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Unformatted text preview: United States Patent [191 Martin Sanchez [54] ADAPTIVEPREDICT IVE CONTROL
SYSTEM [76] Inventor: Juan Martin Sanchez, C/Alava, 75, Barcelona, Spain
[21] Appl. No.: 821,600
[22] 'Filed: Aug. 4, 1977
[30] Foreign Application Priority Data
' Aug. 4. 1976 [GB] United Kingdom ............... 32395/76 [51] Int. Cl.2 ....................... G053 13/02; G06F 15/46
[52] U.S. C1. .................................... 364/106; 364/121;
364/116; 364/501
[58] Field of Search ............... 364/105, 106, 108, 118,
364/121, 501,116 [56] References Cited
U.S. PATENT DOCUMENTS 8/ 1971 Bristol .................................. 364/106
10/1973 Chao et al. ........................... 364/106
3/ 1974 Courtiol ............................... 364/ 106 3,601,588
3,767,900
3,795,799 Offﬂfm 2'
if!) ORiGINAL PATENT
OF THE PREDICTNE CONTROL METHODOLOGY 1N THE U.S.A. 111]  4,197,576
[45] Apr. 8, 1980
3,876,871 4/1975 Sinner .................................. 364/106
3,920,965 11/1975 Sohrwardy .......................... 364/106 Primary Examiner—Joseph F. Ruggiero
Attorney, Agent, or Firm—Ostrolenk;Faber, Gerb &
Soffen [57] ABSTRACT An adaptivepredictive control system for controlling
singleinput singleoutput, or multivariable timevariant
proceSSes with known or unknown parameters and with
or without time delay, is disclosed. The adaptivepre
dictive control system of the present invention updates
on real time the parameters of an adaptivepredictive
model from which the dynamic output vector of the
process being controlled is predicted and the control
vector controlling the operation of this process is com
puted with the objective that the predicted dynamic
output vector becomes equal to the desired dynamic
output vector. 12 Claims, 3 Drawing Figures (Amer/W;
“77'
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makth‘WQV N EBK‘QNKQ 4,197,576 Sheet 2 of 3 U.S. Patent Apr. 8, 1980 m m3
1 .......q..._ II IIIIIIIIIIIIIIIIIIII. ii. 5 ————‘n  
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'6‘ ... ‘0’. ocu 25. 2:. U.S. Patent Apr. 8, 1980 Sheet 3 of 3 4,197,576 FIG. 3 4,197,576 1
ADAPTIVEPREDICT IVE CONTROL SYSTEM BACKGROUND OF THE INVENTION The invention is related to an adaptive control system
for singleinput singleoutput or multivariable timevari
ant processes with known or unknown parameters and
with or without time delays. Such a control system is useful in many diverse ﬁelds 10
such as aeronautics, electronics, chemical engineering,
etc. Examples of processes in which the adaptivepre
dictive control system has been applied are singleinput
singleoutput control of an aircraft where the pitch
angle is controlled by elevator position, and the mul 15
tivariable control of a distillation column where top and
bottom compositions are controlled by reﬂux and steam
ﬂow rates. It is known that the control performance of a system
with a control system based on constant parameters 20
deteriorates when the dynamic parameters of the pro
cess vary in an unforeseen way which is not capable of
direct or indirect measurement. In recent years, control
techniques have been developed to try to solve this
problem, the most noteworthy of which have been 25
based on the model reference adaptive systems theory,
which basically operates in one of the following ways:
(1) Performs a real time adaptive estimation of the pa
rameters and state variables of the process, from which
an adaptive regulator computes the control to be ap 30
plied to the process, or (2) Computes the control to be
applied to the process through an adaptive control
scheme in order to make the process output follow a
model reference output. In general, in both of the above
cases, the control structure requires the design of a
corrector and the difﬁculties encountered in the compu
tation of the parameters of this corrector as the order of
the process increases, severely restricts the ﬁeld of ap
plications of these techniques. BRIEF DESCRIPTION OF THE INVENTION The present invention uses a digital computer to ac
complish the adaptive control of singleinput singleout
put or multivariable timevariant processes with known
or unknown parameters and with or without time de
lays, in such a way that the dynamic output vector of
the process is predicted and the control vector, to be
applied to the process, is computed with the objective
that the predicted dynamic output vector becomes 50
equal to the desired dynamic output vector, and this is
done at every sampling or control instant by a number
of simple and speciﬁc operations. BRIEF DESCRIPTION OF THE DRAWINGS 55 The implementation of the invention will be de
scribed in a general way with reference to the accompa
nying ﬁgures, following this the results of a particular
application of the control system will be shown. FIG. 1 shows the general and conceptual structure of 50
the adaptivepredictive control system. FIG. 2 shows a distillation column On which the
adaptivepredictive control system was implemented to
carry out a multivariable coutrol of the top and bottom
compositions as outputs with reﬂux and steam flow 65
