Model-free adaptive control for industrial processes
US006556980B1
(12) United States Patent
(10) Patent N0.: (45) Date of Patent:
Cheng (54) MODEL-FREE ADAPTIVE CONTROL FOR INDUSTRIAL PROCESSES
US 6,556,980 B1 Apr. 29, 2003
C. L. Phillips et al., Basic Feedback Control Systems, Alternate Second Edition, Prentice—Hall Inc., 1991, pp. 159—163.*
(75) Inventor: George Shu-Xing Cheng, Folsom, CA
(Us)
ings of the IEEE International Conference on Neural Net
(73) Assignee: General Cyberation Group, Inc.,
works, vol. 1, pp. 225—230, Dec. 1995.* D. Gorinevsky et al., “Learning Approximation of Feedfor
Rancho Cordova, CA (US) (*)
Notice:
Y. Ogawara, “Feedback—Error—Learning Neural Network for the Automatic Maneuvering System of a Ship,” Proceed
Subject to any disclaimer, the term of this patent is extended or adjusted under 35
ward Control Dependence on the Task Parameters with
Application to Direct—Drive Manipulator Tracking,” IEEE Transactions on Robotics and Automation, vol. 13, No. 4,
U.S.C. 154(b) by 0 days.
pp. 567—581, Aug. 1997.*
(21) Appl. No.: 09/143,165 (22) Filed: Aug. 28, 1998
J. C. Spall et al., “Model—Free Control of General Discre te—Time Systems,” Proceedings of the 32nd IEEE Confer ence on Decision and Control, vol. 3, pp. 2792—2797, Dec.
(51) (52)
Int. Cl.7 ................................................ .. G06N 3/02 US. Cl. ........................... .. 706/23; 706/14; 706/16;
(58)
Field of Search ............................ .. 706/14, 23, 16,
706/25 706/25
(56)
References Cited
1993.*
C. Ha, “Integrated Flight/Propulsion Control System Design via Neural Network,” Proceedings of the 1993 IEEE Inter national Symposium on Intelligent Control, pp. 116—121,
Aug. 1993.* FL. Lewis, “Neural Network Control of Robot Manipula tors,” IEEE Expert, vol. 11, No. 3, pp. 64—75, Jun. 1996.*
U.S. PATENT DOCUMENTS * cited by examiner 5,159,660 A
* 10/1992 Lu et a1. ..................... .. 706/23
5,335,643 A
*
5,367,612 A
* 11/1994 BoZich et a1. .
8/1994 Abate et al.
123/679 706/23
5,486,996 A *
1/1996 Samad et al.
364/152
5,498,943 A
3/1996 Kimoto et a1. .
318/601
*
5,513,098 A *
4/1996 Spall et a1.
5,517,418
*
5/1996
5,642,722 A
*
7/1997 Schumacher et a1.
5,740,324
*
4/1998
A
5,781,700 A 5,992,383 A
Green et a1.
364/158
A
Mathur et a1.
.........
.......
. . . ..
701/13
123/673 . . . ..
706/16
* 7/1998 Puskorius et a1. .......... .. 706/14 * 11/1999 Scholten et a1. .......... .. 123/399
OTHER PUBLICATIONS
Kosko, Bart, Neural Networks and FuZZy Systems, Prentice
Hall, Englewood Cliffs, NJ, 1992.* DJ. Myers et al., “Efficient Implementation of Piecewise Linear Activation Function for Digital VLSI Neural Net
Primary Examiner—Wilbert L. Starks, Jr.
(74) Attorney, Agent, or Firm—Stout, Uxa, Buyan & Mullins, LLP
(57)
ABSTRACT
An enhanced model-free adaptive controller is disclosed, which consists of a linear dynamic neural network that can
be easily con?gured and put in automatic mode to control simple to complex processes. Two multivariable model-free adaptive controller designs are disclosed. An enhanced anti delay model-free adaptive controller is introduced to control processes with large time delays. A feedforward/feedback model-free adaptive control system with two designs is introduced to compensate for measurable disturbances.
works,” Electronic Letters, Nov. 23, 1989, vol. 25, No. 24, pp. 1662—1663.*
18 Claims, 8 Drawing Sheets
U.S. Patent
Apr. 29, 2003
Sheet 1 0f 8
US 6,556,980 B1
0
14 r(t)
12
H e(t)
+ __
MFA
d(t)
/ ‘
u(t)
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:
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U.S. Patent
Apr. 29, 2003
Sheet 2 0f 8
US 6,556,980 B1
40
u(t) 42
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U.S. Patent
Apr. 29, 2003
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US 6,556,980 B1
U.S. Patent
Apr. 29, 2003
Sheet 4 0f 8
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US 6,556,980 B1
U.S. Patent
Apr. 29, 2003
Sheet 5 0f 8
US 6,556,980 B1
Process
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U.S. Patent
Apr. 29, 2003
Sheet 6 6f 8
US 6,556,980 B1
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U.S. Patent
Apr. 29, 2003
Sheet 7 0f 8
US 6,556,980 B1
[102 dt
U1“) Fcedforward
()
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[104 Process
r(t)
C(t)
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Apr. 29, 2003
Sheet 8 0f 8
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Multiple
US 6,556,980 B1
/-l22
d(t)
Feedforward /l—— \_ Predictors
f MIMO Processes P2
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126
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120
US 6,556,980 B1 1
2 FIG. 4 is a block diagram illustrating a 2x2 multivariable
MODEL-FREE ADAPTIVE CONTROL FOR INDUSTRIAL PROCESSES FIELD OF THE INVENTION
The invention relates to industrial process control, and more particularly to an improved method and apparatus for
model-free adaptive control of industrial processes using enhanced model-free adaptive control architecture and algo rithms as Well as feedforWard compensation for distur bances.
10
FIG. 8 is a block diagram illustrating a SISO model-free
BACKGROUND OF THE INVENTION
A Model-Free Adaptive Control methodology has been described in patent application Ser. No. 08/944,450 ?led on
adaptive anti-delay control system according to this inven 15
Oct. 6, 1997. The methodology of that application, though effective and useful in practice, has some drawbacks as folloWs: 1. The model-free adaptive controller includes a nonlinear neural netWork Which may cause saturation When the controller output is close to its upper or loWer limits; 2. It is difficult for the user to specify a proper sample
interval because it is related to the controller behavior; 3. Changing the controller gain in the absence of error may still cause a sudden change in controller output;
4. The prior multivariable model-free adaptive controller is quite complex and requires the presence of all sub processes in the multi-input-multi-output process; 5. The static gain of the predictor in the prior anti-delay MFA controller is set at 1. It is better if the setting is related to
tion. FIG. 9 is a block diagram illustrating a feedforWard/
feedback model-free adaptive control system according to this invention. FIG. 10 is a block diagram illustrating a predictive 20
feedforWard/feedback model-free adaptive control system according to this invention. FIG. 11 is a block diagram illustrating an M><M multi
25
variable model-free adaptive control system With multiple feedforWard predictors. DESCRIPTION OF THE PREFERRED EMBODIMENTS
A. Single-variable Model-Free Adaptive Control 30
the controller gain. 6. The time constant of the predictor in the prior anti-delay MFA controller is related to the setting of the sample interval. It is better if the setting is related to the process time constant;
model-free control system according to this invention. FIG. 5 is a signal flow diagram illustrating a 3x3 multi variable model-free adaptive control system according to this invention. FIG. 6 is a block diagram illustrating a 2x2 predictive multivariable model-free control system according to this invention. FIG. 7 is a signal flow diagram illustrating a 3x3 predic tive multivariable model-free adaptive control system according to this invention.
FIG. 1 illustrates a single variable model-free adaptive control system, Which is the simplest form of this invention. The structure of the system is as simple as a traditional
single loop control system, including a single-input-single 35
output (SISO) controller 10, a process 12, and signal adders, 14, 16. The signals shoWn in FIG. 1 are as folloWs:
r(t)—Setpoint
SUMMARY OF INVENTION
y(t)—Measured Variable or the Process Variable, y(t)=X
The present invention overcomes the above-identi?ed
draWbacks of the prior art by providing model-free adaptive controllers using a linear dynamic neural netWork. The
40
inventive controller also uses a scaling function to include the controller gain and user estimated process time constant.
