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Claims  |
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We claim:
1. A model predictive control apparatus comprising:
prediction means in which a model approximating a dynamic characteristic of
a controlled system having a plurality of manipulated variables and
controlled variables is used to determine a predictive equation of future
values of the controlled variables; and
arithmetic means adapted to transform limit conditions of a control
condition to manipulated variables, and to calculate a manipulated
variable to minimize an cost function in a quadratic form relating to a
difference between a future reference value and a control variable, and a
manipulated variable, set on the basis of said predictive equation while
satisfying said limit conditions, thus to give the determined manipulated
variable to said controlled system.
2. A model predictive control apparatus as set forth in claim 1, which
further comprises:
an input device for respectively inputting limit conditions, parameters of
the cost function, and controlled variable reference values relating to
future values of controlled variables and manipulated variables of the
controlled system,
said arithmetic means comprising:
cost function transformation means for transforming an cost function in a
quadratic form having, as variables, a predictive controlled variable
based on said predictive equation, a deviation from a reference value of
said controlled variable future value, and a change in the manipulated
variable (manipulated variable future value) to be given to said
controlled system, thus to set an cost function with respect to a
quadratic programming;
limit condition transformation means for transforming a limit condition
inputted from said input device on the basis of said predictive equation
to set a limit condition with respect to a quadratic programming; and
optimal manipulated variable calculation means for sequentially
calculating, by using a quadratic programming, future values of
manipulated variables to minimize the cost function set by said cost
function transformation means and the limit condition set by said limit
condition transformation means.
3. A model predictive control apparatus as set forth in claim 2,
wherein said prediction means is adapted to determine a predictive equation
indicating a future value of a controlled variable y by a past controlled
variable y and a past manipulated variable change rate .DELTA.u,
wherein said limit condition transformation means is such that upper and
lower limit equations relating to a controlled variable y, its change rate
.DELTA.y, a manipulated variable u, and its change rate Au are used as
limit conditions to transform all these conditions to an inequality limit
condition relating to .DELTA.u,
wherein said cost function transformation means is adapted to transform the
cost function to a function of .DELTA.u, and
wherein said optimal manipulated variable calculation means is adapted to
calculate an optimal manipulated variable change rate .DELTA.u by using a
quadratic programming.
4. A model predictive control apparatus as set forth in claim 2, wherein
said arithmetic means further includes cost function adjustment means for
adjusting an inputted cost function to give it to said cost function
transformation means.
5. An input device for inputting control parameters of the model predictive
control apparatus as set forth in claim 1,
said input device comprising:
screen display means for visually displaying various control information on
the screen;
future reference characteristic input means for inputting a new future
reference value from the content displayed on said screen display means;
limit condition input means for inputting a new limit condition
corresponding to said reference characteristic from the content displayed
on said screen display means;
simulation arithmetic means in which said new future reference value and
said new limit condition are used to repeatedly perform said model
predictive control operation with respect to a dynamic characteristic
model of the controlled system to calculate a predictive controlled
variable response indicating a response characteristic of said predictive
controlled variable;
simulation display means for graphically displaying said new future
reference value, said new limit condition, and said predictive controlled
response on said screen display means; and
setting means responsive to a setting command generated after graphic
display to set said new future reference value and said new limit
condition at said model predictive control apparatus.
6. An input device for a model predictive control apparatus as set forth in
claim 5, wherein said future reference characteristic input means allows
said screen display means to display thereon a plurality of transfer
functions stored in advance to input, as a new future reference value, a
response curve that an operator has selected.
7. An input device for a model predictive control apparatus as set forth in
claim 5, wherein said future reference characteristic input means is
adapted to calculate a curve passing through a plurality of coordinates
designated by an operator on said screen to thereby input a new future
reference value.
8. An input device for a model predictive control apparatus as set forth in
claim 5, wherein said limit condition input means is adapted to allow said
screen display means to display thereon a limit condition set in advance
in correspondence with a plurality of transfer functions stored in advance
and a transfer function that an operator has selected to input it as a new
limit condition.
9. An input device for a model predictive control apparatus as set forth in
claim 7, wherein said limit condition input means is adapted to calculate
a reference curve passing through a plurality of coordinates designated by
an operator to thereby input it as a new control condition.