rates as inputs. FIG. 3 shows results of one such experiment on the
adaptive—predective control of a distillation column. 5 35 40 45 2 DETAILED DESCRIPTION OF THE
INVENTION At any sampling instant k, two modes of operation of
the control system are possible; an identiﬁcation mode
and a control mode. Which mode is employed is deter
mined by either a human or an automatic operator 2. In
either case, the modes are as is shown in FIG. 1. 1. Identification mode: In the identiﬁcation mode, the
control vector 111k) is directly applied from the Operator
2 to the apparatus 10 carrying out the process being
controlled and identiﬁcation block 4 as shown by path
1. The identiﬁcation block 4 uses an adaptivepredictive
model stored in computation block 5 to compute an
estimated incremental process output vector d_(k). An
error vector e(k) which represents the difference be
tween the actual and estimated incremental process
output vectors y(k) and d(k), respectively, is used to
update the parameters of the previously mentioned
adaptivepredictive model through an adaptive feed
back mechanism 6. The coutrol vector n(k) is delayed
by r+1 sampling periods in delay 'block 11 before being
acted upon by computation block 5. 2. Control mode: In this mode, the parameters of the
adaptivepredictive model are updated as explained
above. However, as shown by path 7 the control vector
u(k) to be applied to the apparatus 10 carrying out the
process being controlled is computed by the control
block 8, using the same updated adaptivepredictive
model as the identification block 4, in such a manner
that the desired incremental output vector of the pro
cess d1(k+r+ l), at the sampling instant k+r+1, will
be equal to the predicted incremental process output
vector 511'(k+r+ 1) at the same instant k+r+ 1, where
r is the number of sampling time delays observed or
conveniently considered in the process. dl(k+r+ l) is
computed at the instant k by the driver block 9 in re
sponse to the operator 2 input. The input of driver block
9 is set by the Operator of the control system and repre
sents the desired set point value of the output of the
process. Driver block 9 generates the desired process
output trajectory which is the desired dynamic trajec
tory over which the process output reaches the desired
static output. §(k+r+ 1) is the value of this trajectory
at k+r+l. i.e. the desired process output at instant
k+r+ 1. This value is computed at the instant k by the
driver block in response to the operators input y(k) as
set forth in some detail in the description of the opera
tion (f). As gar) does not act on the process output until
the instant k+r+1, the desired output vector of the
process d1(k+r+ 1) at instant k must be known in order
to compute g(k). r is the number of sampling delays
considered on the process. To properly control the process being carried out by
apparatus, 10 the adaptivepredictive control system
uses incremental values of the output, input and measur
able disturbance vectors of the process. Additionally,
the control vector can be limit checked. The speciﬁc
operations that the control system will carry out at
every sampling instant k during the control mode are
described as follows: (3) Measurement (by sensor 12), and, if it is consid
ered convenient, ﬁltering of the output variables of the
process carried out by apparatus to obtain the process
output vector yp(k), the dimension of which is consid
ered to be n. (b) Computation of the incremental process output
vector y(l;) (in computer block 13) by: 4,197,576 1(k)=gp(k)—zptk=w (1)
where 'y is an integer that can be conveniently chosen
and which represents the number of sampling periods
upon which the incremental process vector y(k) is com
puted. _  (c) Computation in identiﬁcation block 4 of the esti
mated incremental process output vector g(k) by the
adaptivepredictive model, which can be deﬁned by: " . f _ (2)
gm: £A,(k‘ 1)J_;(k—r—rl)+ 2 B,(k—1)g(k—:—r} i=1 1': + .EI C,(k —1)1»(k — i— r2)
I: Where the vector g(k—i—r) and w(k—i—r2) are ob
tained by: guc—r—r)=yp(t—t—r)—gptk—i~r—v) (3) gkwr—rz)=gp(t—I—r2)—mk—I—rzyt (4)
where \_lp(l(—— iar) and wp(k—i—r2) are the control and
the measurable disturbance vector, respectively, of di
mensions :11 and m, at the sampling instants k—i —r and
k—i—r2, respectively. In equation 2, the integers h, f
and g can be conveniently chosen, and likewise the
integers n and r2 can also be conveniently chosen taking
into account the available or forecasted measurements
of the output and disturbance vectors, respectively. The
matrices A,{k—l), B,(k— l) and C;(k— 1) of the adap
tive—predictive model have appropriate dimensions and
their values correspond to a past value before being
updated at the instant k. If the dimension of the control
vector is bigger than the dimension of the output vector
then, in most of the cases, supplementary conditions
should be added to obtain a unique control solution, or 10 15 20 25 30 35 simply some of the control vector components can be 40 included in the disturbance vector; as a particular case it
will be considered that n1=n.
