二维广义预测控制下的间接迭代学习控制设计
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"基于二维广义预测控制算法的间接迭代学习控制设计方法"
本文探讨了一种新的控制策略，即基于二维广义预测控制（2D-GPC）的间接迭代学习控制（ILC）系统设计。这一设计方法旨在将学习型控制理论应用于那些已存在局部反馈控制的重复、批处理或定期过程。2D-GPC是一种先进的控制技术，能够考虑系统的时间和空间两个维度，从而提供更全面的预测和控制效果。
在提出的间接ILC系统中，内环采用模型预测控制（MPC），这是一种前瞻性的控制策略，可以根据模型预测未来的系统行为并进行优化决策。同时，内环MPC与一个简单的ILC相结合，构成了外循环。这种设计允许对现有的反馈控制器参数进行综合优化，并简化ILC控制器的设计，从而在2D-GPC框架下实现整体系统的最优控制性能。
通过对控制律的深入分析，研究者发现提出的间接ILC律可直接从标准GPC律导出，这简化了控制器的分析和设计。此外，通过简单的准则，可以评估闭环控制系统的稳定性和收敛性，这是确保系统性能的关键。
文章指出，这种间接ILC方案对于实际工业过程是一个实用且有效的解决方案。数值模拟结果以及与其他控制策略的比较均表明，该方法在改善过程控制性能方面表现出色。该研究强调了ILC在解决复杂控制问题中的潜力，并为实际应用提供了理论基础。
关键词：迭代学习控制（ILC）、二维广义预测控制（2D-GPC）、间接ILC、模型预测控制（MPC）、重复/批处理/定期过程
作者Jia Shi、Hua Zhou、Zhikai Cao和Qingyin Jiang来自于厦门大学化学与生物化学工程学院，他们的研究工作在2014年得到了认可并发表在《过程控制杂志》上，展示了ILC与2D-GPC结合的创新应用，对于控制理论和工业实践都具有重要意义。
Please
cite
this
article
in
press
as:
J.
Shi,
et
al.,
A
design
method
for
indirect
iterative
learning
control
based
on
two-dimensional
generalized
predictive
control
algorithm,
J.
Process
Control
(2014),
http://dx.doi.org/10.1016/j.jprocont.2014.07.004
ARTICLE IN PRESS
G Model
JJPC-1817;
No.
of
Pages
11
J.
Shi
et
al.
/
Journal
of
Process
Control
xxx
(2014)
xxx–xxx
3
The
organization
of
this
paper
is
as
follows:
the
problem
and
design
tasks
of
the
indirect
ILC
are
presented
in
Section
2;
in
Section
3,
the
design
algorithm
of
2D-GPC
is
reviewed,
and
then
the
proposed
2D-GPC
law
is
reformulated
as
an
indirect
ILC
in
Section
4;
in
Section
5,
the
stability
and
convergence
of
control
system
are
investigated;
in
Section
6,
the
proposed
design
method
is
applied
to
a
numerical
plant
controlled
by
a
feedback
control
already
and
some
comparisons
are
given
to
demonstrate
the
applicability
and
effectiveness
of
the
proposed
method;
in
the
last
section,
the
conclusions
are
drawn.
2.
Problem
formulation
2.1.
Process
model
For
simplicity
in
the
notation,
it
is
assumed
in
this
paper
that
a
single-input
and
single-output
process
which
performs
repetitively
a
given
task
over
a
finite
duration,
called
a
batch
or
cycle,
is
described
by
the
Controlled
Auto-regressive
Integrated
Moving
Average
(CARIMA)
model
as
follows
plant
:
A(q
−1
t
)y(t,
k)
=
B(q
−1
t
)
t
u(t,
k)
+
w(t,
k);
t
=
0,
1,
2,
.
.
.,
T;
k
=
1,
2,
.
.
.
(1)
where,
t,
k
indicate
the
discrete-time
and
repetitive/batch/cycle
indices,
respectively,
and
q
−1
t
represents
the
unit
backward
shifting
operator
along
the
time
index
t,
and
then,
t
=
1
−
q
−1
t
denotes
the
backward
difference
operator,
T
is
a
constant
time
duration
of
each
cycle,
y(t,
k),
u(t,
k),
w(t,
k)
are,
respectively,
output,
input
and
unknown
disturbance
of
the
process
at
time
t
in
the
kth
cycle.
