U.S. patent application number 13/514313 was filed with the patent office on 2013-05-30 for method and device for regulating the production of steam in a steam plant.
The applicant listed for this patent is Christoph Backi, Jorg Gadinger, Bernhard Meerbeck, Michael Treuer, Tobias Weissbach, Klaus Wendelberger. Invention is credited to Christoph Backi, Jorg Gadinger, Bernhard Meerbeck, Michael Treuer, Tobias Weissbach, Klaus Wendelberger.
Application Number | 20130133751 13/514313 |
Document ID | / |
Family ID | 43984107 |
Filed Date | 2013-05-30 |
United States Patent
Application |
20130133751 |
Kind Code |
A1 |
Backi; Christoph ; et
al. |
May 30, 2013 |
Method and device for regulating the production of steam in a steam
plant
Abstract
A method for regulating the production of steam from feed water
in an evaporator of a steam plant is provided. A state regulator
calculates a plurality of states of a medium in the evaporator by
means of an observer and, on the basis thereof, determines a feed
water mass flow rate as a regulating variable. In order to obtain a
stable and precise regulation of the temperature of the steam, the
state regulator is a linear-quadratic regulator.
Inventors: |
Backi; Christoph; (Elztal,
DE) ; Gadinger; Jorg; (Nurnberg, DE) ;
Meerbeck; Bernhard; (Kelkheim, DE) ; Treuer;
Michael; (Lorch, DE) ; Weissbach; Tobias;
(Schorndorf, DE) ; Wendelberger; Klaus; (St.
Leon-Rot, DE) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Backi; Christoph
Gadinger; Jorg
Meerbeck; Bernhard
Treuer; Michael
Weissbach; Tobias
Wendelberger; Klaus |
Elztal
Nurnberg
Kelkheim
Lorch
Schorndorf
St. Leon-Rot |
|
DE
DE
DE
DE
DE
DE |
|
|
Family ID: |
43984107 |
Appl. No.: |
13/514313 |
Filed: |
September 28, 2010 |
PCT Filed: |
September 28, 2010 |
PCT NO: |
PCT/EP2010/064376 |
371 Date: |
November 12, 2012 |
Current U.S.
Class: |
137/11 ;
122/451.1 |
Current CPC
Class: |
F01K 13/02 20130101;
F22D 5/26 20130101; Y10T 137/0374 20150401; F01K 13/00 20130101;
F22B 35/00 20130101 |
Class at
Publication: |
137/11 ;
122/451.1 |
International
Class: |
F22D 5/26 20060101
F22D005/26 |
Foreign Application Data
Date |
Code |
Application Number |
Dec 18, 2009 |
DE |
102009047652.0 |
Claims
1-10. (canceled)
11. A method for regulating the production of steam from feed water
in an evaporator of a steam power plant, comprising: calculating a
plurality of medium states in an evaporator by a state controller
by means of an observer; and determining from the plurality of
medium states a feed-water mass flow as a manipulated variable,
wherein the state controller is a linear-quadratic controller.
12. The method as claimed in claim 11, wherein a setpoint value for
the feed-water mass flows is transmitted to an additional
controller for controlling the feed-water mass flow.
13. The method as claimed in claim 11, wherein an enthalpy of the
medium is used as a state variable for calculating a medium
state.
14. The method as claimed in claim 13, wherein deviations of the
absolute enthalpies from enthalpy setpoint values are used as state
variables.
15. The method as claimed in claim 11, wherein a non-linear control
system is used, and wherein the control system is linearized within
a predetermined deviation band around an operating point.
16. The method as claimed in claim 15, wherein the operating point
is actualized by using measured values.
17. The method as claimed in claim 15, wherein the control system
of the state controller includes a matrix equation, for the
calculation of which use is made of medium values which are
measured during the steam.
18. The method as claimed in claim 11, wherein the observer is a
Kalman filter which is designed upon a linear-quadratic state
feedback.
19. The method as claimed in claim 11, wherein the observer
calculates the heat which is yielded to the medium in the
evaporator.
20. A device for regulating the production of steam from feed water
in an evaporator of a steam power plant, comprising: a control
system which includes an observer and a state controller which is
preconfigured to calculate a plurality of medium states in an
evaporator by means of the observer and to determine therefrom a
feed-water mass flow as a manipulated variable of the control
system, wherein the state controller is a linear-quadratic
controller.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application is the US National Stage of International
Application No. PCT/EP2010/064376, filed Sep. 28, 2010 and claims
the benefit thereof. The International Application claims the
benefits of German application No. 10 2009 047 652.0 DE filed Dec.
8, 2009. All of the applications are incorporated by reference
herein in their entirety.
FIELD OF INVENTION
[0002] The invention refers to a method for regulating the
production of steam from feed water in an evaporator of a steam
power plant, in which in a first control system a state controller
calculates a plurality of medium states in the evaporator by means
of an observer and determines therefrom a feed-water mass flow as a
manipulated variable of the first control system.