(d) Computation of the incremental estimation error
vector by:
3(k)=z(k)—g{(k) (5)
(e) Computation in adaptive feedback mechanism 6 of
the updated values at instant k of the parameters agqﬂt),
byq(k) and cﬁq(k), that are the elements in the j"‘ row and q” column of the matrices A,(k), B,(k) and C,(k), respec
tively, by means of the following algorithms: aggk)=ﬂa;jqaj(k)e](k)yq(k—t— Ftl+aqu(k— 1) (6) byqlk) =13byqaﬂkleﬁk)uq(k — r— r)+ bqqik — 1) (7) cards):chqaﬁk)ej(k)wq(k—i_m+cwk _ n where e,(k), yqﬂt—i—rl), uq(k—i—r) and wqﬂt—i—rz)
are the corresponding components of the vectors gar),
y(k—i—r1), u(k—i—r) and wﬂt—i—rz), respectively.
ﬂagq, 3qu and Bcﬁq are coefﬁcients that can be conve
niently tuned, and aﬁk) (j=1,n) are variable gains that
can be easily chosen among the wide range of possibili
ties that the well known gradient parameter identiﬁca
tion techniques permit. A particular choice of these
variable gains can be the following: (3) 45 50 55 65 4
h n (9)
ajm = 1/[1 + '2' 2 Bag”4k — r— n)“ +
f: q:
f n g m
2 2 Bby'q uq(k —— 1' 7 r)2 + E 2 BEGq quc — t — 12):]
i=lq=l i=1q=1
U:1”) (f) Computation in driver block 9 of the desired incre
mental output vector _d1(k +r+ 1), which can be carried
out, as follows: . 1. Computation of the desired process output vector
gp(k+r+ I) of dimension (nX l) which can be done in
various ways, such as using a model reference with
desired dynamics and also the previously measured or
forecasted process outputs. For example, this last type
of design can be deﬁned by the following equation: 1 (10}
ink+r+I)=I_E]Egp(k+r+l—rt~0+ 5
smgt+1_0 f: Where yp(k+r+lr1i) and y(k+1——i) are the pro
cess output vector and the driver block input vector at
the sampling instant k+r+ l —r1—i and k+ l —i, re
spectively. y(k+1—i) is a vector of dimension n. that is
generated directly by the operator; and the matrices
F,(i=1, t) and H16 :1, s), as well as the integers t and s,
can be chosen freely to take into account the desired
dynamics. An illustration of this choice is given in the
Experimental Example below. 2. From the value of the desired output vector of the
process gp(k+r+1). the desired incremental output
vector 511(k+r+ 1) can be easily computed in various
manners; a particular one, usually convenient when
y>r, is given by the following equation: gl(k+r+)=gp(i+r+1)—yp(k+r+t—v) (11)
If found necessary the value of g1(k+r+ 1) can be limit
checked. (g) Computation of the control vector (in control
block 8) may be made according to the following: 1. From the updated adaptivepredictive model (up
dated by the output of adaptive feedback mechanism 6),
the predicted incremental process output vector
g’(k+r+1) at the sampling instant k+r+1, will de
pend upon the incremental control vector t_1_(k), and is
given by the equation: " (12)
a’i‘tk+r+1):,21(t)£(t+r+ivn_n+ [2 _£ magi + t — a r=l _§C,(k)y(k+r+l—r2—1) t=l The incremental control vector 3(k) is computed by
making the predicted incremental process output vector
g1'(k+r+l) equal to the desired incremental output
g1(k+r+1), and is given by: 501:) = s.~l(t)gl(k + r + i) — . “31 arI é BKAMk +1—0—
;: 2 4,197,576 5 continued a
lit—10c) _2 A,(Ic)£(k + r+ 1 a r1—t) — I: q
314(k) 2 C,(k)y(k + r + l — r2 — 0
i=1 2. From not), the control vector will be computed by: EpU‘)=£(k)+!p(k_7) (14) (h) If desired, the control vector gpac) can be limit
checked before being applied to the process. In its implementation the adaptivepredictive control
system can use incremental input, output and distur
bance vectors as described in the above Operations. An