X(t)—Process Output u(t)—Controller Output d(t)—Disturbance, the disturbance caused by noise or
load changes. e(t)—Error betWeen the Setpoint and Measured Variable,
The controller gain can compensate for the process steady state gain, and the time constant provides information of the dynamic behavior of the process. The setting for the sample
The control objective is to make the measured variable
interval becomes selectable through a Wide range Without affecting the controller behavior. TWo more multivariable
y(t) track the given trajectory of its setpoint r(t) under
model-free adaptive controller designs (compensation
variations of setpoint, disturbance, and process dynamics. In
method and prediction method) are disclosed. An enhanced anti-delay model-free adaptive controller is introduced to control processes With large time delays. The method to select the parameters for the anti-delay MFA predictor is disclosed. AfeedforWard/feedback model-free adaptive con
other Words, the task of the MFA controller is to minimiZe the error e(t) in an online fashion.
trol system With tWo designs (compensation and prediction method) is used to compensate for measurable disturbances.
1
55
BRIEF DESCRIPTION OF THE DRAWINGS
2
- 5 Mr) - y(t)] -
factors in the MFA controller. 60
tion. FIG. 2 is a block diagram illustrating the architecture of
FIG. 2 illustrates the architecture of a SISO MFA con
troller. A linear multilayer neural netWork 18 is used in the design of the controller. The neural netWork has one input layer 20, one hidden layer 22 With N neurons, and one output
a single-variable model-free adaptive controller according to this invention. FIG. 3 is a block diagram illustrating a multivariable
_ l
( )
The minimiZation of ES(t) is done by adjusting the Weighting
FIG. 1 is a block diagram illustrating a single-variable
model-free adaptive control system according to this inven
1
E30) = for
layer 24 With one neuron. 65
The input signal e(t) to the input layer 20 is ?rstly
model-free adaptive control system according to this inven
converted to a normaliZed error signal E1 With a range of —1
tion.
to 1 by using the normaliZation unit 26, Where
denotes
US 6,556,980 B1 3
4
a normalization function. The output of the normalization
and then ?ltered by activation function 36 to produce the output o(.) of the neural netWork 18 With a range of 0 to 1. A de-normaliZation function 38 de?ned by
unit 26 is then scaled by a scaling function
25:
D(x)=100x,
(5)
maps the o(.) signal back into the real space to produce the The value of E1 at time t is computed With function
controller output u(t).
and
The algorithm governing the input-output of the controller consists of the folloWing difference equations: 10
(3) 1v
(6)
mm = Z Won-(n). Where KC>0 is de?ned as controller gain and TC is the user selected process time constant. These are important param eters for the MFA controller since KC is used to compensate
15
for the process steady-state gain and TC provides information
a
for the dynamic behavior of the process. When the error
signal is scaled With these parameters, the controller’s behavior can be manipulated by adjusting the parameters.
M2
20
The use of TC as part of the scaling function permits a
broad choice of sample intervals, TS, because the only restriction is that TS must conform to the formula TS0, called
40
ships. Each input signal is conveyed separately to each of the
performance or keep the system in a stable range.
An online learning algorithm is developed to continu ously update the values of the Weighting factors of the MFA controller as follows:
neurons in the hidden layer 22 via a path Weighted by an individual Weighting factor We, Where i=1, 2, . . . N, and j=1, 2, . . . N. The inputs to each of the neurons in the hidden layer 45
an”) Amy-(n) = a2” Mn) awn-(ohm).
are summed by adder 30 to produce signal pj. Then the signal p]- is ?ltered by an activation function 32 to produce q], where j denotes the jth neuron in the hidden layer.
Mill") — MMmdmqJ-(n),
_
ApieceWise continuous linear function f(X) mapping real numbers to [0,1] de?ned by
f(x)=1, if x>%
(11)
Where preferably 11>0 is the learning rate, and the partial derivative 6y(n)/6u(n) is the gradient of y(t) With respect to u(t), Which represents the sensitivity of the output y(t) to variations of the input u(t).
(4c) 55
By selecting 6W) 614(1)
Where preferably a>0, and b>0, is used as the activation function in the neural netWork. The constants of the activa tion function can be selected quite arbitrarily. The reason for
using a linear function f(X) to replace the conventional sigmoidal function is that the linear activation function Will
6w)
(10)
60
(12)
as described in patent application Ser. No. 08/944,450, the
resulting learning algorithm is as folloWs:
not cause saturation near the limits as the sigmoidal function
may do.
Each output signal from the hidden layer is conveyed to the single neuron in the output layer 24 via a path Weighted
65
by an individual Weighting factor h], where j=1, 2, . . . N.
The equations (1) through (14) Work for both process
These signals are summed in adder 34 to produce signal Z(.),
direct-acting or reverse acting types. Direct-acting means
US 6,556,980 B1 6
5
r1(t), r2(t)—Setpoint of controllers C11 and C22, respectively.
that an increase in the process input Will cause its output to increase, and vice versa. Reverse-acting means that an increase in the process input Will cause its output to
e1(t), e2(t)—Error between the setpoint and measured variable.
decrease, and vice versa. To keep the above equations Working for both direct and reverse acting cases, e(t) needs to be calculated differently based on the acting type of the
V110), v22(t)—Output of controller C11 and C22, respectively.
V210), v12(t)—Output of compensators C21 and C12, respectively.
process as follows:
u1(t), u2(t)—Inputs to the process, or the outputs of the 2x2 con troller set.
e(t)=r(t)—y(t), if direct acting
(15a)
e(t)=—[r(t)—y(t)], if reverse acting
(15b)
x110), X210), X120): x22(t)—OutlOut of Process G11> G21> G12 and 10
G22, respectively. d1(t), d2(t)—Disturbance to y, and y2, respectively.
This is a general treatment for the process acting types. It applies to all model-free adaptive controllers to be intro duced beloW.
y1(t), y2(t)—Measured Variables of the 2x2 process.
The relationship betWeen these signals are as folloWs:
B. Multivariable Model-Free Adaptive Control FIG. 3 illustrates a multivariable feedback control system With a model-free adaptive controller. The system includes a set of controllers 44, a multi-input multi-output (MIMO) process 46, and a set of signal adders 48 and 50, respectively, for each control loop. The inputs e(t) to the controller are
20
presented by comparing the setpoints r(t) With the measured variables y(t), Which are the process responses to controller
outputs u(t) and the disturbance signals d(t). Since it is a
25
multivariable system, all the signals here are vectors repre
The controllers CM and C22 have the same structure as the
SISO MFA controller shoWn in FIG. 2. The input and output
sented in bold case as folloWs.
relationship in these controllers is represented by the fol
loWing equations: 30
For Controller C11:
35
Where superscript T denotes the transpose of the vector, and subscript M denotes the total element number of the vector. There are three methods to construct a multivariable
model-free adaptive control system: decoupling, compensation, and prediction. The decoupling method is
40
described in patent application Ser. No. 08/944,450, and other tWo methods are introduced in the folloWing.
1. Compensation Method Without losing generality, We Will shoW hoW a multivari able model-free adaptive control system Works With a
45
2-input-2-output (2x2) system as illustrated in FIG. 4, Which is the 2x2 arrangement of FIG. 3. In the 2x2 MFA control system, the MFA controller set 52 consists of tWo controllers
C11, C22, and tWo compensators C21, and C12. The process 54 has four sub-processes G11, G21, G12, and G22. The process outputs as measured variables y1 and y2 are
used as the feedback signals of the main control loops. They are compared With the setpoints r1 and r2 at adders 56 to produce errors el and e2. The output of each controller associated With one of the inputs v11 or v22 is combined With
the output of the compensator associated With the other input by adders 58 to produce control signals 111 and u2. The output of each sub-process is cross added by adders 60 to produce measured variables y1 and y2. Notice that in real applications
55
60
the outputs from the sub-processes are not measurable and only their combined signals y1 and y2 can be measured.
estimated process time constants for G11 and G22, respec
tively. Ei11(n) is the delayed and scaled error signal of e1(n); and Ei22(n) is the delayed and scaled error signal of e2(n).
Thus, by the nature of the 2x2 process, the inputs 111 and u2 to the process are interconnected With its outputs y1 and y2.
The change in one input Will cause both outputs to change. In this 2x2 system, the element number M in Equation 16 equals to 2 and the signals shoWn in FIG. 4 are as folloWs:
In these equations, preferably 11>0 and 11>0 are the learning rate; KC11>0 and KC22>0 are the controller gain for CM and C22, respectively; and TC11>0 and TC22>0 are
65
The compensators C12 and C21 can be designed to include a ?rst-order dynamic block by the folloWing Laplace trans fer functions:
US 6,556,980 B1 8 For Compensator C21 V21(S) V11(S)
For Compensator C12 V12(S) V22(S)
15
In these equations, V11(S), V21(S), V12(S), and V22(S) are the Laplace transform of signals v11(t), v21(t), v12(t), and v22(t), respectively; S is the Laplace transform operator; KC21>0 and KC12>0 are the compensator gain; and TC21 and TC12 are the compensator time constants, for C21 and C12, respectively. In the applications Where only static compen sation is considered, TC21 and TC12 can be set to 0. If the sub-process G21=0, meaning that there is no interconnection from loop 1 to loop 2, the compensator C21 should be
Wherel=1, 2, . . . M; m=1, 2, . . . M; and l#m.