BACKGROUND OF INVENTION
[0003] The efficiency of a steam power plant increases with the
temperature of the steam which is produced in the power plant
boiler and with the constancy of the quality of the steam which is
provided downstream of the evaporator unit. The production of steam
is carried out in a steam power plant as a rule from feed water
which is preheated in a high-pressure preheater, also referred to
as an economizer, and is then evaporated in an evaporator. During
this, the feed water is brought to a high pressure upstream of the
high-pressure preheater by means of a feed water pump and is pushed
through the high-pressure preheater and evaporator.
[0004] The controlling of the steam temperature downstream of the
evaporator is carried out by setting a mass flow of the feed water
as a manipulated variable which is introduced into the evaporator.
The dynamic response of the steam temperature with this manipulated
variable is very sluggish so that an adjustment of the feed-water
mass flow to the temperature which is to be controlled comes into
effect only after several minutes. In addition, the temperature to
be controlled is greatly influenced by numerous disturbances, such
as load changes, sootblowing in the boiler, changes of fuel, etc.
An accurate temperature control is very difficult to achieve for
these reasons.
SUMMARY OF INVENTION
[0005] It is an object of the invention to disclose a method with
which the steam temperature can be both accurately and stably
controlled.
[0006] This object is achieved by the state controller being a
linear-quadratic controller according to the invention. Such a
linear-quadratic controller (LQR) can include a linear-quadratic
optimum state feedback. In this case, its parameters can be
determined in such a way that an effectiveness criterion for the
controlling quality can be optimized. As a result of this, a both
accurate and stable control can be achieved.
[0007] In this case, the invention is based on the consideration
that during state controlling a plurality--which are partially not
measurable--of states for determining the manipulated variable, or
the controller actuating signal, are fed back. For the present
application case, this means that states, such as a temperature, a
pressure, an enthalpy or another state variable, at a plurality of
points along the evaporator can be used in the algorithm. Since
these states, however, are not measurable, there is a requirement
for a so-called observer circuit by means of which the required
states, which can be characterized by state variables, can be
estimated or calculated. The terms "estimate", "calculate" and
"determine" are used as synonyms in the following text. The
advantage of this concept is that disturbances which act upon the
evaporator can be reacted to very quickly and accurately.
[0008] The steam power plant is a plant operated by steam power. It
can be, or comprise, a steam turbine, a steam processing plant or
any other plant which is operated by the energy of steam. Any
system in which water is evaporated can be understood as an
evaporator in the following text, wherein a preheater, especially a
high-pressure preheater, can be included. The medium can be feed
water, steam or a mixture of feed water and steam. A medium
state--also referred to as state for simplicity in the following
text--can be an energy, a temperature, a pressure, an enthalpy or
another state of the medium.
[0009] A control loop, which controls the controlled variable on
the basis of an estimated state, for example in the form of a state
space representation, can be understood as a state controller in
the following text. In this case, a state, or a plurality of
states, within the controlled system can be estimated by means of
an observer and fed again, that is to say fed back, to the
controlled system, or to the controller. The feedback, which
together with the controlled system forms the control loop, can
take place by means of the observer, which therefore can replace a
measuring device. The observer calculates or estimates the states
of the system, in this case of the medium in the evaporator, and
can include a state differential equation, an output equation and
an observer vector. The output of the observer can be compared with
the output of the controlled system. The difference can have an
effect upon the state differential equation via the observer
vector. Furthermore, it is advantageous if the observer works
independently of the state controller.
[0010] The state controller expediently uses a state of the steam
leaving the evaporator as a controlled variable, such as the steam
temperature or the enthalpy of the steam. The feed-water mass flow
is advantageously used as a manipulated variable.
[0011] In an advantageous embodiment of the invention, a setpoint
value for the feed-water mass flow at a controller of a second
control system is transmitted for controlling the feed-water mass
flow. This can use the setpoint value as a controlled variable. As
a manipulated variable of the second control system, the rotational
speed of a feed-water pump, the position of a valve, e.g. in the
feed-water line, or another parameter which is suitable for
adjusting the feed-water mass flow can be directly or indirectly
used.
[0012] It is also advantageous if an enthalpy of the medium is used
as a state variable for calculating the medium states. A plurality
of states and, as a result of it, a plurality of enthalpies are
expediently used. The steam parameters, such as enthalpy and/or
pressure and temperature, depending upon the load case, are to be
kept at desired values and correspondingly controlled in the case
of load changes. The advantages of an enthalpy-state control, that
is to say a use of an enthalpy or a product from enthalpy and
another variable, such as a water mass flow, as a state, are that
state controls achieve a greater control effectiveness and
controlling becomes quicker. Also, advantages arise in respect to
process engineering: The process is expediently designed so that
slightly superheated steam, which lies close to the saturation
steam limit, issues at the evaporator exit. With changing pressure,
e.g. during variable-pressure operation, the evaporation end point
or the saturation steam point changes, which, in consideration of
temperature, can lead to wet steam being produced. When the
enthalpy is being used as a state variable, the pressure does not
have to be explicitly taken into consideration along with it since
the enthalpy combines both temperature and pressure in a
variable.