alternative method of implementing the system is to
compute the incremental input, output and disturbance
vectors with respect to some constant vectors chosen
conveniently and, consequently, in the Specific equa
tions described above the equation 1, 3, 4, 11 and 14
need to be respectively modiﬁed as follows: 1(kl=rp<k)rpc (15)
gk—i—r)=g,(ki—r)—u_pc (16)
E(k*l—r2l=ﬂp(k—i—TZ)—Epc (It)
g1(k+r+l)=gp(k+r+l)iypc (l8) caesium... (19) Likewise, when it is considered coavenient to give
Specific values to some of the adaptivepredictive model
parameters (for instance, because of a certain knowl
edge of the process), theSe values can be given to the
respective parameters, and the corresponding B coefﬁ
cients will be set to zero. Also it is possible to stop the
updating operations of the adaptivepredictive model
parameters as long as it is considered convenient. When the system performs in its identiﬁcation mode,
it only needs to carry out the operations a to e, and this
identiﬁcation action can be performed in real time or
offline, and even in between the sampling intervals. It will be observed that in the operation g to compute 10 15 20 25 30 35 6 gain; and also the dynamics of the process can be modi
fied in an analogous way; in this case the control system
will control the process through the coatrol of the mod
iﬁed process. EXPERIMENTAL EXAMPLE: Multivariable
control of a binary distillation column The adaptivepredictive control system, previously
described, has been implemented for the multivariable
control of top and bottom compositions (in weight % of
methanol) of a binary distillation column, at the Chemi
cal Engineering Department, University of Alberta,
Edmonton, Alberta (Canada). As shown in FIG. 2, the feed flow 11 enters into the
distillation column 10 at the fourth ashtray, the top
product condensates in 12 by cooling water, and falls to
the container 13. The objective of the experiment is to
control the composition of the bottom product 15, that
goes away from the bottom of the column. We have used as control variables, the reﬂux ﬂow
rate 16 and the steam ﬂow rate .17, that heats the re
boiler 18 in the bottom of the column. To accomplish
the experiment we have used a digital computer 19, that
takes the measurements of top and bottom compositions
made by a composition recorder 20 and a gas chroma
tography system 21, reSpectively, and that controls the
set point of the ﬂow recorder controllers 22 and 23. In
addition, the column had the following equipment: two
liquid level indicator controllers 24, two ﬂow recorders
25, a pressure indicator controller 26, two temperature
recorder controllers 27 and a ﬂow recorder controller
28. The control variables were the reﬂux and the steam
flow rates, and the sampling period was of 256 sec. Due
to this large sampling period, there is no time delay
between top composition and reﬂux and steam flow
rates. There exists a measurement time delay of one
sampling period between bottom composition and
steam ﬂow rate, because of the analysis time needed to
measure the bottom composition, and the time delay
between bottom composition and reﬂux rate was ob  served to be two sampling intevals. No signiﬁcant dis n(k), the matrix B1(k) must be inverted. The risk of 45 singularity of the matrix 131(k) can almost always be
avoided by adding time delays to the components of the
input and output process vector, and controlling the
resultant process. An illustrative experimental example
of this procedure is presented in this patent application. Another way of implementing the control system is