10. An input device for a model predictive control apparatus as set forth
in claim 8, wherein said limit condition input means is adapted to
implement a predetermined operation to said new future reference value to
thereby input it as a new control condition.
11. An input device for a model predictive control apparatus as set forth
in claim 1,
said input device comprising:
cost function memory means for storing an cost function serving as an
operation index of said process equipment with at least a difference
between said predictive controlled variable and said future reference
value and said manipulated variable being as a parameter;
screen display means for displaying said cost function on the screen;
cost function input means adapted to update said cost function by
parameters of said cost function inputted through a picture on the screen
to form a new cost function;
simulation arithmetic means for repeatedly performing said predictive
control operation to calculate a group of values of said new cost
function;
simulation display command means for allowing said screen display means to
graphically display thereon the values of said new cost function; and
setting means responsive to a setting command generated after graphic
display to set said new cost function at said model predictive control
apparatus.
12. An input device for a model predictive control apparatus as set forth
in claim 11, wherein a control cost function indicating control
performance with respect to said process equipment is used as said cost
function.
13. An input device for a model predictive control apparatus as set forth
in claim 11, wherein an economical cost function indicating an operation
cost of said process equipment is used as said cost function.
14. A model predictive control apparatus as set forth in claim 1, wherein
said apparatus further comprises:
an input device for inputting control specification parameters;
reading means for reading said control specification parameters input
through said input device;
calculating means for calculating optimal values of proposed parameters in
a quadratic cost function, including a control horizon, weighting factors,
and parameters of a pole assignment polynomial of a closed loop, on the
basis of a model of controlled system and control specification
parameters;
display means for visually displaying the parameters on a screen; and
transfer means for transferring the proposed parameters to said display
means and said arithmetic means.
15. The model predictive control apparatus as set forth in claim 14,
wherein said reading means receives a first robust performance parameter
relating to a threshold value through said input device; and wherein said
calculating means further comprises:
means for obtaining sensitivity factors of changes in future controlled
variables with respect to increments in the manipulated variables,
means for forming a sensitivity matrix by arranging the sensitivity
factors,
means for obtaining singular values of the sensitivity matrix, and
means for determining the control horizon by comparing the singular values
with said first robust performance parameter, a determined control horizon
being displayed by said display means and transferred to said arithmetic
means.
16. The model predictive control apparatus as set forth in claim 14,
wherein said reading means receives a second robust performance parameter
relating to a threshold value of stability margin through said input
device; and wherein said calculating means further comprises:
means for varying the weighting factors and the parameters of the pole
assignment polynomial of a closed loop step by step with constant
increments,
means for obtaining a value of a sensitivity function,
means for comparing an obtained sensitivity function value with said second
robust parameter to judge whether the maximum singular value of the
sensitivity function satisfies a predetermined requirement, and
means for repeating said varying of said weighting factors and parameters
until said requirement is satisfied, determined weighting factors or
parameters of the pole assignment polynomial of a closed loop being
displayed by said display means and transferred to said arithmetic means.
17. The model predictive control apparatus as set forth in claim 14,
wherein said reading means receives a third robust performance parameter
relating to robust stability margin through said input device; and wherein
said calculating means further comprises:
means for varying the weighting factors and the parameters of the pole
assignment polynomial of a closed loop step by step with constant
increments,
means for obtaining a value of a complementary sensitivity function,
means for comparing an obtained value of the complementary sensitivity
function with said third robust parameter to judge whether the maximum
singular value of the complementary sensitivity function satisfies a
predetermined requirement, and
means for repeating said varying of said weighting factors and parameters
until said requirement is satisfied, determined weighting factors or
parameters of the pole assignment polynomial of a closed loop being
displayed by said display means and transferred to said arithmetic means.
18. A model predictive control apparatus comprising:
prediction means in which a model approximating a dynamic characteristic of
a controlled system is used to determine a predictive equation of future
values of controlled variables;
arithmetic means for calculating or determining a manipulated variable to
minimize an cost function in a quadratic form relating to a difference
between a future reference value and a controlled variable, and a
manipulated variable set on the basis of said predictive equation while
satisfying a limit condition to give the manipulated variable thus
calculated to said controlled system;
response time constant setting means for setting a response time constant
indicating a rise time at which said controlled system should be operated;
weighting factor parameter calculation means for calculating a weighting
factor including said response time constant at its exponential part, the
value thereof increasing with lapse of time, and
cost function setting means for constructing a new cost function in which
the calculated weighting coefficient is built in to set it as said cost
function.