[0013] Deviations of the absolute enthalpies from enthalpy setpoint
values are advantageously used as state variables. As a result of
this, controlling can be carried out at equilibrium at zero and the
mathematical problem can be simplified.
[0014] The LQR process relates to linear controlling problems. By
converting temperature measured values and temperature setpoint
values to enthalpies the mathematical controller problems when
using enthalpy states can be linearized and as a result access can
be made to a simpler calculation because a linear relationship
exist between input and output enthalpies. The conversion is
expediently carried out by means of corresponding water/steam table
relationships, using, for example, the measured steam pressure.
[0015] When the evaporation system is being controlled by means of
state control, there is the problem, however, that the state at the
evaporator inlet can certainly be specified by means of an
enthalpy, but the enthalpy at the evaporator inlet cannot be
adjusted since pressure and temperature of the feed water can be
altered to only an insignificant degree and are unsuitable as a
manipulated variable. Therefore, the feed-water mass flow is
expediently used as a manipulated variable and during the
calculation of the states is multiplied by these.
[0016] The feed-water flow, however, acts upon the controlled
variable enthalpy at the evaporator inlet and outlet in a
non-linear manner so that the controller problem, despite using
enthalpies, is non-linear. For solving this problem, a
linearization is expediently used when calculating the states. In
the present case, it is advantageously assumed that the states move
only around a deviation band around an operating point. In these
deviation bands, which are expediently predetermined, the system
can be assumed as being linear.
[0017] This linearization is practical for a state only for the
operating point and the deviation band lying around this. If the
actual state migrates from the deviation band then the
linearization leads to unfavorable results. It is therefore
advantageous to actualize the operating point. This expediently
takes place by the operating point being actualized by the
inputting of measured values. The measured values are expediently
current measured values which were recorded by measuring a
currently existing medium parameter, such as pressure, temperature,
and the like. The operating point which is taken as a basis for the
state calculation can be adapted to a current medium state. Use can
be made of a non-linear control system which is linearized by
inputting current measured values. As a result of the
linearization, a very robust dynamic response is achieved, i.e. the
control quality no longer depends upon the current operating point
of the plant.
[0018] A further advantageous embodiment of the invention provides
that the control system of the state controller includes a matrix
equation, for example in the form of a feedback matrix, for the
calculation of which measured medium values are used during the
steam production. Therefore, the state feedback can be carried out
via a matrix equation, for example, the parameters of which are
determined at least partially by using current measured values. By
using current measured values, for example in an online calculation
of the feedback matrix, the controller can be continuously adapted
to the actual operating conditions. As a result of this, a
load-dependent change of the dynamic evaporator behavior can be
automatically taken into consideration. Also, as a result of this
step, an increase of the robustness of the control algorithm can be
achieved. Due to the fact that the control algorithm is very
robust, only very few parameters have to be set when putting into
service. The time and cost for putting into service is therefore
considerably reduced compared with all previously known
methods.
[0019] The matrix equation is advantageously calculated by means of
an instrumentation and control technique of the steam power plant.
The instrumentation and control technique can be an open-loop
control system in this case which controls the steam power plant
during its normal operation. In order to keep the mathematical
modules of the instrumentation and control technique simple, it is
advantageous if the matrix equation is converted into a set of
scalar differential equations. A relatively simple integration of
the matrix equation can be achieved by means of an integration
backward over time. Since in the actual case no information from
the future is available, an integration which is equivalent to a
backward integration can be achieved if the set of scalar
differential equations is integrated with inverse signs, which
stably leads to the same steady-state solution.
[0020] In an advantageous embodiment of the invention, the observer
is a Kalman filter, which is designed for the linear-quadratic
state feedback. The interaction of the linear-quadratic controller
with the Kalman filter is referred to as an LQG
(Linear-Quadratic-Gaussian) controller or LQG algorithm.
[0021] The observer advantageously calculates the heat which is
yielded to the medium in the evaporator. This can be defined as a
disturbance variable and used in the control algorithm. In this
case, not only the enthalpies, or a parameter along the evaporator
derived therefrom, but the disturbance variable can additionally be
defined as a state and estimated or determined especially by means
of the observer. Disturbances, which directly have an effect upon
the evaporator, are expressed by the temperature rise in the
evaporator changing. By means of such observing of the disturbance
variables, a very fast, accurate, but at the same time robust,
reaction to corresponding disturbances is possible.
[0022] The invention also refers to a device for regulating the
production of steam from feed water in an evaporator of a steam
power plant, having a control system which comprises an observer
and a state controller which is configured for calculating a
plurality of medium states in the evaporator by means of an
observer and for determining therefrom a feed-water mass flow as a
manipulated variable of the first control system.
[0023] It is proposed that the state controller is a
linear-quadratic controller. An accurate and stable control can be
achieved.