to put the adaptivepredictive model in form that the
vector goo will not be the estimation of the vector y(k),
but the estimation of any other output or input vector in
a previous sampling instant. The error of this estimation
will then be used to update the adaptivepredictive
model. In some cases, an equivalent wayof applying the
control system presented here, is to decompose it to a 50 55 set of singleoutput multiinput systems, each one of 60 which will impose a condition to be veriﬁed by the
components of the control vector at every sampling
instant, and from the, set of the n corresponding linear
equations the control vector can be computed at every
sampling instant. Finally, the static gains of the process can be modiﬁed
by multiplying the components of its output, input and
disturbance vectors or incremental vectors by scalars 65 turbance was acting upon the process. To avoid the problem of the singularity of Bl(k),
previously discussed, a sampling time delay was added
to the t0p composition measurement; consequently, the
correSponding component of the process output vector
related to the top composition at the sampling instant k,
is the measurement of the top composition at instant
k— 1; likewise, this component at instant k+ 1 is already
known at instant k. in accordance with the previously described circum
stances, at every sampling instant k, the sequence of
operations performed by the adaptivepredictive con
trol system during its control action were: 1. Measurement of top and bottom compositions to
obtain the process output vector Mk), the components
of which are the top composition measured at k—l,
yp1(k), and the bottom composition measured at k,
yam. 2. The number of sampling time delays considered for
the process r is, in this case, equal to l, and the integer
7 was chosen equal to 2; consequently the incremental output vector is computed by: 10") ﬂailMk4) (20) 4,197,576 ‘7 3. In the adaptivepredictive model, the integers h, f
and r1 were chosen equal to 3, 4 and 0, respectively, and
no disturbance vector was considered; consequently,
the estimated incremental output vector ¢_:I_(k) was com puted by:
3 (2)
6320‘) 1:1 yak  1'}
a
‘s 3,0: —1)[ui(k—i— 1)]
'= u(k — i— 1) where d1 and y: are the cOmponents related to the top
camposition; and :12 and y; are the components related
to the bottom composition. ul and uz are the incremental
reﬂux and steam ﬂow rates respectively. The incremen tal control vector u(k — i — 1) is obtained by:
_:_4_(k—i'—l)=g,{k—i—I)gp(k—r—3) (22) where gp(k—i—— l) is the control vector applied at in
stant k—i—l. The matrices A,(k—1) (i=1, 3) and
B,{k— 1) (i=1, 4) were chosen being: amik —1l0]
A1(k—l)=[o 0.:A2(k—l)= ;A3(k  1) =
0 ﬂunk — 1)] [° ° ]
0 ﬂunk — 1 3.“. _ 1) = [bunk — homo: — I)
0 15:22“: r 1) [alllik — 1) o
; 32(k — l) = [bunk — n b212(k — 1) 330: — I) =
bunk — l) bzzzﬂt — 1)] D U
B k — I =
4( ) [bunk , no 4. Computation of the estimation error vector as indi
cated in equation 5. ' 5. Computation of the updated values at instant k of
the parameters of the matrices A,(k) (i=1, 3) and B,(k)
(i=1, 4), according to the equations 6, 7 and 9, taking
into account that no disturbances were c0nsidered and
that the value of the coefﬁcients [3 corresponding to the
nonzero parameters in the t0p and bottom rows were
set to 1 and 0.1, respectively, and the B's corresponding
to remaining zero parameters in both the rows were set
equal 0. 6. The components of the desired process output
vector dp(k + 2) at instant k + 2, dpi(k + 2) and dp2(k + 2).