19. A model predictive control apparatus as set forth in claim 18, which
further comprises:
arithmetic means for calculating a stability margin parameter indicating a
stability with respect to a change in the controlled system of the model
predictive control system where said new cost function is set;
simulation means for recording the value of said stability margin parameter
corresponding to an instantaneous value of said response time constant
while changing the value of the response time constant set at said
response time constant setting means; and
display means for visually displaying the relationship between the value of
the recorded response time constant and the value of the stability margin
parameter.
20. A model predictive control apparatus as set forth in claim 18, which
further comprises:
arithmetic means for calculating a stability margin parameter indicating a
stability with respect to a change of the controlled system of the model
predictive control system where said new cost function is set;
stability margin parameter setting means for storing the designated
stability margin parameter; and
response time constant adjustment means for changing the value of the
response time constant held by said response time constant setting means
until the value of said calculated stability margin parameter becomes in
correspondence with the value of the stability margin parameter stored in
said stability margin parameter setting means.
21. A model predictive control apparatus as set forth in claim 18, wherein
said new cost function is an cost function expressed below, obtained by
multiplying the term relating to a controlled variable y(k+j), a reference
value y*(k+j), a manipulated variable increment .DELTA.u(k+j), and
polynomial D(Z.sup.-1) for determining a closed loop pole assignment by
weighting factor .rho.=exp(-.DELTA./Tr) where .DELTA. is a control period,
and Tr is a response time constant:
##EQU43## |
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Claims |
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Description |
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TECHNICAL FIELD
This invention relates to a model predictive control apparatus adapted for
predicting future movement or trend of a control response on the basis of
a dynamic characteristic model of a controlled system to calculate
manipulated variables while taking such a prediction in consideration, and
an input device for a model predictive control, which is adapted to carry
out setting of the operation condition, manipulated variables, or the like
at this model predictive control apparatus.
BACKGROUND ART
In recent years, in the process control system, there have been frequently
used model predictive control technologies to construct a linear discrete
time model on the basis of an impulse response or a step response of the
process in order to conduct optimal control/operation while satisfying a
large number of limits imposed on the process (plant) to calculate in
sequence, from a predictive equation or formula derived from this model,
such an optimal manipulated variables to minimize an cost function in
quadratic form relating to deviations from reference or objective values
of controlled variable's future values and manipulated variable's future
values.
These technologies aim at determining manipulated variables applied at the
present time point in order that a controlled variable future value to
follow a reference value trajectory as close as possible is provided under
a necessary minimum change in the manipulated variable.
Such model predictive control apparatus has merits as recited below.
1) Control response stable with respect to a process having a long dead
time can be realized,
2) Quick response property can be improved by a feed-forward control using
a future reference value,
3) Such model predictive control apparatus can be applied to a
multi-variable control system as well,
4) Without necessity of an accurate dynamic characteristic model of a
controlled system, it is possible to easily design a control system from a
step response, for example.
5) By including a physical law or a non-linear dynamics of a controlled
system (process) into the predictive model, fine control can be expected,
6) It is possible to directly insert limit condition relating to an
operation of a controlled system (e.g., upper and lower limiters, change
rate limiters, etc.) into control rule, and the like.
Until now, various predictive control systems have been proposed. These
systems are explained, e.g., in the following literatures.
(1) Nishitani: Application of Model Predictive Control, Measurement and
Control (Japanese) Vol. 28, No. 11, pp. 996-1004 (1989), and
(2) D. W. Clarke & C. Mohtadi: Properties of Generalized Predictive
Control, Automatica 25-6 pp. 859 (1989), etc. Particularly, in the
literature (2), a Generalized Predictive Control (GPC) including various
model predictive control systems has been proposed. In accordance with
this control system, when a future reference value y* is given, a control
response future value y(k+i)(i=1, . . . , Np) is predicted on the basis of
a model of a controlled system (process) to calculate or determine a
manipulated variable increment .DELTA.u(K) which minimizes a control cost
function indicating control performance:
##EQU1##
where parameter L is a prediction starting time, parameter Np is a
prediction horizon, parameter Nu is a control horizon, parameter .lambda.
is a weighting factor or coefficient, and D(Z.sup.-1) is a pole assignment
polynomial.