25
disabled by selecting KC21=0. Similarly, if G12=0, one should select K12=0 to disable C12. The compensator sign factors KS21 and K512 are a set of
In the equation, Vlm(S) and Vmm(S) are the Laplace transform of signals vlm(t) and vmm(t), respectively; S is the Laplace transform operator; Kclm>0 is the compensator gain; and TCI'" is the compensator time constant. KSI'" is the compensator sign factor, Which is selected based on the acting types of the sub-processes as folloWs:
constants relating to the acting types of the process as folloWs:
KSI’"=1, if G” and GI," have different acting types
(38a)
KSI’"=—1, if G” and GI," have the same acting type
(38b)
KS2,=1, if G22 and G21 have different acting types
(30a)
KS21=—1, if G22 and G21 have the same acting type
(30b)
Wherel=1, 2, . . . M; m=1, 2, . . . M; and l#m.
KS12=1, if G11 and G12 have different acting types
(30c) 35
2. Prediction Method As illustrated in FIG. 6, a 2x2 predictive MFA controller set 74 consists of tWo controllers C11, C22, and tWo predic
KS12=—1, if G11 and G12 have the same acting type
(30d)
tors C21, and C12. The process 76 has four sub-processes
G11> G21> G12 and 622
These sign factors are needed to assure that the MFA
The process outputs as measured variables y1 and y2 are
compensators produce signals in the correct direction so that the disturbances caused by the coupling factors of the
used as the feedback signals of the main control loops. They are compared With the setpoints r1 and r2 and predictor outputs y21 and y12, respectively, at adders 78 to produce
multivariable process can be reduced.
A3><M multivariable model-free adaptive control system is given in the folloWing. If M=3, it applies to the above-stated 3x3 MFA control system. For Controller C”:
input of the predictor that connects to the other main loop. The output of each sub-process is cross added by adders 80 to produce measured variables y1 and y2.
tively. e1(t), e2(t)—Error betWeen the setpoint and measured variable as modi?ed by the predictor outputs y21 and 55
y12, respectively. u1(t), u2(t)—Output of controller CM and C22, respec
tively. y21(t), y12(t)—Output of predictors C21, and C12, respec
tively. X11(t), X21(t), X12(t), X22(t)—Output of process G11, G21, G12 and G22, respectively. d1(t), d2(t)—Disturbance to y1 and y2, respectively. y1(t), y2(t)—Measured Variables of the 2x2 process. The relationship betWeen these signals are as folloWs: 65
US 6,556,980 B1 10 control system, the MFA controller set 82 consists of three
y2(l)=x21(l)+x22(t)
controllers C11, C22, C33, and siX predictors C21, C31, C12,
(39d)
C32, C13, C23. The process 84 has nine sub-processes G11 through G33. The process outputs as measured variables y1,
The controllers C11 and C22 have the same structure as the
y2, and y3 are used as the feedback signals of the main
SISO MFA controller shown in FIG. 2. The input and output relationship in these controllers is the same as presented in
control loops. They are compared With the setpoints r1, r2, r3 and related predictor outputs y21, y31, y12, y32, y13, and y23,
Equations (18) to (27), eXcept that the controller outputs are now 111 and u2 instead of VM and v22.
For Controller C11 10
N
(40)
mm) = K3161 (n) + 100 a2 hj-1(n)q}1(n)+ b ,
respectively, at adders 86 to produce errors e1, e2, and e3. The output of each controller is used as the input of the predictor that connects to the other main loops. Without losing generality, a set of equations that apply to an arbitrary M><M multivariable model-free adaptive control
system is given in the folloWing. If M=3, it applies to the
j:l
above-stated 3x3 MFA control system. 15
For Controller C22
For Controller C” N
N
(41)
(45)
mm) = 1
25
lm lm
_
1
]
_1<S K, [1 TCMSH, 30 Where l=1, 2, . . . M; m=1, 2, . . . M; and l#m.
In the equation, Ylm(S) and U,(S) are the Laplace trans
form of signals ylm(t) and ul(t), respectively; S is the Laplace
For Predictor C12 C
s =
12( )
_
transform operator; Kclm>0 is the predictor gain, TCI'" is the predictor time constant, and KSI'" is the predictor sign factor,
Y12(S) U16) l2 l2
(43) 35 Which is selected based on the acting types of the sub processes as folloWs: 1
J
_ KS Kc [1- W . 40
In these equations, U1(S), U2(S), Y21(S), and Y12(S) are the Laplace transform of signals u1(t), u2(t), y21(t), and y12(t), respectively; S is the Laplace transform operator; KC21>0 and KC12>0 are the predictor gain, and TC21 and TC12 are the predictor time constants, for C21 and C12, respec tively. The predictive signals Will alloW the MFA controllers
KS”"=1, if Gm, is direct acting
(47a)
KSI’"=—1, if Gm, is reverse acting
(47b)
Where l=1, 2, . . . M; m=1, 2, . . . M; and l#m.
C. Anti-Delay Model-Free Adaptive Control 45
Model-Free Adaptive Control for processes With large time delays Was described in patent application Ser. No. 08/944,450 ?led on Oct. 6, 1997. As illustrated in FIG. 8, a
to make corrective adjustments based on the changes in its input to compensate for the coupling factors from the other
SISO anti-delay model-free adaptive control system consists of an MFA anti-delay controller 88, a process With large time
loop. The predictive signals Will quickly decay to 0 based on the predictor time constant. This design Will not cause a bias
delays 90, and a special delay predictor 92. The above-stated
at the controller input and output. The predictor sign factors KS21 and K512 are a set of constants relating to the acting types of the process as folloWs:
in the anti-delay MFA control system. The input to controller 94 is calculated through adder 96
KS21=1, if G12 is direct acting
(44a)
MFA controller can be used as the basic MFA controller 94
as
55
(48) The delay predictor can be designed in a generic ?rst
KS21=—1, if G12 is reverse acting
(44b)
KS12=1, if G21 is direct acting
(44C)
KS12=—1, if G21 is reverse acting
(44d) 60
order-lag-plus-delay form represented by the folloWing Laplace transfer function: ms) = Y(S) + ms)
(49)
These sign factors are needed to assure that the MFA K(l - If“)
predictors produce signals in the correct direction so that the disturbances caused by the coupling factors of the multi variable process can be reduced.
A3>0 is the feedforWard predictor gain; Tcf>0 is the feedforWard predictor time constant; and K5 is the predictor sign factor, Which is selected based on the acting types of the sub-processes as folloWs:
15
KS=1, if G1,2 is direct acting
(58a)
KS=—1, if G1,2 is reverse acting
(58b)
Without losing generality, FIG. 11 illustrates an M><M multivariable model-free adaptive control system With mul tiple feedforWard predictors 122. Each main controller 116 can have none to several feedforWard predictors depending on its measurable disturbances. This design can be applied to other MFA control systems such as anti-delay, cascade,
25
etc.
or an equivalent thereof, Wherein a is an arbitrary constant
What is claimed is: 1. A controller for a process having a process output Which is controlled by a control signal applied to an input of said process, said controller including a neural netWork
and b=1/z. 7. The controller of claim 6, in Which said neural netWork
has an input layer including a plurality of input neurons arranged to receive normaliZed, scaled and delayed forms of said error signal, a hidden layer including a plurality of hidden neurons each arranged to sum the signals received by each of said input neurons Weighted by an individual ?rst Weighting factor, an output layer including a single neuron
comprising: a) an error input representative of the difference betWeen a predetermined setpoint and said process output; b) a normaliZation unit for normaliZing said error input to a predetermined range of values; c) a scaling function for scaling said normaliZed error input to produce a value E1 of the form
and arranged to produce a control signal for application to said process input, said control signal being such as to cause said process output to change and thereby reduce said error signal; c) said neural netWork having a pieceWise linear activa tion function. 5. The controller of claim 4, in Which said controller is a computer program embodied in a digital medium. 6. The controller of claim 4, in Which said pieceWise linear activation function f(X) is of the form
35
arranged to sum the output of said hidden neurons ?ltered
through said activation function and Weighted by individual second Weighting factors, and a control signal output Which is a function of the output of said output neuron, said ?rst
and second Weighting factors, respectively, being iteratively modi?ed in accordance With the formulae
or an equivalent thereof, in Which KC is the controller gain; TC is the user-selected time constant of said process; is the normaliZation function of said normaliZation unit; and e(t) is the value of said error input at any given time; d) a layer of input neurons having as their inputs succes
45
sively time-delayed values of E1;
or equivalents thereof, Wherein AWl-j-(Il) is the iterative change in the Weighting factor for the signal from a given
e) a layer of hidden neurons each having as its output the sum of individually Weighted ones of said successively
input neuron to a given hidden neuron, Ahj-(n) is the iterative
change in the Weighting factor for the output of said given
time-delayed values of E1;
hidden neuron, a is the arbitrary constant of the activation
f) an output neuron having as its output the sum of a ?rst
function f(x), 1] is the learning rate, 6y(t)/6u(t) is the gradient
function of the individually Weighted outputs of said hidden neurons; and
g) a control output Which is at least in part the denormal iZed value of a second function of the output of said
55
of the variation of said process output With respect to a variation in said control signal, e(n) is the raW error signal, El-(n) is the normaliZed and scaled error signal at the ith input
neuron, h]- is the Weighting factor for the output of said given hidden neuron, and qj-(n) is the output of said given hidden
output neuron.