[0024] The device is advantageously designed for executing one, a
plurality, or all of the method steps proposed above.
BRIEF DESCRIPTION OF THE DRAWINGS
[0025] The invention is explained in more detail based on exemplary
embodiments which are depicted in the drawings.
[0026] In the drawing:
[0027] FIG. 1 shows a detail from a steam power plant with an
evaporator,
[0028] FIG. 2 shows a schematic arrangement of a control
cascade,
[0029] FIG. 3 shows a model of the evaporator,
[0030] FIG. 4 shows a linear system model as a basis for a
controller design,
[0031] FIG. 5 shows a structure of an observer and
[0032] FIG. 6 shows an overview of a controller construction.
DETAILED DESCRIPTION OF INVENTION
[0033] FIG. 1 shows a schematic view of a detail from a steam power
plant with a steam power plant which comprises a steam turbine 2, a
boiler 4, and evaporator 6 and a superheater 8. The boiler 4 gives
off heat to the evaporator 6, into which flows feed water 10 which
is pumped by a feed-water pump 12 to the evaporator 6 and which
absorbs the heat. By means of a valve 14, the feed-water flow can
be controlled.
[0034] As a result of the absorption of heat, the feed water 10 is
evaporated in the evaporator 6, and the resulting steam 16 flows on
to the superheater 8 in order to be superheated there to form live
steam and then to be fed to the steam turbine 2. For controlling
the temperature of the steam 16, the feed-water flow is controlled
by means of the valve 14 and/or the feed-water pump 12, wherein a
setpoint flow of the feed water 10 upstream of the evaporator 6 is
the controlled variable and a valve position and/or a pump output
is the manipulated variable.
[0035] A temperature sensor 18 and a pressure sensor 19 measure the
temperature T.sub.w and the pressure p.sub.w respectively of the
feed water 10 and a sensor 20 measures the actual feed-water flow
m.sub.i upstream of the evaporator 6.
[0036] A temperature sensor 22 and a pressure sensor 24 measure the
temperature T.sub.D and the pressure p.sub.D respectively of the
steam 16 downstream of the evaporator 6.
[0037] The evaporator 6 can include a preheater, which is not
shown. This, however, is insignificant for the invention and in the
following text a system consisting of an evaporator having a
preheater is also understood by the term "evaporator".
[0038] The evaporator 6 is a once-through steam generator, in which
the passage of water or steam flow is forced by the feed pump 12.
The feed water 10 in this case can flow consecutively through a
feed-water preheater and the evaporation system, especially also
the superheater 8, so that the heating of the feed water 10 up to
saturation steam temperature, the evaporating and the superheating
are carried out continuously in one pass. No drum is required in
this case. The evaporator 6 is especially part of a Benson boiler.
This can be operated in the supercritical range, wherein the feed
water 10 can be brought to a pressure of over 230 bar by the
feed-water pump 12. The feed-water mass flow can be controlled in
dependence upon load.
[0039] In FIG. 2, a control cascade with a first or external
control system 26 and a second or internal control system 28 is
schematically shown. The external control system 26 comprises a
linear-quadratic controller 30, especially an LQG controller. The
measured actual feed-water flow m.sub.i, the measured temperature
T.sub.w of the feed water 10, the measured temperature T.sub.D and
the measured pressure p.sub.D of the steam 16 and also the setpoint
temperature T.sub.S of the steam 16 downstream of the evaporator 6
are fed to this controlled as input variables. The setpoint
temperature T.sub.S of the steam 16 is the controlled variable of
the controller 30. The setpoint mass flow m.sub.S of the feed water
10 is issued by the controller 30 as a manipulated variable.
[0040] This setpoint mass flow m.sub.S is passed to a control loop
32 of the internal control system 28 as a setpoint value for the
controlled variable.
[0041] The measured feed-water flow m.sub.i is the controlled
variable of the control loop 32. The control loop 32 has a position
of the control valve 14 and/or an output of the feed-water pump 12
as a manipulated variable.
[0042] The controller 30 does not directly influence the process
via an actuating element, but transmits the setpoint value m.sub.S
for feed-water mass flow to the subordinated control loop 32, with
which it therefore forms a cascade consisting of an external
control system 26 and an internal control system 28. The measured
temperature T.sub.W and the pressure p.sub.W of the feed water 10
upstream of the evaporator 6 are required by the controller 30 as
additional information in order to determine the specific enthalpy
h.sub.i of the feed water 10 upstream of the evaporator 6. The
enthalpy h.sub.i can be determined via the water-steam table. From
the steam pressure p.sub.D and the steam temperature T.sub.D, the
specific enthalpy h.sub.2 of the steam 16 downstream of the
evaporator 6 is calculated.