In this control technology, since a predictive equation for determining
future values of controlled variables or manipulated variables is
represented by a function relating to past controlled variables or
manipulated variables, prediction is carried out every time on the basis
of past controlled variables or manipulated variables so that a controlled
variable's future value becomes closer to a corresponding reference or
objective value to determine a manipulated value applied at that time
point. At this time, it is necessary to determine manipulated variables in
order to satisfy the limit conditions relating to controlled
variables/manipulated variables.
Meanwhile, as a general method of determining an optimal solution to
minimize an cost function in a quadratic form while satisfying the limit
conditions or constraints, there is a quadratic programming (QP) (With
respect to QP, see Konno and Yamashita "Non-linear Programming" (Nikka
Giren), Sekine "Mathematical Programming" (Iwanani Shoten), etc.). In
order to use this QP, the cost function and the constraints must relate to
only manipulated variables which are a parameter to be optimized.
However, as the constraints imposed on the process, there are not only
those relating the manipulated variable which is a parameter to be
optimized, but also those relating to controlled variable or those
relating to controlled variable change rate. Accordingly, with
conventional control systems, it was impossible to solve manipulated
variables which can satisfy the above-mentioned latter constrains by QP as
well.
As stated above, in the conventional model predictive control technology,
since while there exist not only constrains imposed on the process
relating to manipulated variable but also those relating to controlled
variable and controlled variable change rate, manipulated variables which
satisfy constrains relating to those controlled variables could not be
solved by QP, it was impossible to conduct a control in which constrains
relating to controlled variable with respect to the process are also taken
into consideration.
It is to be noted that several of model predictive control systems in which
constrains relating to controlled variable/manipulated variable/future
value thereof of the process are taken into consideration have been
already proposed by the inventors of this application. For example, there
are
(3) Ohya and Iino "Model predictive control system in which constrains
relating to controlled variable and manipulated variable are taken into
consideration" (Preliminary Report of Science Lecture Meeting No. 29 of
Measurement Automatic Control Society JS-2-4, p. 19, July (1990)),
(4) Ohya and Iino "Model Predictive Control System" (Japanese Patent
Application No. 111800/1990), and
(5) Iino and Ohya "Model Predictive Control Apparatus" (Japanese Patent
Application No. 138541/1990), etc.
In accordance with these control systems, upper and lower limit conditions
expressed below with respect to values from a present or current time k up
to a certain time point in future are given to a controlled variable y(k),
a controlled variable change rate .DELTA.y(k)=y(k)-y(k-1), a manipulated
variable u(k), a manipulated variable change rate .DELTA.u(k)=u(k)-u(k-1):
y.sub.min (k+i).ltoreq.y(k+i).ltoreq.y.sub.max (k+i) (2)
.DELTA.y.sub.min (k+i).ltoreq..DELTA.y(k+i).ltoreq..DELTA.y.sub.max
(k+i)(3)
where i=1, 2, 3, . . . Np (Np is a prediction horizon and indicates a time
range in which a controlled variable predictive value is taken into
consideration).
u.sub.min (k+i).ltoreq.u(k+i).ltoreq.u.sub.max (k+i) (4)
.DELTA.u.sub.min (k+i).ltoreq..DELTA.u(k+i).ltoreq..DELTA.u.sub.max
(k+i)(5)
where i=0, 1, 2, 3, . . . Nu (Nu is a control horizon and indicates a time
range of a future optimal manipulated variable calculated at a time by
control operation). Then, manipulated variables to minimize the
above-mentioned cost function J in a quadratic form are calculated while
satisfying the above-mentioned upper and lower limit conditions to give
the manipulated values thus calculated to a controlled system.
Meanwhile, in order to execute the above-described model predictive
control, it is necessary to select in advance equations of the predictive
model, and a large number of various control parameters included in the
control cost function (1) or the upper and lower limit equations (2) to
(5). Further, a process operator must suitably change the predictive model
equation and/or various control parameters with a view to rationally
adjusting diverse future reference value response characteristics or a
large number of limit conditions depending on the operating condition
varying every moment on the basis of the operation experience of the
operator.