2. The controller of claim 1, in Which said control output is the sum of said denormaliZed value and the value Kce(t),
neuron ?ltered by said activation function. 8. A multivariable model-free adaptive process control
or an equivalent thereof.
system, comprising:
3. The controller of claim 1, in Which said ?rst and second functions are both of the form
65
a) a plurality of processes, each process having a ?rst process output responsive to a control signal and a sub-process having an output Which is additively com bined With said ?rst process output of another of said plurality of processes to form a second process output of said other process;
US 6,556,980 B1 15
16
b) a plurality of predetermined setpoints; c) a plurality of controllers;
plurality of processes to form a second process output of said other process;
b) c) d) e)
d) a plurality of cornpensators; e) each of said controllers having an iteratively adjusted ?rst control output Which is a function of an error signal
representing the difference betWeen said second pro cess output of one of said plurality of processes and a
?rst control output Which is a function of an error signal
corresponding one of said setpoints;
f) each said cornpensator having said ?rst control output
10
of a corresponding controller as its input, the output of
said cornpensator being additively combined with said ?rst control output of another of said controllers to form a second control output Which is the input to one each of said processes and sub-processes; g) said controllers each including a neural netWork With
representing the difference betWeen said second pro cess output of one of said plurality of processes plus the outputs of said plurality of predictors, and a corre
sponding one of said setpoints; f) said controllers each including a neural netWork With an 15
input layer including a plurality of input neurons arranged to receive norrnaliZed, scaled and delayed forms of said error signal, a hidden layer including a plurality of hidden neurons each arranged to sum the
an input layer including a plurality of input neurons arranged to receive norrnaliZed, scaled and delayed
signals received by each of said input neurons Weighted by an individual ?rst Weighting factor, and an output neuron Which surns the individually Weighted outputs of hidden neurons, the Weighting factors for said hid den neuron outputs being iteratively adjusted, and an activation function f(X) of the form
forms of said error signal, a hidden layer including a plurality of hidden neurons each arranged to sum the
signals received by each of said input neurons Weighted by an individual ?rst Weighting factor, and an output neuron Which surns the individually Weighted outputs of hidden neurons, the Weighting factors for said hid den neuron outputs being iteratively adjusted, and an activation function f(X) of the form
a plurality of predetermined setpoints; a plurality of controllers; a plurality of predictors; each of said controllers having an iteratively adjusted
25
f(x)=0, if x%
or an equivalent thereof, Wherein a is an arbitrary constant
h) each said controller being arranged to produce a control signal u(n) Which is the sum of the output v(n) of said neural netWork and the outputs of all the cornpensators associated With the other said controllers, v(n) being of
signal u(n) of the form 35 u(n) : Kce(n) + 100
the form
v(n) : Kce(n) + 100
or an equivalent thereof, in Which KC is the controller gain;
e(n) is said error signal; hj-(n) is the Weighting factor for the jth hidden neuron output; and qj-(n) is the jth hidden neuron output; and h) each of said predictors having as its input the output of
a
or an equivalent thereof, in Which KC is the controller gain;
e(n) is said error signal; hj-(n) is the Weighting factor for the jth hidden neuron output; and qj-(n) is the jth hidden neuron output; and i) each of said cornpensators having an input-output relationship of the form CS _
a
45
a controller associated With another of said predictors,
and having an input-output relationship of the form
50
or an equivalent thereof, in Which K5 is a sign factor, KC is
the predictor gain, TC is the predictor time constant, and S is the Laplace transform operator.
KSKC
( )_ TCS+ 1’
11. The system of claim 10 in Which said plurality of processes includes ?rst and second processes, said ?rst and
or an equivalent thereof, in Which K5 is a sign factor, KC is
second processes having, respectively, ?rst and second sub
the cornpensator gain, TC is the cornpensator time constant, and S is the Laplace transform operator.
processes; the process outputs of said ?rst and second
9. The system of claim 8, in Which K5 is 1 if said other process and said sub-process have different acting types, and —1 if they have the same acting type.
processes being responsive, respectively, to ?rst and second
control signals generated, respectively, by ?rst and second aO
10. Arnultivariable rnodel-free adaptive predictive control
system, comprising: a) a plurality of processes, each process having a ?rst process output responsive to a control signal and a sub-process having an output Which is additively corn bined With said ?rst process output of another of said
ones of said plurality of controllers; said plurality of pre dictors includes ?rst and second predictors, the input of said ?rst predictor being said ?rst control signal; and the input of
said second predictor being said second control signal; KS of 5
said ?rst predictor is 1 if said second sub-process is direct acting and —1 if it is reverse acting; and KS of said second predictor is 1 if said ?rst sub-process is direct acting and —1 if it is reverse acting.
US 6,556,980 B1 17
18 feedforWard signal being added to said input of said model free adaptive controller. 16. The system of claim 15, in Which K5 is 1 if said sub-process is direct acting, and —1 if said sub-process is
12. A feedforWard-feedback process control system, com
prising: a) a process to be controlled; b) a sub-process representing a knoWn disturbance to the output of said process; c) a model-free adaptive controller having an error input and a control output arranged to control said process; and
d) a model-free adaptive feedforWard controller having said disturbance as its input and arranged to produce a feedforWard signal Which is a function of said distur
reverse acting.
17. A process control system for handling large time
delays, comprising: a) a process having a process input and a process output, said output responding to said process input With a 10
bance; e) said feedforWard signal being connected to modify said control output.
large time delay; b) a model-free adaptive controller having an error input
15
13. The system of claim 12, in Which said model-free adaptive feedforWard controller has an input-output relation ship of the form
Which is the difference betWeen a predetermined set point and a ?rst function of said process output; said controller further having a control output Which is applied to said process as said process input; and
c) a delay predictor Which has-as its inputs said control output and a second function of said process output,
said ?rst function of said process output being the
output of said delay predictor; d) said output of said delay predictor being subtractively
GfAS) =
applied to said setpoint to produce said error input. 18. The system of claim 17, in Which said output of said or an equivalent thereof, in Which Kcf is the feedforWard
gain; Tcf is the feedforWard time constant; Ksf is the feed forWard sign factor, S is the Laplace operator, and said
delay predictor is of the form 25
feedforWard signal is added to said control output. 14. The system of claim 13, in Which K“ is 1 if said process and said sub-process have different acting types, and —1 if they have the same acting type. 15. The system of claim 12, in Which said feedforWard controller is a predictor, and said feedforWard controller has an input-output relationship of the form
YAS) = Y(S) +
TS+1
U(S),
or an equivalent thereof, Wherein Y(S), U(S), and YC(S) are
the Laplace transform of signals y(t), u(t) and yC(t), respec tively; y(t) is the said second function of process output, u(t) is the said control output, and yC(t) is the said output of the
delay predictor; K, T, "n being the parameters for the predictor, the value of K being set as K=1/KC or an equiva 35
lent there of, Wherein KC is the controller gain of said controller, the value of T being set as the estimated process time constant of said process, and the value of '5 being set as
or an equivalent thereof, Wherein K5 is the predictor sign
factor, Kf is the predictor gain, Tcf is the predictor time constant, and S is the Laplace transform operator, said
the estimated process delay time of said process. *
*
*
*
*
(12) United States Patent
(10) Patent N0.: (45) Date of Patent:
Cheng (54) MODEL-FREE ADAPTIVE CONTROL FOR INDUSTRIAL PROCESSES
US 6,556,980 B1 Apr. 29, 2003
C. L. Phillips et al., Basic Feedback Control Systems, Alternate Second Edition, Prentice—Hall Inc., 1991, pp. 159—163.*
(75) Inventor: George Shu-Xing Cheng, Folsom, CA
(Us)
ings of the IEEE International Conference on Neural Net
(73) Assignee: General Cyberation Group, Inc.,
works, vol. 1, pp. 225—230, Dec. 1995.* D. Gorinevsky et al., “Learning Approximation of Feedfor
Rancho Cordova, CA (US) (*)
Notice:
Y. Ogawara, “Feedback—Error—Learning Neural Network for the Automatic Maneuvering System of a Ship,” Proceed
Subject to any disclaimer, the term of this patent is extended or adjusted under 35
ward Control Dependence on the Task Parameters with
Application to Direct—Drive Manipulator Tracking,” IEEE Transactions on Robotics and Automation, vol. 13, No. 4,
U.S.C. 154(b) by 0 days.
pp. 567—581, Aug. 1997.*
(21) Appl. No.: 09/143,165 (22) Filed: Aug. 28, 1998
J. C. Spall et al., “Model—Free Control of General Discre te—Time Systems,” Proceedings of the 32nd IEEE Confer ence on Decision and Control, vol. 3, pp. 2792—2797, Dec.