related to top and bottom compositions, reSpectively,
are computed by the following scalar equations, that are
a particular case of the equation 10: 2 2 (23)
dpmk + 2) = 2: [mo + 2 — n + 2 humor +1_o
f=l 1':
2 3 (24)
“in!“ + 2) = _E]f2ty2(k + 1 — 0 + if hzil’lik + l — 1‘)
l= — where v1(k+ 1—i) and v2(k+l—i) are the components
related to the top and bottom compositions, respec
tively, of the driver block input vector y_(k+l—i) at 10 15 20 25 30 35 1‘” 45 50 55 65 instant k+ l —i. The parameters of equations 23 and 24
were chosen equal to those of a second order model,
without and with a sampling time delay respectively, a
natural frequency of 0.0056 rad/sec. a damping ratio
and static gain equal to 1. Given that the value of the
previously mentioned static gain is unity. the compo
nents v1(k+l—i) and v;(k+l—i) have the physical
meaning of being the setpoint values for top and bottom
compositions, respectively, at instant k+1—i. In equation 23 the value y1(k+l) was previously
computed by: ylik+ l)=ypl(k+ i)ypl("¢" I) (25) Note that yp1(k+1) is the value of the top composi
tion measured at instant k. From 919(k+2), the desired incremental process out
put vector d_1(k+2) is computed by: £l(k+2)=ép(k+2)—gp(kl (26)
The components of 511(k+2), de+2) and
dlzik +2), related to the top and bottom compositions,
were limited to the absolute values of 0.3 and 0.6%,
respectively.
7. Computation of the control vector by: 4
an = Bi‘(kmik + 2) —Bi"‘(k) 2 Break + 1 — n — j: (27) 3
314(k) z A.(k)y(k + 2 — n
i=1 — 59(10= E(k)+ﬂp(k — 2) (23)
8. The absolute and the incremental value of upﬂt)
was limit checked before being applied to the process.
FIG. 3 shows, from the beginning of the control
action, the resultsof a 6 hrs. 24 min. experiment in
which the distillation column was controlled by the
adaptivepredictive control system. In FIG. 3, the diagrams A, B, C and D represent, in
the Yaxis, the top composition (94;), the bottom compo
sition (9.2:), the reflux flow rate (g/s) and the steam flow
rate (g/s), respectively, and in the Xaxis the time in
sampling instants. The initial values of the parameters of the adaptive
predictive model were rationally chosen. and the con—
trol system performed in its identiﬁcation mode for two
sampling instants before starting the control action.
When the control action starts, the control system
drives the process top and bottom compositions from
96.5 and 1% to 96 and 3%, respectively. Later on, at the
instant 29, while the bottom composition is held at 3%,
the top composition is driven to 97%, and at the instant
55, the bottom composition is driven fmm 3 to 5% and
the top composition is held at 97%. Note that the multivariable control problem of a
binary distillation column, that the adaptivepredictive
control system has solved commendably, has been for a
long time an often cited example of difﬁculties in inter
acting multivariable chemical processes. In summary, the adaptivepredictive control system
described uses a digital computer to accomplish the
adaptive control of single—input singleoutput or mul
tivariabie timevariant processes with known or un
known parameters and with or without time delays, in 4,197,576 9 such a way that the dynamic output vector of the pro
cess is predicted and the control vector, to be applied to
the process, is computed with the objective that the
predicted dynamic output vector becomes equal to the
desired dynamic process output vector. What is claimed is: 1. A method for generating a control vector during
each of a plurality of sampling instants it, said control
vector to be applied to an apparatus which carries out a
process having at least one input variable and at least
one output variable, at least one of said input variables
deﬁning a process input vector, said apparatus varying
said process input vector in accordance with the value
of said control vector, said method comprising the steps
of: (A) storing a model which is capable of predicting the
dynamic value of a process output vector, which
vector is composed of at least one of said process
output variables, at a future sampling instant
k+r+l as a function of said control vector; (B) generating a desired dynamic process output vec
tor at each of said sampling instants k, said desired
dynamic process output vector being representa
tive of a desired value of said process output vector
at said future instant k+r+ 1; and (C) generating, at each of said sampling instants k,
that control vector which said model predicts will
cause said dynamic process output vector to be
equal to said desired dynamic process output vec
tor at said future sampling instant k+r+ l. 2. The method of claim 1, wherein said desired dy
namic process output vector is generated taking into
account the desired dynamics for said process and as a
function of both a desired steady state process output
vector and said dynamic process output vector. 3. The method of claim 2, wherein said step of gener—
ating said desired dynamic process output vector in—
cludes the step of generating an incremental desired
dynamic output vector representative of the incremen
tal difference between the desired dynamic process
output vector and said dynamic process output vector. 4. The method of claim 1 wherein said control vector