Accordingly, in the model predictive control, it is necessary to monitor
and adjust parameters more than those in the conventional PID control. In
addition, it is necessary to manipulate a plant operation so that various
operation indices such as economical cost function, etc. indicating the
operation cost, or the production amount of the process, etc. are
satisfied while making a comparison between a present process state and a
future process state.
However, a console which has been used for a conventional PID control has
only a function to indicate or display a present operating state, or
present and past operating states. Accordingly, simply using such a
console for a model predictive control makes it difficult to conduct an
accurate display of information and quick inputting operation.
The conventional model predictive control system is of a structure such
that a model predictive control operation unit and control parameters
calculation means are provided with respect to one input/output process.
Namely, a process of one input/output system having a single manipulated
variable and a single controlled variable is an object to be controlled.
However, many processes such as chemical, iron and steel, cement, paper
making, foods or the like constitute a multivariable system
(multi-input/output system) where a plurality of control variables such as
temperature, pressure, flow rate, liquid level, and the like interfere
with each other. Accordingly, an effective control system is expected for
these controlled systems. In the case where the model predictive control
is applied to these controlled systems, the following problems arise.
First, in these multi-input/output systems, there are instances where the
number of manipulated variables and the number of controlled variables are
different. In a multi-variable control system design method using an
easily available transfer function conventionally proposed, it is the
premise that the number of manipulated variables and the number of
controlled variables are equal to each other. For example, an example
thereof is described in "Design Theory of Linear Control System"
(Japanese) Publication of Society of Instrumentation, Control Engineers,
Chapter 6 (pp. 186-221). Accordingly, this design method cannot be used
for design of the model predictive control system as it is.
Hence, a model predictive control system which can be applied also in the
case where the number of manipulated variables and the number of
controlled variables are different is required.
Secondly, in the model predictive control system, since the characteristic
of the control system, particularly stability or robust property with
respect to characteristic change, i.e., stability margin in so called a
Nyquist stability criterion varies to much degree depending on how to
select cost function parameters L, Np, Nu, .lambda., D(Z.sup.-1) included
in the above-described cost function of the equation (1), it is necessary
to suitably make adjustment (tuning) of the above-mentioned parameters at
the time of starting of a control apparatus.
However, in the conventional model predictive control apparatus, the
relationship between the cost function parameters and the control
characteristic is not caused to become clear, so an operator empirically
determined these cost function parameters while repeating trial-and-error.
For this reason, labor is required for making an adjustment so that the
control system is sufficiently stabilized, and it takes much time for
starting of the control apparatus.
Further, in the conventional model predictive control systems, since
control operation is carried out by placing emphasis on minimization of
the cost function of the equation (1), there may take place the case where
a closed loop pole determining a transient response characteristic of the
control system cannot be suitably assigned. As a result, there may take
place the problem that even if the control response is stable or quick,
there results an oscillatory response form.
An object of this invention is to provide a model predictive control
apparatus directed for a controlled system of multi-input/output including
the case where the number of manipulated variables and that of controlled
variables are different, and capable of calculating, by using QP, optimal
manipulated variables to minimize an cost function while satisfying not
only the limit condition relating to manipulated variables, but also the
limit condition relating to controlled variables and their change rates.
Another object of this invention is to provide an input device suitable for
a control apparatus of the model predictive control system.
A further object of this invention is to provide a model predictive control
apparatus such that cost function parameters are automatically set to
respective optimal values.