(51) (52)
Int. Cl.7 ................................................ .. G06N 3/02 US. Cl. ........................... .. 706/23; 706/14; 706/16;
(58)
Field of Search ............................ .. 706/14, 23, 16,
706/25 706/25
(56)
References Cited
1993.*
C. Ha, “Integrated Flight/Propulsion Control System Design via Neural Network,” Proceedings of the 1993 IEEE Inter national Symposium on Intelligent Control, pp. 116—121,
Aug. 1993.* FL. Lewis, “Neural Network Control of Robot Manipula tors,” IEEE Expert, vol. 11, No. 3, pp. 64—75, Jun. 1996.*
U.S. PATENT DOCUMENTS * cited by examiner 5,159,660 A
* 10/1992 Lu et a1. ..................... .. 706/23
5,335,643 A
*
5,367,612 A
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5,486,996 A *
1/1996 Samad et al.
364/152
5,498,943 A
3/1996 Kimoto et a1. .
318/601
*
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5,517,418
*
5/1996
5,642,722 A
*
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5,740,324
*
4/1998
A
5,781,700 A 5,992,383 A
Green et a1.
364/158
A
Mathur et a1.
.........
.......
. . . ..
701/13
123/673 . . . ..
706/16
* 7/1998 Puskorius et a1. .......... .. 706/14 * 11/1999 Scholten et a1. .......... .. 123/399
OTHER PUBLICATIONS
Kosko, Bart, Neural Networks and FuZZy Systems, Prentice
Hall, Englewood Cliffs, NJ, 1992.* DJ. Myers et al., “Efficient Implementation of Piecewise Linear Activation Function for Digital VLSI Neural Net
Primary Examiner—Wilbert L. Starks, Jr.
(74) Attorney, Agent, or Firm—Stout, Uxa, Buyan & Mullins, LLP
(57)
ABSTRACT
An enhanced model-free adaptive controller is disclosed, which consists of a linear dynamic neural network that can
be easily con?gured and put in automatic mode to control simple to complex processes. Two multivariable model-free adaptive controller designs are disclosed. An enhanced anti delay model-free adaptive controller is introduced to control processes with large time delays. A feedforward/feedback model-free adaptive control system with two designs is introduced to compensate for measurable disturbances.
works,” Electronic Letters, Nov. 23, 1989, vol. 25, No. 24, pp. 1662—1663.*
18 Claims, 8 Drawing Sheets
U.S. Patent
Apr. 29, 2003
Sheet 1 0f 8
US 6,556,980 B1
0
14 r(t)
12
H e(t)
+ __
MFA
d(t)
/ ‘
u(t)
Controller
$180
6 x0 t +
Process
y(t L
+
Fig. l
44
48 r(t)
f e0)
MFA
Controllers
d(t)
46
f n0)
MIMO
:
Processes
x0)
0 ya)
U.S. Patent
Apr. 29, 2003
Sheet 2 0f 8
US 6,556,980 B1
40
u(t) 42
Fig. 2.
U.S. Patent
Apr. 29, 2003
v l]
C11 i
1
Sheet 3 0f 8
+
‘"1
F
0
>
v21
C 12 l V12
58 v
j
Controller
Fig. 4
’
US 6,556,980 B1
U.S. Patent
Apr. 29, 2003
Sheet 4 0f 8
'
Fig. 5
US 6,556,980 B1
U.S. Patent
Apr. 29, 2003
Sheet 5 0f 8
US 6,556,980 B1
Process
(12
U.S. Patent
Apr. 29, 2003
Sheet 6 6f 8
US 6,556,980 B1
rl
y1 D
r2
I‘
y2>
3
) ”
a """"""" '
'od?t'féi'lé'r'"
Y3
"""""" 3551556655 """"" "35'
Fig. 7
, VVVVVVVVVVVVVVVVVVVVVVVVVVVV ,4 ,,,,, 1 1
MFA
[90 ; '
Controller
wlth large time delays
F2 Delay
Process
‘
MFA Anti-Delay Predictor Controller 4
Fig. 8
d(t) +
X t
()
y(t) ’
+
>
U.S. Patent
Apr. 29, 2003
Sheet 7 0f 8
US 6,556,980 B1
[102 dt
U1“) Fcedforward
()
Gfc
[104 Process
r(t)
C(t)
[98
r100
NIFA Controller
Process Gpl
Fig. 9
K112 yét)
dt
Feedforward
()
G
fc
K104 Process
Gp2
[110 _ 6(0
MFA Controller
O
11 t
1 14
[100 Process Gp 1
+
y1(t)
y2(t)
+ 1 08
Fig. 10
yo) >
U.S. Patent
Apr. 29, 2003
Sheet 8 0f 8
Y1“)
Multiple
US 6,556,980 B1
/-l22
d(t)
Feedforward /l—— \_ Predictors
f MIMO Processes P2
[116 r(t)
_ e(t)
[118 u(t)
MlMO MFA : +
Controllers
MIMO Processes
126
Fig. 11
120
US 6,556,980 B1 1
2 FIG. 4 is a block diagram illustrating a 2x2 multivariable
MODEL-FREE ADAPTIVE CONTROL FOR INDUSTRIAL PROCESSES FIELD OF THE INVENTION
The invention relates to industrial process control, and more particularly to an improved method and apparatus for
model-free adaptive control of industrial processes using enhanced model-free adaptive control architecture and algo rithms as Well as feedforWard compensation for distur bances.
10
FIG. 8 is a block diagram illustrating a SISO model-free
BACKGROUND OF THE INVENTION
A Model-Free Adaptive Control methodology has been described in patent application Ser. No. 08/944,450 ?led on
adaptive anti-delay control system according to this inven 15
Oct. 6, 1997. The methodology of that application, though effective and useful in practice, has some drawbacks as folloWs: 1. The model-free adaptive controller includes a nonlinear neural netWork Which may cause saturation When the controller output is close to its upper or loWer limits; 2. It is difficult for the user to specify a proper sample
interval because it is related to the controller behavior; 3. Changing the controller gain in the absence of error may still cause a sudden change in controller output;
4. The prior multivariable model-free adaptive controller is quite complex and requires the presence of all sub processes in the multi-input-multi-output process; 5. The static gain of the predictor in the prior anti-delay MFA controller is set at 1. It is better if the setting is related to
tion. FIG. 9 is a block diagram illustrating a feedforWard/
feedback model-free adaptive control system according to this invention. FIG. 10 is a block diagram illustrating a predictive 20
feedforWard/feedback model-free adaptive control system according to this invention. FIG. 11 is a block diagram illustrating an M><M multi
25
variable model-free adaptive control system With multiple feedforWard predictors. DESCRIPTION OF THE PREFERRED EMBODIMENTS
A. Single-variable Model-Free Adaptive Control 30
the controller gain. 6. The time constant of the predictor in the prior anti-delay MFA controller is related to the setting of the sample interval. It is better if the setting is related to the process time constant;
model-free control system according to this invention. FIG. 5 is a signal flow diagram illustrating a 3x3 multi variable model-free adaptive control system according to this invention. FIG. 6 is a block diagram illustrating a 2x2 predictive multivariable model-free control system according to this invention. FIG. 7 is a signal flow diagram illustrating a 3x3 predic tive multivariable model-free adaptive control system according to this invention.
FIG. 1 illustrates a single variable model-free adaptive control system, Which is the simplest form of this invention. The structure of the system is as simple as a traditional
single loop control system, including a single-input-single 35
output (SISO) controller 10, a process 12, and signal adders, 14, 16. The signals shoWn in FIG. 1 are as folloWs:
r(t)—Setpoint
SUMMARY OF INVENTION
y(t)—Measured Variable or the Process Variable, y(t)=X
The present invention overcomes the above-identi?ed
draWbacks of the prior art by providing model-free adaptive controllers using a linear dynamic neural netWork. The
40
inventive controller also uses a scaling function to include the controller gain and user estimated process time constant.