A(q
−1
t
),
B(q
−1
t
)
are
both
operator
polynomials
characterizing
the
dynamics
of
the
process
and
formulated
by
A(q
−1
t
)
=
1
+
a
1
q
−1
t
+
a
2
q
−2
t
+
·
·
·
+
a
n
q
−n
t
(2)
B(q
−1
t
)
=
b
1
q
−1
t
+
b
2
q
−2
t
+
·
·
·
+
b
m
q
−m
t
(3)
where
integers
n,
m
>
0
are
the
orders
of
input
and
output,
and
a
i
;
i
=
1,
2,
.
.
.,
n
,
b
i
;
i
=
1,
2,
.
.
.,
m
are
the
parameters
of
the
model.
In
most
industrial
processes,
it
has
been
found
that
CARIMA
model
is
usually
adopted
for
the
model
based
controller
design
since
it
is
very
simple
and
easy
to
be
identified
from
the
process
information.
2.2.
System
structure
of
indirect
ILC
To
guarantee
the
real-time
control
performances,
it
is
assumed
in
this
paper
that
a
feedback
control,
formulated
by
the
following
discrete-time
model,
has
been
designed
and
implemented
fb
:
t
u(t,
k)
=
G
fb
(q
−1
t
)e(t,
k)
(4)
where,
e(t,k)
and
t
u(t,
k)
are,
respectively,
the
control
error
and
time-wise
increment
of
control,
and
the
linear
transfer
function
G
fb
(q
−1
t
)
has
the
rational
form
as
G
fb
(q
−1
t
)
=
N
fb
(q
−1
t
)
D
fb
(q
−1
t
)
=
˜
a
0
+
˜
a
1
q
−1
t
+
·
·
·
+
˜
a
n
1
q
−n
1
t
˜
b
0
+
˜
b
1
q
−1
t
+
·
·
·
+
˜
b
m
1
q
−m
1
t
(5)
Generally,
model
(4)
represents
any
linear
feedback
control
law,
such
as
the
PID
control.
With
this
control
law,
the
closed-loop
control
system
can
be
depicted
as
the
dot-line
block
shown
in
Fig.
2.
For
the
reason
of
budget
or
safety,
it
is
assumed
in
this
paper
that
any
change
to
the
existing
feedback
control
system
is
not
allowed
except
for
the
parameter
optimization
of
the
control
law.
For
application
of
ILC
scheme,
therefore,
the
ILC
law
had
to
be
designed
as
supervisor
above
the
existing
control
system,
as
the
dash-line
block
shown
in
Fig.
2.
Thus,
it
is
results
in
an
indirect
ILC
scheme
to
be
considered.
2.3.
Design
tasks
For
the
indirect
ILC
system
as
shown
in
Fig.
2,
two
design
tasks
should
be
considered:
one
is
to
design
a
simple
ILC
above
the
existing
control
system
to
improve
the
control
performance
from
cycle
to
cycle,
the
other
is
to
optimize
the
feedback
control
law
of
the
inner
loop
to
guarantee
the
control
performance
of
the
whole
system
as
good
as
possible.
3.
2D-GPC
scheme
As
there
are
two
controllers,
iterative
learning
controller
and
real-time
feedback
controller,
to
be
designed
and
optimized
respectively,
the
integrated
design
algorithm
should
be
developed
to
ensure
control
performance
of
the
whole
system.
In
this
section,
the
design
method
of
2D-GPILC,
proposed
in
our
previous
studies
[15,16],
will
be
reviewed,
and
then
it
will
be
reformulated
as
an
indirect
ILC
scheme
in
the
next
section.
3.1.
Iterative
learning
control
law
For
the
processes
described
by
model
(1),
the
ILC
law
to
be
design
is
assumed
as
follows
t
u(t,
k)
=
t
u(t,
k
−
1)
+
r(t,
k)
t
u(t,
0)
≡
0;
t
=
0,
1,
2,
.
.
.,
T
(6)
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