A still further object of this invention is to provide a model predictive
apparatus in which an oscillation of a controlled value y in a rise
response characteristic is suppressed.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a functional block diagram showing the configuration the entirety
of a model predictive control system according to an embodiment of this
invention,
FIG. 2 is a flowchart showing a flow of the control system by the model
predictive control apparatus shown in FIG. 1,
FIG. 3 is a functional block diagram of the input device 10,
FIG. 4 is a flowchart for discriminating an input content from on a picture
on screen,
FIG. 5 is a functional block diagram of a model predictive control
apparatus,
FIG. 6 is an explanatory view of an ordinary display picture on screen,
FIG. 7 is an explanatory view of a reference model input mode picture on
screen of pictures on screen for inputting a reference value response,
FIG. 8 is an explanatory view of a free-form curve input mode picture on
screen of pictures on screen for inputting a reference value response,
FIGS. 9, 10, 11, 12 and 13 are explanatory views of a limit condition
input-mode picture on screen,
FIG. 10 is an explanatory view of a limit value input mode picture on
screen by a reference model input,
FIG. 11 is an explanatory view of a limit value input mode picture on
screen, by a free-form curve input reference model input,
FIG. 12 is an explanatory view of a control deviation threshold value input
mode picture on screen,
FIG. 13 is an explanatory view of a control deviation threshold value input
mode having an attenuation characteristic,
FIG. 14 is an explanatory view of an example of a display picture on
screen,
FIG. 15 is an explanatory view of an example of a display picture on
screen,
FIG. 16 is an explanatory view of an input mode picture on screen of an
cost function,
FIG. 17 is an explanatory view of a display mode picture on screen of an
cost function,
FIG. 18 is an explanatory view showing a display example of an intersecting
portion of a controlled variable predictive value curve and a limit value
curve,
FIG. 19 is a block diagram showing the configuration of a multi-variable
model predictive control apparatus of this invention,
FIG. 20 is a generalized Nyquist diagram for discriminating stability of a
multi-variable control system,
FIGS. 21A and 21B are characteristic diagrams showing a sensitivity
characteristic and a complementary sensitivity characteristic for
discriminating stability and robust property of the control system,
respectively,
FIG. 22 is a flowchart indicating a processing procedure of cost function
parameter adjustment means,
FIG. 23 is a block diagram showing the configuration of a distilling column
temperature control system,
FIG. 24 is a diagram showing a temperature control response characteristic
of a distilling column by a conventional model predictive control,
FIG. 25 is a diagram showing a temperature control response characteristic
of a distilling column by a model predictive control according to this
invention,
FIG. 26 is a diagram showing the configuration of a conventional model
predictive control apparatus,
FIG. 27 is a graph showing a control response characteristic example by a
conventional model predictive control apparatus,
FIG. 28 is a graph showing a closed loop pole assignment of the control
system in the example of FIG. 26,
FIG. 29 is a block diagram showing an embodiment of a model predictive
control apparatus of this invention,
FIG. 30 is a diagram for explaining a closed loop pole assignment by
weighting of an cost function and an improvement in a control response,
FIG. 31 is a flowchart for explaining a processing procedure in stability
margin parameter calculation means,
FIG. 32 is a graph showing the relationship between a response time
constant Tr and a stability margin parameter .epsilon.,
FIG. 33 is a flowchart for explaining a processing procedure in response
time constant calculation means,
FIG. 34 is a graph showing a control response characteristic example by a
model predictive control apparatus of this invention, and
FIG. 35 is a graph showing a closed loop pole assignment of the control
system in the example of FIG. 34.
DISCLOSURE OF THE INVENTION
In accordance with this invention, there is provided a model predictive
control apparatus comprising: prediction means in which a model
approximating a dynamic characteristic of a controlled system having a
plurality of manipulated variables and controlled variables is used to
determine a predictive equation of future values of the controlled
variables; and arithmetic means adapted to transform limit conditions of a
control condition to manipulated variables, and to calculate a manipulated
variable to minimize an cost function in a quadratic form relating to a
difference between a future reference value and a manipulated value, set
on the basis of the predictive equation while satisfying the limit
conditions, thus to give the calculated manipulated variable to the
controlled system.
In the model predictive control apparatus of this invention, since an
approach is employed to transform the cost function and all the
constraints to constraints relating to a manipulated variable change rate
which is a parameter to be optimized to calculate, by using QP, a
manipulated variable change rate to minimize the transformed cost function
while satisfying all the transformed constrains, control can be carried
out by taking into consideration not only the constrains relating to
manipulated variables but also the constrains relating to controlled
variables. Thus, satisfactory control function can be provided also with
respect to a controlled system such as a plant, etc. in which constrains
are added with respect to not only manipulated variables but also
controlled variables.
Further, in accordance with this invention, there is provided an input
device for inputting control parameters of the model predictive control
apparatus, comprising: screen display means for visually displaying
various control information on a screen; future reference characteristic
input means for inputting a new future reference value from the content
displayed on the screen display means; limit condition input means for
inputting a new limit condition corresponding to the reference
characteristic from the content displayed on the screen display means;
simulation arithmetic means adapted for repeatedly applying model
predictive control operation to a dynamic characteristic model of a
controlled system by using the new future reference value and the new
limit condition to calculate a predictive controlled variable response
indicating a response characteristic of the predictive controlled
variable; simulation display means for allowing the screen display means
to graphically display thereon the new future reference value, the new
limit condition and the predictive controlled variable response; and
setting means responsive to a setting command generated subsequently to
the graphic display to set the new future reference value and the new
limit condition at the model predictive control apparatus.