[0043] FIG. 3 shows a model of the evaporation system in the
evaporator 6 which is split into three delay elements 34 of the
first order so that a delaying behavior of the third order is
created in its series connection. The three delay elements can be
PT.sub.1 elements in each case which are realized by means of a
negatively back-feeding integrator 36. The time constants of these
delay elements are dependent upon load and become larger with
falling load, and vice versa. Depending upon each delay element 34,
a state x.sub.i is specified, with i=1, 2, 3, wherein the state
x.sub.1 specifies the output enthalpy h.sub.2. An input state is
characterized by the input enthalpy h.sub.1 of the evaporation
system. The two mean states x.sub.2, x.sub.3 are calculated and not
measurable states, which are estimated by means of the observer.
All the states x.sub.i are time-dependent variables.
[0044] Feed water 10 with the enthalpy h.sub.1 flows into the
evaporation system. In principle, this enthalpy h.sub.1 could be
used as a manipulated variable of the first or external control
system 26 since with enthalpies instead of temperatures the
assumption of a linear behavior of the evaporation system is
justified. However, the enthalpy h.sub.1 can hardly be adjusted
since the pressure p.sub.W and the temperature T.sub.W of the feed
water are hardly adjustable in sufficient measure and fast enough
in order to be able to serve as a manipulated variable.
[0045] For solving this problem, the actual mass flow m.sub.i of
the feed water 10 is multiplied by the enthalpy h.sub.1 so that an
output is created from the product. This is simply adjustable by
means of the feed-water pump 12 and/or by the valve 14 and can
therefore be used as a manipulated variable. Since the enthalpy
h.sub.1 is basically constant, the actual mass flow m.sub.i of the
feed water 10 alone can be used as a manipulated variable.
[0046] Accordingly, in the dynamic model, which is shown in FIG. 3,
m.sub.i is multiplied by the present enthalpy in each case in each
delay element 34, as is shown by multipliers 38, so that an output
is formed as a variable. Added to these outputs, in each of the
three delay stages 34, is 1/3 of an assumed firing output Q.sub.F
in each case so that the overall firing output Q.sub.F is
introduced into the dynamic model of the overall evaporation
system.
[0047] This output sum is multiplied by a time function element G
which includes a delaying time constant in the denominator, e.g.
the delaying time constant t of a PT.sub.1 element at full load.
Also, G=(mt).sup.-1 includes a feed-water mass flow m in the
denominator, e.g. that at full load, so that according to the time
function element G a specific enthalpy per time is available. This
is integrated in each delay element 34 by means of the integrators
36 in each case so that an enthalpy is available as a result. This
is subtracted from the input enthalpy of the respective delay
element 34. It is produced as equations for the states x.sub.i
according to the three delay elements 34:
x . 1 = 1 mt ( Q F 3 + m 1 ( x 2 - x 1 ) ) ##EQU00001## x . 2 = 1
mt ( Q F 3 + m 2 ( x 3 - x 2 ) ) ##EQU00001.2## x . 3 = 1 mt ( Q F
3 + m 3 ( h 1 - x 3 ) ) . ##EQU00001.3##
[0048] The state x.sub.1 is the output enthalpy h.sub.2. It is to
be seen that a state x is constant, that is to say its derivative
is zero, if the enthalpy difference across a delay element 34
multiplied by the feed-water flow m.sub.i in addition to the third
of the firing output Q.sub.F is zero, i.e. is inversely
proportional to the enthalpy difference times feed-water mass flow
m.sub.i and Q.sub.F/3. In this case, the system is in a steady
state and therefore in equilibrium of feed water supply and
heating.
[0049] These three equations are not linear since the states
x.sub.i are multiplied by the feed-water flow m.sub.i. This is
correct since the changeable yield of firing heat is to be produced
non-linearly. This non-linearity of the firing heat is simulated in
the state model--more precisely in the observer which is described
in more detail in FIG. 5--by the multiplication of states x.sub.i
with the feed-water flow m.sub.i. As a result of this, the change
of the feed-water flow m.sub.i stands as a corresponding variable
for compensation of the changeable firing power (Q.sub.F).
Consequently, the feed-water flow m.sub.i is used as a manipulated
variable of the first control system 26.
[0050] In order to be able to use an LQ regulator or an LQG
controller, this non-linear equation system must be converted by
means of linearization into a linear system. To this end, the
states and the input are first expressed as a sum of steady-state
values and the deviations around these steady-state values. The
stable states result from the non-linear system equations by the
time derivates of the states being set to zero. This means that any
time change of the states in the system no longer takes place and
these are in a steady-state neutral position. The stable state is
additionally defined as a setpoint state.
[0051] Correspondingly applicable to the stable state is:
h 2 = h 1 + Q F m s , ##EQU00002##
[0052] wherein m.sub.s is the desired feed-water mass flow with
which the stable state is achieved, in which state the feed-water
flow is just large enough for it to absorb the heat feed Q.sub.F
with constant output enthalpy h.sub.2 downstream of the evaporator.
By conversion, the manipulated value m.sub.s of the first control
system is obtained:
m s = Q F h 2 - h 1 . ##EQU00003##
[0053] It is then further assumed for the linearization that the
states and the input move only around a deviation band around an
operating point. Therefore, the system can be assumed as being
linear at this operating point. As operating points, setpoint
states are selected, with u representing the input of the
system:
x.sub.i=x.sub.i,soll+.DELTA.x.sub.i
u=m.sub.s+.DELTA.u.