X(t)—Process Output u(t)—Controller Output d(t)—Disturbance, the disturbance caused by noise or
load changes. e(t)—Error betWeen the Setpoint and Measured Variable,
The controller gain can compensate for the process steady state gain, and the time constant provides information of the dynamic behavior of the process. The setting for the sample
The control objective is to make the measured variable
interval becomes selectable through a Wide range Without affecting the controller behavior. TWo more multivariable
y(t) track the given trajectory of its setpoint r(t) under
model-free adaptive controller designs (compensation
variations of setpoint, disturbance, and process dynamics. In
method and prediction method) are disclosed. An enhanced anti-delay model-free adaptive controller is introduced to control processes With large time delays. The method to select the parameters for the anti-delay MFA predictor is disclosed. AfeedforWard/feedback model-free adaptive con
other Words, the task of the MFA controller is to minimiZe the error e(t) in an online fashion.
trol system With tWo designs (compensation and prediction method) is used to compensate for measurable disturbances.
1
55
BRIEF DESCRIPTION OF THE DRAWINGS
2
- 5 Mr) - y(t)] -
factors in the MFA controller. 60
tion. FIG. 2 is a block diagram illustrating the architecture of
FIG. 2 illustrates the architecture of a SISO MFA con
troller. A linear multilayer neural netWork 18 is used in the design of the controller. The neural netWork has one input layer 20, one hidden layer 22 With N neurons, and one output
a single-variable model-free adaptive controller according to this invention. FIG. 3 is a block diagram illustrating a multivariable
_ l
( )
The minimiZation of ES(t) is done by adjusting the Weighting
FIG. 1 is a block diagram illustrating a single-variable
model-free adaptive control system according to this inven
1
E30) = for
layer 24 With one neuron. 65
The input signal e(t) to the input layer 20 is ?rstly
model-free adaptive control system according to this inven
converted to a normaliZed error signal E1 With a range of —1
tion.
to 1 by using the normaliZation unit 26, Where
denotes
US 6,556,980 B1 3
4
a normalization function. The output of the normalization
and then ?ltered by activation function 36 to produce the output o(.) of the neural netWork 18 With a range of 0 to 1. A de-normaliZation function 38 de?ned by
unit 26 is then scaled by a scaling function
25:
D(x)=100x,
(5)
maps the o(.) signal back into the real space to produce the The value of E1 at time t is computed With function
controller output u(t).
and
The algorithm governing the input-output of the controller consists of the folloWing difference equations: 10
(3) 1v
(6)
mm = Z Won-(n). Where KC>0 is de?ned as controller gain and TC is the user selected process time constant. These are important param eters for the MFA controller since KC is used to compensate
15
for the process steady-state gain and TC provides information
a
for the dynamic behavior of the process. When the error
signal is scaled With these parameters, the controller’s behavior can be manipulated by adjusting the parameters.
M2
20
The use of TC as part of the scaling function permits a
broad choice of sample intervals, TS, because the only restriction is that TS must conform to the formula TS0, called
40
ships. Each input signal is conveyed separately to each of the
performance or keep the system in a stable range.
An online learning algorithm is developed to continu ously update the values of the Weighting factors of the MFA controller as follows:
neurons in the hidden layer 22 via a path Weighted by an individual Weighting factor We, Where i=1, 2, . . . N, and j=1, 2, . . . N. The inputs to each of the neurons in the hidden layer 45
an”) Amy-(n) = a2” Mn) awn-(ohm).
are summed by adder 30 to produce signal pj. Then the signal p]- is ?ltered by an activation function 32 to produce q], where j denotes the jth neuron in the hidden layer.
Mill") — MMmdmqJ-(n),
_
ApieceWise continuous linear function f(X) mapping real numbers to [0,1] de?ned by
f(x)=1, if x>%
(11)
Where preferably 11>0 is the learning rate, and the partial derivative 6y(n)/6u(n) is the gradient of y(t) With respect to u(t), Which represents the sensitivity of the output y(t) to variations of the input u(t).
(4c) 55
By selecting 6W) 614(1)
Where preferably a>0, and b>0, is used as the activation function in the neural netWork. The constants of the activa tion function can be selected quite arbitrarily. The reason for
using a linear function f(X) to replace the conventional sigmoidal function is that the linear activation function Will
6w)
(10)
60
(12)
as described in patent application Ser. No. 08/944,450, the
resulting learning algorithm is as folloWs:
not cause saturation near the limits as the sigmoidal function
may do.
Each output signal from the hidden layer is conveyed to the single neuron in the output layer 24 via a path Weighted
65
by an individual Weighting factor h], where j=1, 2, . . . N.
The equations (1) through (14) Work for both process
These signals are summed in adder 34 to produce signal Z(.),
direct-acting or reverse acting types. Direct-acting means
US 6,556,980 B1 6
5
r1(t), r2(t)—Setpoint of controllers C11 and C22, respectively.
that an increase in the process input Will cause its output to increase, and vice versa. Reverse-acting means that an increase in the process input Will cause its output to
e1(t), e2(t)—Error between the setpoint and measured variable.
decrease, and vice versa. To keep the above equations Working for both direct and reverse acting cases, e(t) needs to be calculated differently based on the acting type of the
V110), v22(t)—Output of controller C11 and C22, respectively.
V210), v12(t)—Output of compensators C21 and C12, respectively.
process as follows:
u1(t), u2(t)—Inputs to the process, or the outputs of the 2x2 con troller set.
e(t)=r(t)—y(t), if direct acting
(15a)
e(t)=—[r(t)—y(t)], if reverse acting
(15b)
x110), X210), X120): x22(t)—OutlOut of Process G11> G21> G12 and 10
G22, respectively. d1(t), d2(t)—Disturbance to y, and y2, respectively.
This is a general treatment for the process acting types. It applies to all model-free adaptive controllers to be intro duced beloW.
y1(t), y2(t)—Measured Variables of the 2x2 process.
The relationship betWeen these signals are as folloWs:
B. Multivariable Model-Free Adaptive Control FIG. 3 illustrates a multivariable feedback control system With a model-free adaptive controller. The system includes a set of controllers 44, a multi-input multi-output (MIMO) process 46, and a set of signal adders 48 and 50, respectively, for each control loop. The inputs e(t) to the controller are
20
presented by comparing the setpoints r(t) With the measured variables y(t), Which are the process responses to controller
outputs u(t) and the disturbance signals d(t). Since it is a
25
multivariable system, all the signals here are vectors repre
The controllers CM and C22 have the same structure as the
SISO MFA controller shoWn in FIG. 2. The input and output
sented in bold case as folloWs.
relationship in these controllers is represented by the fol
loWing equations: 30
For Controller C11:
35
Where superscript T denotes the transpose of the vector, and subscript M denotes the total element number of the vector. There are three methods to construct a multivariable
model-free adaptive control system: decoupling, compensation, and prediction. The decoupling method is
40
described in patent application Ser. No. 08/944,450, and other tWo methods are introduced in the folloWing.
1. Compensation Method Without losing generality, We Will shoW hoW a multivari able model-free adaptive control system Works With a
45
2-input-2-output (2x2) system as illustrated in FIG. 4, Which is the 2x2 arrangement of FIG. 3. In the 2x2 MFA control system, the MFA controller set 52 consists of tWo controllers
C11, C22, and tWo compensators C21, and C12. The process 54 has four sub-processes G11, G21, G12, and G22. The process outputs as measured variables y1 and y2 are
used as the feedback signals of the main control loops. They are compared With the setpoints r1 and r2 at adders 56 to produce errors el and e2. The output of each controller associated With one of the inputs v11 or v22 is combined With
the output of the compensator associated With the other input by adders 58 to produce control signals 111 and u2. The output of each sub-process is cross added by adders 60 to produce measured variables y1 and y2. Notice that in real applications
55
60
the outputs from the sub-processes are not measurable and only their combined signals y1 and y2 can be measured.
estimated process time constants for G11 and G22, respec
tively. Ei11(n) is the delayed and scaled error signal of e1(n); and Ei22(n) is the delayed and scaled error signal of e2(n).
Thus, by the nature of the 2x2 process, the inputs 111 and u2 to the process are interconnected With its outputs y1 and y2.