is an incremental control vector representative of the
incremental variation in the input vector of said process
which said model predicts will cause said dynamic pro
cess output vector to be equal to said desired dynamic
output vector at said future sampling instant k+r+ l. 5. The method of claim 3 wherein said control vector
is an incremental control vector representative of the
incremental variation in the input vector of said process
which said model predicts will cause said dynamic pro
cess output vector to be equal to said desired dynamic
output vector at said future sampling instant k+r+ 1. 6. The method of claim 1, further including the step
of periodically updating the parameters of said model in
such a manner that the difference between the actual
dynamic process output vector at sampling instant
k+r+! and the dynamic process output vector which
said model predicted would result at sampling instant
k+r+l is reduced towards zero. 7. The method of claim 6, wherein said step of updat—
ing the parameters of said model comprises the steps of: (A) periodically generating an estimated process out
put vector representative of the dynamic process
output vector which said model, as updated during
some first predetermined prior sampling instant,
estimates should have occurred at sampling instant 5 ll) 15 20 25 30 35 45 50 55 60 65 10 k as a result of the generation of said control vector
at said prior sampling instant k—r— I; (B) periodically generating an estimated error vector
representative of the difference between said esti
mated process output vector at said sampling in
stant k and said dynamic process output vector at
said sampling instant k; " (C) periodically modifying the parameters of said
model as a function of said estimated error vector. 8. The method of claim 7, further including the step
of generating an incremental process output vector
representative of the difference between the actual dy—
namic process output vector at instant k and the actual
dynamic process output vector at some second prior
sampling instant. 9. The method of claim 8, wherein said estimated
process output vector is the value estimated by the
model, as updated at said ﬁrst prior sampling instant, of
the incremental dynamic process output vector. 10. The method of claim 9, wherein said step of gen
erating an estimated error vector comprises the step of
determining the difference between said incremental
process output vector and said estimated process output
vector. 11. A control system for controlling a process having
at least one input variable and at least one output vari
able, said control system comprising: driver block means responsive to a set point vector
1(k) and an instantaneous process output vector
ypﬂt) for generating a desired incremental pr0cess
output vector d1(k+r+ 1) during each of a piural
ity of sampling intervals k, said desired incremental
output vector d1(k+r+ 1) corresponding to the
desired incremental change in output vector of said
process between the sampling interval 1: and the
sampling interval k+r+ 1; control block means responsive to said desired incre
mental output vector d1(k+r+ 1) for generating an
incremental control vector 30:) during each said
sampling interval 1: in accordance with an adap
tivepredictive model, said adaptivepredictive
model serving to predict the process output vector
and to determine the incremental control vector
g(k) which must be applied to the process during
sampling interval k to make the predicted process
Output vector equal to the desired process output
vector during sampling interval k+r+1 as deter
mined by said incremental desired output vector
d1(k+r+ 1); identiﬁcation block means responsive to said incre
mental control vector par) and an incremental pro
cess output vector y(k) for generating an estimated
incremental process output vector c_l(k) during each
said sampling interval k in accordance with said
adaptivepredictive model said estimated incre
mental process output vector d(k) being represen
tative of the incremental process output which the
adaptive—predictive mode], as updated during a
sampling interval prior to sampling interval k, pre—
dicts should occur during interval k as a result of
the generation of the incremental comrol vector
g(k—r— 1) during sampling interval k—r— 1; means for generating an estimated error vector gar)
during each of said samplingintervals k, said esti
mated error vector e(k) being representative of the
difference between said estimated incremental pro
cess output vector got) and said incremental output
vector y(lt); and 4,197,576 11 12
feedback means responsive to said estimated error such a manner that said estimated error vector e(k)
_ , _ IS reduced towards zero.
vector 90‘) for modifymg the parameters 0f 531d 12. The method of _claim 1 further including the step
adaptive predictive model during each said sam or applying said control VCCtOf 10 said apparatus in a 5 manner which will cause said apparatus to vary said process input vector in accordance therewith.
parameters of' said adaptivepredictive model in * * * * * pling interval k, said feedback means to modify the IO [5 20 25 30 35 45 55 65 ...
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 Spring '11
 Guelesr

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