[0054] Under the assumption that the products of the deviations,
that is to say .DELTA.u.DELTA.x.sub.i, are very small and can be
disregarded, the following linearized state equation is
produced:
.DELTA. x . 1 = 1 m T ( Q F h 2 s - h 1 ( .DELTA. x 2 - x 1 ) - h 2
s - h 1 3 .DELTA. u ) ##EQU00004## .DELTA. x . 2 = 1 m T ( Q F h 2
s - h 1 ( .DELTA. x 3 - x 2 ) - h 2 s - h 1 3 .DELTA. u )
##EQU00004.2## .DELTA. x . 3 = 1 m T ( Q F h 2 s - h 1 ( .DELTA. x
3 ) - h 2 s - h 1 3 .DELTA. u ) ##EQU00004.3## y = x 1 s + .DELTA.
x ##EQU00004.4##
[0055] Therefore, an output offset x.sub.1s remains and is added
directly to the output.
[0056] Consideration is to be given to the fact that the
differential equations apply only to small deviations around the
operating point. The operating point is defined in this case by the
load-dependent setpoint enthalpy downstream of the evaporator
h.sub.2S=x.sub.1S. The operating points are therefore to be
adjusted based on current measurements. This is effected by
variables in matrices A and B, which result from the basic
equations of the linearized model:
{dot over (x)}(t)=A(t)x(t)+B(t)u(t)
y(t)=C(t)x(t)+D(t)u(t),
[0057] wherein the input u(t) in many cases does not have a direct
effect upon the output y(t) and therefore D(t) is zero. In this
way, the matrices A and B change with the load or with the current
setpoint value of the enthalpy h.sub.2S downstream of the
evaporator 6. This means that the dynamics are adapted to the
current load case and the process is therefore adjusted over the
entire load range.
[0058] FIG. 4 shows a basic schematic diagram of a state
controller. A state controller is a linear controller in which
actual states of a process 40 are compared with the corresponding
setpoint states and the resulting difference multiplied by a factor
is applied to the process. If applied specifically to the
evaporation system, the calculated actual states x(t) are compared
with predetermined setpoint states x.sub.soll(t). Indicated here,
and in the following text, by the bold lettering is a vector or a
matrix which in the present case includes the three states x.sub.1,
x.sub.2, x.sub.3 and Q.sub.F as a fourth variable or the
corresponding setpoint variables. As a factor, a feedback vector
K(t) with the variables K.sub.1, K.sub.2, K.sub.3 can be used. u(t)
is the manipulated variable and y(t) is the output variable of the
process.
[0059] In order to be able to implement this controlling principle
of the state feedback, the current values of the actual states x(t)
have to be known and made available. Now, however, in actual
processes it is not always possible for all the states to be
measured. In the present system, the states x.sub.2, x.sub.3 and
Q.sub.F, for example, cannot be measured. The reason for this lies
in the fact that the accurate point of the two states inside the
evaporator cannot be determined. The first two delay elements of
the model only reproduce the time dynamic of the process. This,
however, says nothing about the local dynamic, which is why a
measuring point for the temperature cannot be determined.
Furthermore, wet steam is present in the case if the states x.sub.2
and x.sub.3, which makes a determination of its enthalpy
additionally more difficult. Therefore, another way must be found
in order to determine the states.
[0060] This state determination, or state estimation, can be
achieved by means of a state feedback. Controlling per state
feedback is a purely proportional control. This means that the
states only multiplied by a factor are negatively fed back. This
type of feedback can lead to a control deviation, which means that
predetermined setpoint values are not achieved. In order to ensure
that these setpoint values are achieved, the implementation of an
integral-action component is advisable. In a simple embodiment of a
state feedback, the implementation of an integral-action component
is achieved via a circuit in which the control difference between
output value and command value is fed back via an integrator and
also applied to the manipulated variable.
[0061] In the present case, however, another way is selected,
specifically the implementation of an observer or
disturbance-variable observer which is a state estimator. This
includes an integral-action component in order to determine the
states, as a result of which the remaining control deviation
disappears. Furthermore, it has the advantage that a disturbance
variable influencing the process can be estimated by it. This
allows a faster controlling of the process since the dimension of
the disturbance variable becomes directly visible in an estimated
state. Without the disturbance-variable observer, the disturbance
variable and its influence upon the process can be seen only
indirectly via the changes of the individual states.
[0062] In the present system, there two disturbance variables, for
which an estimate by means of disturbance-variable observers is a
possibility. For one thing, this is the fluctuation of the firing
heat output Q.sub.F, which is fed to the evaporator 6, and for
another thing, this is the fluctuation of the enthalpy h.sub.1
upstream of the evaporator 6. The fluctuation of h.sub.1, however,
can be determined via the water-steam table from the measurement of
pressure and temperature and therefore does not necessarily have to
be estimated.