In accordance with this input device, when a future reference that the
model predictive control apparatus should follow or a limit condition that
the model predictive control apparatus should follow is inputted,
simulation is carried out to display it on the screen. Thus, before a new
future reference, etc. is set at the model predictive control apparatus,
reasonableness of a newly selected reference, etc. or safety of the plant
operation is conjectured in advance.
Further, in accordance with this invention, there is provided an input
device for the model predictive control apparatus, comprising: cost
function memory means for storing an cost function serving as an operation
index of the controlled system such as a process equipment with at least a
deviation between the predictive controlled variable and the future
reference value and the manipulated variable being as a parameter; screen
display means for displaying the cost function on the screen; cost
function input means for updating the cost function by parameters of the
cost function inputted through the screen to form a new cost function;
simulation arithmetic means for repeatedly performing the predictive
control operation to calculate a group of values of the new cost function;
simulation display command means for allowing the screen display means to
graphically display values of the new cost function; and setting means
responsive to a setting command generated after the graphic display to set
the new cost function at the model predictive control apparatus.
In this input device, when an cost function or any parameter of the cost
function is altered, simulation of evaluation is carried out by a new cost
function to display it on the screen. Thus, it is possible to confirm
reasonableness as an operation index of a selected cost function before a
new cost function is set at the model predictive control apparatus.
Moreover, in accordance with this invention, there is provided a model
predictive control apparatus comprising: prediction means for predicting a
plurality of controlled variable future variables y.sub.i on the basis of
a dynamic characteristic model of a multi-input/output plant in which
there are a plurality of manipulated variables and controlled variables;
arithmetic means for calculating such a plurality of optimal manipulated
variables to minimize an cost function in a quadratic form expressed
below, having, as function parameters, a prediction starting time L, a
prediction horizon Np, a control horizon Nu, a weighting coefficient
.lambda., and a pole assignment polynomial D(z.sup.-1) of the closed loop
with respect to a deviation signal between the controlled variable future
value y.sub.i and a future reference value y.sub.i * to give it to a
controlled system;
##EQU2##
and parameter adjustment means for adjusting the cost function parameters.
In this invention, since the predictive equation for predicting a future
controlled variable used for derivation of a control operational equation
is in a form such that it can be applied even in the case where the number
of manipulated variables and that of controlled variables are different,
the control operational equation thus derived can be also applied to a
multi-input/output process in which the number of manipulated variables
and that of controlled variables are different.
Further, in accordance with this invention, there is provided a model
predictive control apparatus comprising: prediction means for determining
a predictive equation of future values of controlled variables by using a
model obtained by approximating a dynamic characteristic of a controlled
system; arithmetic means for calculating a manipulated variable to
minimize an cost function in a quadratic form relating to a difference
between a future reference value and a manipulated variable, set on the
basis of the predictive equation while satisfying limit conditions to give
the manipulated value thus calculated to the controlled system; response
time constant setting means for setting a response time constant
indicating a rise time at which the controlled system should be operative;
weighting factor parameter calculation means for calculating a weighting
factor including the response time constant in an index part, the value
thereof increasing with passage of time; and cost function setting means
for constructing a new cost function in which the calculated weighting
factor is built in to set it as the cost function.
In this invention, when a response time constant is inputted, a weighting
factor of an exponential function corresponding to this time constant is
determined, and the weighting factor thus determined is added to the cost
function. Accordingly, it is possible to designate a response time
constant of the model predictive control system. Thus, it is possible to
assign the pole of the control system in a complex plane discriminating
stability into a stable region, thus to effectively improve a transient
response characteristic particularly attenuation factor. Further, since it
is possible to evaluate stability margin of the control system, a suitable
response time constant in which stability is taken into consideration can
be set. In addition, when a stability margin is given as a control
specification, there can be provided a configuration to automatically
adjust a response time constant so that there results a control system to
satisfy it. Accordingly, suitable stability and the transient res | | |
