
Nonlinear
predictor
Pure-feedback
systems
Time-delay
Neural
networks
a
b
s
t
r
a
c
t
This
paper
presents
an
adaptive
neural
control
design
for
nonlinear
pure-feedback
systems
with
an
input
time-delay.
Novel
state
variables
and
the
corresponding
transform
are
introduced,
such
that
the
state-
feedback
control
of
a
pure-feedback
system
can
be
viewed
as
the
output-feedback
control
of
a
canonical
system.
An
adaptive
predictor
incorporated
with
a
high-order
neural
network
(HONN)
observer
is
pro-
posed
to
obtain
the
future
system
states
predictions,
which
are
used
in
the
control
design
to
circumvent
the
input
delay
and
nonlinearities.
The
proposed
predictor,
observer
and
controller
are
all
online
imple-
mented
without
iterative
predictive
calculations,
and
the
closed-loop
system
stability
is
guaranteed.
The
conventional
backstepping
design
and
analysis
for
pure-feedback
systems
are
avoided,
which
renders
the
developed
scheme
simpler
in
its
synthesis
and
application.
Practical
guidelines
on
the
control
imple-
mentation
and
the
parameter
design
are
provided.
Simulation
on
a
continuous
stirred
tank
reactor
(CSTR)
and
practical
experiments
on
a
three-tank
liquid
level
process
control
system
are
included
to
verify
the
reliability
and
effectiveness.
© 2011 Elsevier Ltd. All rights reserved.
1.
Introduction
The
identification
and
control
for
time-delay
systems
have
been
an
active
topic
in
both
academic
and
engineering
fields
since
the
presence
of
delays
in
the
control
systems,
e.g.
process
control,
net-
work
systems,
may
deteriorate
the
performance
or
even
trigger
instability
[1].
During
the
past
decades,
the
stability
analysis
and
stabilization
control
of
system
with
delays
in
its
state
variables
have
been
significantly
advanced
[2,3].
On
the
other
hand,
the
track-
ing
control
of
system
with
delays
in
its
input
is
more
practically
useful
but
technically
challenge
[1].
In
this
issue,
Smith
[4]
pro-
posed
a
predictor-based
structure
to
deprive
the
time-delay
from
the
closed-loop
characteristic
equation,
which
successfully
reme-
dies
the
malicious
effects
of
the
input
delay.
By
taking
the
merit
of
Smith
predictor
(SP),
many
improved
schemes
[5–9]
have
been
developed
to
enhance
the
robustness
and
the
disturbance
rejec-
tion.
To
address
unknown
parameters,
Rad
et
al.
[10]
established
an
adaptive
time-delay
controller
(ATDC)
with
an
online
parame-
ter
estimation.
Recently,
Normey-Rico
et
al.
[11]
proposed
a
novel
夽
This
work
was
supported
by
National
Natural
Science
Foundation
of
China
(60974046
and
61011130163).
This
work
was
conducted
when
Jing
Na
was
with
School
of
Automation,
Beijing
Institute
of
Technology,
Beijing
100081,
China.
∗
Corresponding
author.
E-mail
addresses:
najing25@163.com
(J.
Na),
xmren@bit.edu.cn
(X.
Ren).
kind
of
dead-time
compensators
(DTC)
where
the
analytical
param-
eter
design
results
are
derived
to
retain
the
robustness
and
tracking
performance.
For
the
system
with
communication
delays,
a
con-
troller
based
on
the
network
disturbance
(ND)
and
communication
disturbance
observer
(CDOB)
was
studied
in
[12]
to
achieve
the
same
effectiveness
as
SP.
In
[13],
predictive
control
was
applied
to
networked
control
systems
(NCS)
with
random
delays.
To
elimi-
nate
periodic
disturbances,
repetitive
control
methodology
has
also
been
extended
to
time-delay
systems
[14–16].
Different
to
other
controllers,
the
intrinsic
plant
delay
is
considered
as
a
useful
ele-
ment
in
these
repetitive
control
designs.
Despite
their
successful
applications,
it
is
noted
that
all
of
aforementioned
schemes
primar-
ily
focus
on
linear
time-delay
systems
with
precisely
known
mod-
els,
and
thus
cannot
be
directly
applied
for
nonlinear
time-delay
systems.
To
accommodate
the
nonlinearities
and
input-delay,
the
princi-
ple
of
SP
was
extended
to
nonlinear
time-delay
systems
in
[17,18].
Henson
and
Seborg
[19]
presented
a
time-delay
compensator
for
SISO
nonlinear
processes
by
using
a
nonlinear
state
predictor
and
an
input–output
linearization
controller.
An
alternative
compensa-
tion
strategy
incorporating
the
input–output
linearization
with
the
internal
model
control
(IMC)
and
a
feedback
compensation
term
was
developed
by
Hu
and
Rangaiah
[20],
while
an
input–output
feedback
linearization
with
only
output
measurement
was
further
exploited
in
[21].
In
[22],
an
adaptive
generic
model
control
was
investigated
based
on
the
nonlinear
state
predictor
(NSP)
and
the
modified
strong
tracking
filter
(MSTF).
Nevertheless,
most
of
these
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