[0063] A non-measurable disturbance variable is the fluctuation in
the firing heat output Q.sub.F, which has a great influence upon
the present process. The fluctuation is induced as a result of
varying calorific values of the fired primary energy carrier (coal,
oil or gas). Therefore, it would make sense to define the firing
heat output Q.sub.F as a new estimated state Q=X.sub.4. The dynamic
is selected for dX.sub.4/dt=0. With this information, an extended
state-space form can be deduced for the observer.
[0064] Described in the following text is the observer, which is
also referred to a disturbance observer or disturbance-variable
observer since it observes the disturbance. FIG. 5 shows the
structure of the disturbance-variable observer. The model of the
evaporation system in the evaporator 6 corresponding to FIG. 3 is
to be seen, but with small changes. Thus, the states X.sub.1,
X.sub.2 and X.sub.3 stand for the estimated states, wherein the
state X.sub.1=H.sub.2 also specifies the estimated enthalpy H.sub.2
at the outlet of the evaporator 6 and not the actual and measurable
enthalpy h.sub.2. Despite the large letter, a specific enthalpy is
indicated by H.sub.2. This estimated enthalpy H.sub.2 is compared
with the enthalpy h.sub.2, which is measured via pressure and
temperature, and the difference, that is to say the observer error
e, is applied to the observed, that is to say calculated, process,
but not directly but as a product with an observer correction L,
that is with the so-called observer vector. This is a
four-dimensional vector, that is to say includes four components,
L.sub.1, L.sub.2, L.sub.3 and L.sub.4, which are multiplied in each
case by the observer error--by a scalar.
[0065] The reconstruction of the system states is carried out by
the calculation of a dynamic system model parallel to the real
process. The deviation between measured variables from the process
and the corresponding values which are determined by the system
model is the observer error e. The individual states of the system
model are corrected in each case by the observer error which is
weighted by L.sub.i, as a result of which this is stabilized.
[0066] In each of the three delay elements 34, the corresponding
correction component is applied to the observer error with the aim
of achieving the balanced state, that is to say the state of
equilibrium. The estimated firing output Q--in contrast to the
actual firing output Q.sub.F--is used in this case as a fourth
component X.sub.4 of the state vector X, and the correction
component L.sub.4 with the observer error e is correspondingly
applied to the estimated firing output Q.
[0067] The observer correction L, also referred as feedback vector,
is to be calculated in this case so that the observer error is
corrected, that is to say disappears. The observer can be realized
as a non-linear observer since the input variable m.sub.i is
measurable. The non-linear system can therefore be transcribed
directly into a state space representation. This is generally known
under the term of extended Lunenburg observer or extended Kalman
filter (EKF). A non-linear model is computed parallel to the
process. The feedback vector L(t), which stabilizes the observer
error, is, however, produced from a linear model. The linearization
is carried out by using the measured feed-water mass flow m.sub.i
in each case.
[0068] Controlling, in the first control system 26, involves a
linear-quadratic controller, especially an LQG controller 30. An
LQG controller is a common implementation of a linear-quadratic
(LQ) regulator and a Kalman filter. An LQ regulator can be a
so-called optimum regulator upon which a quadratic effectiveness
criterion is based. With this effectiveness criterion and an
algorithm, a feedback vector K(t) of the state control is
calculated. A Kalman filter is a special observer or state
estimator, in which both measurement inaccuracies at the output
(measured noises) and modeling inaccuracies (process noises) can be
taken into consideration or modeled together. By means of an
algorithm, the additional feedback vector L(t) can be determined
for the observer.
[0069] Such an LQG controller is shown in FIG. 6. Transmitted to
the LQG-controller module, as inputs, are the measured enthalpy
h.sub.2 downstream of the evaporator 6, the current feed-water mass
flow m.sub.i, the enthalpy h.sub.1 upstream of the evaporator 6 and
the setpoint enthalpy h.sub.2s downstream of the evaporator 6,
which can be calculated from the setpoint temperature of the steam
16 and its pressure. Also, calculation matrices A, B, A.sub.Obs,
C.sub.Obs, R.sub.Regler, Q.sub.Regler, R.sub.Obs and Q.sub.Obs are
transmitted.
[0070] A, B, A.sub.Obs, C.sub.Obs result from the linearized system
representation, R.sub.Regler, Q.sub.Regler, R.sub.Obs and Q.sub.Obs
include weighting factors for adjusting the desired dynamic
response (sensitivity, aggressiveness).
[0071] The output is the delivered feed-water mass flow m.sub.s,
which is calculated from the difference of the disturbance-variable
injection m.sub.Gs and the state deviation .DELTA.m. In this case,
consideration is to be given to the fact that the
disturbance-variable injection m.sub.Gs is calculated with the
estimated firing heat output Q. This disturbance-variable injection
In.sub.Gs is precontrolled in other concepts via the coal mass
flow, but here it is calculated directly via the estimated firing
heat output Q. The state variable .DELTA.m, however, is the result
of the state control.