The change in one input Will cause both outputs to change. In this 2x2 system, the element number M in Equation 16 equals to 2 and the signals shoWn in FIG. 4 are as folloWs:
In these equations, preferably 11>0 and 11>0 are the learning rate; KC11>0 and KC22>0 are the controller gain for CM and C22, respectively; and TC11>0 and TC22>0 are
65
The compensators C12 and C21 can be designed to include a ?rst-order dynamic block by the folloWing Laplace trans fer functions:
US 6,556,980 B1 8 For Compensator C21 V21(S) V11(S)
For Compensator C12 V12(S) V22(S)
15
In these equations, V11(S), V21(S), V12(S), and V22(S) are the Laplace transform of signals v11(t), v21(t), v12(t), and v22(t), respectively; S is the Laplace transform operator; KC21>0 and KC12>0 are the compensator gain; and TC21 and TC12 are the compensator time constants, for C21 and C12, respectively. In the applications Where only static compen sation is considered, TC21 and TC12 can be set to 0. If the sub-process G21=0, meaning that there is no interconnection from loop 1 to loop 2, the compensator C21 should be
Wherel=1, 2, . . . M; m=1, 2, . . . M; and l#m.
25
disabled by selecting KC21=0. Similarly, if G12=0, one should select K12=0 to disable C12. The compensator sign factors KS21 and K512 are a set of
In the equation, Vlm(S) and Vmm(S) are the Laplace transform of signals vlm(t) and vmm(t), respectively; S is the Laplace transform operator; Kclm>0 is the compensator gain; and TCI'" is the compensator time constant. KSI'" is the compensator sign factor, Which is selected based on the acting types of the sub-processes as folloWs:
constants relating to the acting types of the process as folloWs:
KSI’"=1, if G” and GI," have different acting types
(38a)
KSI’"=—1, if G” and GI," have the same acting type
(38b)
KS2,=1, if G22 and G21 have different acting types
(30a)
KS21=—1, if G22 and G21 have the same acting type
(30b)
Wherel=1, 2, . . . M; m=1, 2, . . . M; and l#m.
KS12=1, if G11 and G12 have different acting types
(30c) 35
2. Prediction Method As illustrated in FIG. 6, a 2x2 predictive MFA controller set 74 consists of tWo controllers C11, C22, and tWo predic
KS12=—1, if G11 and G12 have the same acting type
(30d)
tors C21, and C12. The process 76 has four sub-processes
G11> G21> G12 and 622
These sign factors are needed to assure that the MFA
The process outputs as measured variables y1 and y2 are
compensators produce signals in the correct direction so that the disturbances caused by the coupling factors of the
used as the feedback signals of the main control loops. They are compared With the setpoints r1 and r2 and predictor outputs y21 and y12, respectively, at adders 78 to produce
multivariable process can be reduced.
A3><M multivariable model-free adaptive control system is given in the folloWing. If M=3, it applies to the above-stated 3x3 MFA control system. For Controller C”:
input of the predictor that connects to the other main loop. The output of each sub-process is cross added by adders 80 to produce measured variables y1 and y2.
tively. e1(t), e2(t)—Error betWeen the setpoint and measured variable as modi?ed by the predictor outputs y21 and 55
y12, respectively. u1(t), u2(t)—Output of controller CM and C22, respec
tively. y21(t), y12(t)—Output of predictors C21, and C12, respec
tively. X11(t), X21(t), X12(t), X22(t)—Output of process G11, G21, G12 and G22, respectively. d1(t), d2(t)—Disturbance to y1 and y2, respectively. y1(t), y2(t)—Measured Variables of the 2x2 process. The relationship betWeen these signals are as folloWs: 65
US 6,556,980 B1 10 control system, the MFA controller set 82 consists of three
y2(l)=x21(l)+x22(t)
controllers C11, C22, C33, and siX predictors C21, C31, C12,
(39d)
C32, C13, C23. The process 84 has nine sub-processes G11 through G33. The process outputs as measured variables y1,
The controllers C11 and C22 have the same structure as the
y2, and y3 are used as the feedback signals of the main
SISO MFA controller shown in FIG. 2. The input and output relationship in these controllers is the same as presented in
control loops. They are compared With the setpoints r1, r2, r3 and related predictor outputs y21, y31, y12, y32, y13, and y23,
Equations (18) to (27), eXcept that the controller outputs are now 111 and u2 instead of VM and v22.
For Controller C11 10
N
(40)
mm) = K3161 (n) + 100 a2 hj-1(n)q}1(n)+ b ,
respectively, at adders 86 to produce errors e1, e2, and e3. The output of each controller is used as the input of the predictor that connects to the other main loops. Without losing generality, a set of equations that apply to an arbitrary M><M multivariable model-free adaptive control
system is given in the folloWing. If M=3, it applies to the
j:l
above-stated 3x3 MFA control system. 15
For Controller C22
For Controller C” N
N
(41)
(45)
mm) = 1
25
lm lm
_
1
]
_1<S K, [1 TCMSH, 30 Where l=1, 2, . . . M; m=1, 2, . . . M; and l#m.
In the equation, Ylm(S) and U,(S) are the Laplace trans
form of signals ylm(t) and ul(t), respectively; S is the Laplace
For Predictor C12 C
s =
12( )
_
transform operator; Kclm>0 is the predictor gain, TCI'" is the predictor time constant, and KSI'" is the predictor sign factor,
Y12(S) U16) l2 l2
(43) 35 Which is selected based on the acting types of the sub processes as folloWs: 1
J
_ KS Kc [1- W . 40
In these equations, U1(S), U2(S), Y21(S), and Y12(S) are the Laplace transform of signals u1(t), u2(t), y21(t), and y12(t), respectively; S is the Laplace transform operator; KC21>0 and KC12>0 are the predictor gain, and TC21 and TC12 are the predictor time constants, for C21 and C12, respec tively. The predictive signals Will alloW the MFA controllers
KS”"=1, if Gm, is direct acting
(47a)
KSI’"=—1, if Gm, is reverse acting
(47b)
Where l=1, 2, . . . M; m=1, 2, . . . M; and l#m.
C. Anti-Delay Model-Free Adaptive Control 45
Model-Free Adaptive Control for processes With large time delays Was described in patent application Ser. No. 08/944,450 ?led on Oct. 6, 1997. As illustrated in FIG. 8, a
to make corrective adjustments based on the changes in its input to compensate for the coupling factors from the other
SISO anti-delay model-free adaptive control system consists of an MFA anti-delay controller 88, a process With large time
loop. The predictive signals Will quickly decay to 0 based on the predictor time constant. This design Will not cause a bias
delays 90, and a special delay predictor 92. The above-stated
at the controller input and output. The predictor sign factors KS21 and K512 are a set of constants relating to the acting types of the process as folloWs:
in the anti-delay MFA control system. The input to controller 94 is calculated through adder 96
KS21=1, if G12 is direct acting
(44a)
MFA controller can be used as the basic MFA controller 94
as
55
(48) The delay predictor can be designed in a generic ?rst
KS21=—1, if G12 is reverse acting
(44b)
KS12=1, if G21 is direct acting
(44C)
KS12=—1, if G21 is reverse acting
(44d) 60
order-lag-plus-delay form represented by the folloWing Laplace transfer function: ms) = Y(S) + ms)
(49)
These sign factors are needed to assure that the MFA K(l - If“)
predictors produce signals in the correct direction so that the disturbances caused by the coupling factors of the multi variable process can be reduced.
A3>0 is the feedforWard predictor gain; Tcf>0 is the feedforWard predictor time constant; and K5 is the predictor sign factor, Which is selected based on the acting types of the sub-processes as folloWs:
15
KS=1, if G1,2 is direct acting
(58a)
KS=—1, if G1,2 is reverse acting
(58b)
Without losing generality, FIG. 11 illustrates an M><M multivariable model-free adaptive control system With mul tiple feedforWard predictors 122. Each main controller 116 can have none to several feedforWard predictors depending on its measurable disturbances. This design can be applied to other MFA control systems such as anti-delay, cascade,
25
etc.
or an equivalent thereof, Wherein a is an arbitrary constant
What is claimed is: 1. A controller for a process having a process output Which is controlled by a control signal applied to an input of said process, said controller including a neural netWork
and b=1/z. 7. The controller of claim 6, in Which said neural netWork
has an input layer including a plurality of input neurons arranged to receive normaliZed, scaled and delayed forms of said error signal, a hidden layer including a plurality of hidden neurons each arranged to sum the signals received by each of said input neurons Weighted by an individual ?rst Weighting factor, an output layer including a single neuron
comprising: a) an error input representative of the difference betWeen a predetermined setpoint and said process output; b) a normaliZation unit for normaliZing said error input to a predetermined range of values; c) a scaling function for scaling said normaliZed error input to produce a value E1 of the form
and arranged to produce a control signal for application to said process input, said control signal being such as to cause said process output to change and thereby reduce said error signal; c) said neural netWork having a pieceWise linear activa tion function. 5. The controller of claim 4, in Which said controller is a computer program embodied in a digital medium. 6. The controller of claim 4, in Which said pieceWise linear activation function f(X) is of the form
35
arranged to sum the output of said hidden neurons ?ltered
through said activation function and Weighted by individual second Weighting factors, and a control signal output Which is a function of the output of said output neuron, said ?rst
and second Weighting factors, respectively, being iteratively modi?ed in accordance With the formulae
or an equivalent thereof, in Which KC is the controller gain; TC is the user-selected time constant of said process; is the normaliZation function of said normaliZation unit; and e(t) is the value of said error input at any given time; d) a layer of input neurons having as their inputs succes
45
sively time-delayed values of E1;
or equivalents thereof, Wherein AWl-j-(Il) is the iterative change in the Weighting factor for the signal from a given
e) a layer of hidden neurons each having as its output the sum of individually Weighted ones of said successively
input neuron to a given hidden neuron, Ahj-(n) is the iterative
change in the Weighting factor for the output of said given
time-delayed values of E1;
hidden neuron, a is the arbitrary constant of the activation
f) an output neuron having as its output the sum of a ?rst
function f(x), 1] is the learning rate, 6y(t)/6u(t) is the gradient
function of the individually Weighted outputs of said hidden neurons; and
g) a control output Which is at least in part the denormal iZed value of a second function of the output of said
55
of the variation of said process output With respect to a variation in said control signal, e(n) is the raW error signal, El-(n) is the normaliZed and scaled error signal at the ith input
neuron, h]- is the Weighting factor for the output of said given hidden neuron, and qj-(n) is the output of said given hidden
output neuron.
2. The controller of claim 1, in Which said control output is the sum of said denormaliZed value and the value Kce(t),
neuron ?ltered by said activation function. 8. A multivariable model-free adaptive process control
or an equivalent thereof.
system, comprising:
3. The controller of claim 1, in Which said ?rst and second functions are both of the form
65
a) a plurality of processes, each process having a ?rst process output responsive to a control signal and a sub-process having an output Which is additively com bined With said ?rst process output of another of said plurality of processes to form a second process output of said other process;
US 6,556,980 B1 15
16
b) a plurality of predetermined setpoints; c) a plurality of controllers;
plurality of processes to form a second process output of said other process;
b) c) d) e)
d) a plurality of cornpensators; e) each of said controllers having an iteratively adjusted ?rst control output Which is a function of an error signal
representing the difference betWeen said second pro cess output of one of said plurality of processes and a
?rst control output Which is a function of an error signal
corresponding one of said setpoints;
f) each said cornpensator having said ?rst control output
10
of a corresponding controller as its input, the output of
said cornpensator being additively combined with said ?rst control output of another of said controllers to form a second control output Which is the input to one each of said processes and sub-processes; g) said controllers each including a neural netWork With
representing the difference betWeen said second pro cess output of one of said plurality of processes plus the outputs of said plurality of predictors, and a corre
sponding one of said setpoints; f) said controllers each including a neural netWork With an 15
input layer including a plurality of input neurons arranged to receive norrnaliZed, scaled and delayed forms of said error signal, a hidden layer including a plurality of hidden neurons each arranged to sum the
an input layer including a plurality of input neurons arranged to receive norrnaliZed, scaled and delayed
signals received by each of said input neurons Weighted by an individual ?rst Weighting factor, and an output neuron Which surns the individually Weighted outputs of hidden neurons, the Weighting factors for said hid den neuron outputs being iteratively adjusted, and an activation function f(X) of the form
forms of said error signal, a hidden layer including a plurality of hidden neurons each arranged to sum the
signals received by each of said input neurons Weighted by an individual ?rst Weighting factor, and an output neuron Which surns the individually Weighted outputs of hidden neurons, the Weighting factors for said hid den neuron outputs being iteratively adjusted, and an activation function f(X) of the form
a plurality of predetermined setpoints; a plurality of controllers; a plurality of predictors; each of said controllers having an iteratively adjusted
25
f(x)=0, if x%
or an equivalent thereof, Wherein a is an arbitrary constant
h) each said controller being arranged to produce a control signal u(n) Which is the sum of the output v(n) of said neural netWork and the outputs of all the cornpensators associated With the other said controllers, v(n) being of
signal u(n) of the form 35 u(n) : Kce(n) + 100
the form
v(n) : Kce(n) + 100
or an equivalent thereof, in Which KC is the controller gain;
e(n) is said error signal; hj-(n) is the Weighting factor for the jth hidden neuron output; and qj-(n) is the jth hidden neuron output; and h) each of said predictors having as its input the output of
a
or an equivalent thereof, in Which KC is the controller gain;
e(n) is said error signal; hj-(n) is the Weighting factor for the jth hidden neuron output; and qj-(n) is the jth hidden neuron output; and i) each of said cornpensators having an input-output relationship of the form CS _
a
45
a controller associated With another of said predictors,
and having an input-output relationship of the form
50
or an equivalent thereof, in Which K5 is a sign factor, KC is
the predictor gain, TC is the predictor time constant, and S is the Laplace transform operator.
KSKC
( )_ TCS+ 1’
11. The system of claim 10 in Which said plurality of processes includes ?rst and second processes, said ?rst and
or an equivalent thereof, in Which K5 is a sign factor, KC is
second processes having, respectively, ?rst and second sub
the cornpensator gain, TC is the cornpensator time constant, and S is the Laplace transform operator.
processes; the process outputs of said ?rst and second
9. The system of claim 8, in Which K5 is 1 if said other process and said sub-process have different acting types, and —1 if they have the same acting type.
processes being responsive, respectively, to ?rst and second
control signals generated, respectively, by ?rst and second aO
10. Arnultivariable rnodel-free adaptive predictive control
system, comprising: a) a plurality of processes, each process having a ?rst process output responsive to a control signal and a sub-process having an output Which is additively corn bined With said ?rst process output of another of said
ones of said plurality of controllers; said plurality of pre dictors includes ?rst and second predictors, the input of said ?rst predictor being said ?rst control signal; and the input of
said second predictor being said second control signal; KS of 5
said ?rst predictor is 1 if said second sub-process is direct acting and —1 if it is reverse acting; and KS of said second predictor is 1 if said ?rst sub-process is direct acting and —1 if it is reverse acting.
US 6,556,980 B1 17
18 feedforWard signal being added to said input of said model free adaptive controller. 16. The system of claim 15, in Which K5 is 1 if said sub-process is direct acting, and —1 if said sub-process is
12. A feedforWard-feedback process control system, com
prising: a) a process to be controlled; b) a sub-process representing a knoWn disturbance to the output of said process; c) a model-free adaptive controller having an error input and a control output arranged to control said process; and
d) a model-free adaptive feedforWard controller having said disturbance as its input and arranged to produce a feedforWard signal Which is a function of said distur
reverse acting.
17. A process control system for handling large time
delays, comprising: a) a process having a process input and a process output, said output responding to said process input With a 10
bance; e) said feedforWard signal being connected to modify said control output.
large time delay; b) a model-free adaptive controller having an error input
15
13. The system of claim 12, in Which said model-free adaptive feedforWard controller has an input-output relation ship of the form
Which is the difference betWeen a predetermined set point and a ?rst function of said process output; said controller further having a control output Which is applied to said process as said process input; and
c) a delay predictor Which has-as its inputs said control output and a second function of said process output,
said ?rst function of said process output being the
output of said delay predictor; d) said output of said delay predictor being subtractively
GfAS) =
applied to said setpoint to produce said error input. 18. The system of claim 17, in Which said output of said or an equivalent thereof, in Which Kcf is the feedforWard
gain; Tcf is the feedforWard time constant; Ksf is the feed forWard sign factor, S is the Laplace operator, and said
delay predictor is of the form 25
feedforWard signal is added to said control output. 14. The system of claim 13, in Which K“ is 1 if said process and said sub-process have different acting types, and —1 if they have the same acting type. 15. The system of claim 12, in Which said feedforWard controller is a predictor, and said feedforWard controller has an input-output relationship of the form
YAS) = Y(S) +
TS+1
U(S),
or an equivalent thereof, Wherein Y(S), U(S), and YC(S) are
the Laplace transform of signals y(t), u(t) and yC(t), respec tively; y(t) is the said second function of process output, u(t) is the said control output, and yC(t) is the said output of the
delay predictor; K, T, "n being the parameters for the predictor, the value of K being set as K=1/KC or an equiva 35
lent there of, Wherein KC is the controller gain of said controller, the value of T being set as the estimated process time constant of said process, and the value of '5 being set as
or an equivalent thereof, Wherein K5 is the predictor sign
factor, Kf is the predictor gain, Tcf is the predictor time constant, and S is the Laplace transform operator, said
the estimated process delay time of said process. *
*
*
*
*