[0072] The LQG controller 30 comprises the observer 42, which is
shown in FIG. 5, to which are fed, as input variables, the measured
input enthalpy h.sub.1, the measured output enthalpy h.sub.2 and
the measured feed-water flow m.sub.i. The feedback vector L(t) is
additionally fed to the observer for compensating the observer
error e. The feedback vector L(t) is calculated by means of a
solver L KR of the Kalman-Riccati differential equation, to which
are transmitted the calculation matrices A.sub.Obs, C.sub.Obs,
R.sub.Obs, and Q.sub.Obs.
[0073] As an additional module, the LQG controller 30 comprises a
module 44 for calculating the setpoint states X.sub.s which are
required for the state feedback. The inputs into the module 44 are
the input enthalpy h.sub.1 and the setpoint output enthalpy
h.sub.2s. For the state feedback, however, the LQG controller 30
does not use the states X(t) directly, but uses the deviation of
the states from their operating point, that is to say from the
setpoint states X.sub.s(t). As state variables to be additionally
used, therefore, deviations of the absolute enthalpies from
enthalpy setpoint values are provided. The deviation of each state
x.sub.i from its operating point X.sub.is becomes zero at the
operating point. If the weighted sum X(t)-X.sub.s(t)=0, then no
controller intervention takes place. Therefore, the states X(t) are
compared directly with the setpoint states X.sub.s(t) and the
difference is used in addition.
[0074] The LQG controller 30 also comprises a solver L RR for the
controller Riccati differential equation which calculates the
feedback vector K(t). To this are transmitted the calculation
matrices A, B, R.sub.Regler and Q.sub.Regler. The use of the
feedback vector K(t) is similar to that of the feedback vector
L(t). Whereas the aim of L(t) is to compensate the observer error e
by multiplication and feedback, the feedback vector K(t) is
multiplied by a state error and serves for state control, that is
to say for a fluctuation correction for compensating the control
error of the LQG controller 30. From the difference of the state
vector X(t) with the components X.sub.1, X.sub.2 and X.sub.3 and
the also three-dimensional state vector for the setpoint states
X.sub.s(t), the dynamic control component of the LQG controller 30
is produced, with which the state control is executed:
K.sub.1(X.sub.1-X.sub.1s)+K.sub.2(X.sub.2-X.sub.2s)+K.sub.3(X.sub.3-X.su-
b.3s)=.DELTA.m.
[0075] The dynamic control component, or the state deviation
.DELTA.m, is a component of the feed-water mass flow which is
compared with the calculated disturbance-variable injection
m.sub.Gs, that is to say which supplements the disturbance-variable
injection. The disturbance-variable injection m.sub.Gs is a
calculated setpoint mass flow, also referred to as basic setpoint
value, which results from the quotient of the estimated firing
output Q and the enthalpy difference .DELTA.h, resulting therefrom,
across the evaporation system.
[0076] The dynamic control component .DELTA.m is negatively added
to this setpoint mass flow, or basic setpoint value m.sub.Gs, so
that the setpoint feed-water mass flow m.sub.s is created, being
the manipulated variable of the first control system 26. This
setpoint mass flow m.sub.s is transmitted as a manipulated variable
to the second control system 28, which adjusts this setpoint mass
flow m.sub.s by means of a suitable component, or a plurality of
suitable components, e.g. the feed-water pump 12 and/or the valve
14.
[0077] The calculation of the two feedback vectors, specifically
the observer correction L(t) and the vector K(t) for the control
correction, is known to the person skilled in the art who is
familiar with thermodynamic state calculations. For this purpose,
the filter problem is to be solved with the solver L KR of the
Kalman-Riccati differential equation and the Controller problem is
to be solved with the solver L RR for the controller Riccati
differential equation. The solving of the LQ controller problem is
carried out via the matrix-Riccati DGL:
S ( t ) t = A T ( t ) S ( t ) + S ( t ) A ( t ) - S ( t ) B ( t ) R
Re gler - 1 B T ( t ) S ( t ) + Q Re gler . ##EQU00005##
[0078] With the solution matrix S(t), the controller feedback
matrix K(t) can also be calculated:
K(t)=R.sub.Regler.sup.-1B.sup.T(t)S(t).
[0079] The same applies to the solving of the Kalman filter
problem, which is also solved via a matrix-Riccati DGL:
P ( t ) t = A ( t ) P ( t ) + P ( t ) A T ( t ) - P ( t ) C T ( t )
R Obs - 1 C ( t ) P ( t ) + Q Obs . ##EQU00006##
[0080] In this case, the observer feedback matrix L(t) can be
calculated by means of the solution matrix P(t):
L(t)=P(t)C.sup.T(t)R.sub.Obs.sup.-1.
[0081] P and S are the matrices according to which the
matrix-Riccati equations are solved and in this case represent only
intermediate variables in order to determine L and K.
* * * * *