Note: Descriptions are shown in the official language in which they were submitted.
CA 02922313 2016-02-24
Method.for improving metering profiles of displacement pumps
The present invention concerns a method for improving metering
profiles of positive displacement pumps. Positive displacement pumps
generally have a moveable displacer element delimiting a metering
chamber which is connected by way of valves to a suction line and a
pressure line. The result of this is that delivery fluid can alternately be
sucked into the metering chamber by way of the suction line by an
oscillating movement of the displacer element and can be urged out of the
metering chamber by way of the pressure line. A drive for the oscillating
movement of the displacer element is associated with the displacer
element.
There are for example electromagnetically driven diaphragm pumps
in which the displacer element is a diaphragm which can be reciprocated
between two extreme positions, wherein the volume of the metering
chamber is at a minimum in the first extreme position while the volume of
the metering chamber is at a maximum in the second extreme position. If
therefore the diaphragm is moved from its first position into the second
then the pressure in the metering chamber will fall so that delivery fluid is
sucked into the metering chamber by way of the suction line. In the return
movement, that is to say in the movement from the second into the first
position, the connection to the suction line is closed, the pressure of the
delivery fluid will rise by virtue of the decreasing volume in the metering
chamber so that the valve to the pressure line is opened and the delivery
fluid is delivered into the pressure line. Delivery fluid is alternately
sucked
into the metering chamber from the suction line and delivered from the
metering chamber into the pressure line alternately by the oscillating
movement of the diaphragm. The delivery fluid flow into the pressure line
is also referred to as the metering profile. That metering profile is
substantially determined by the movement profile of the displacer element.
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In the case of electromagnetically driven diaphragm pumps the
diaphragm is connected to a pressure portion which in most cases is
supported in resiliently prestressed fashion at least partially within a
solenoid. As long as the
solenoid does not have a current flowing
therethrough so that no magnetic flux is built up in its interior the
resilient
prestressing provides that the pressure portion and therewith the
diaphragm remains in a predetermined position, for example the second
position, that is to say the position in which the metering chamber is at the
largest volume.
If now a current is impressed on the solenoid a magnetic flux is
produced which moves the appropriately designed pressure portion within
the solenoid from its second position into the first position whereby the
delivery fluid in the metering chamber is delivered therefrom into the
pressure line.
Therefore activation of the solenoid substantially abruptly involves a
stroke movement of the pressure portion and therewith the metering
diaphragm from the second position into the first position.
Typically such electromagnetically driven diaphragm pumps are used
when the fluid volume to be metered is markedly greater than the volume
of the metering chamber so that the metering speed is essentially
determined by the frequency or the cycling of the flow of current through
the solenoid. If for example the metering speed is to be doubled then the
solenoid is briefly powered with a current twice as frequently in the same
time, which in turn has the result that the movement cycle of the
diaphragm is shortened and takes place twice as frequently.
Such a magnetic metering pump is described for example in EP 1
757 809.
The use of such magnetic metering pumps however encounters its
limits when only low metering speeds are required so that the abrupt
metering action of an entire stroke movement is not wanted.
Above-mentioned EP 1 757 809 B1 therefore already proposes
providing a position sensor with which the position of the pressure portion
or the diaphragm connected thereto can be determined. Closed-loop
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control of the movement can then be effected by a comparison between the
actual position of the pressure portion and a predetermined target position
of the pressure portion.
The closed-loop control of the movement of the pressure portion
.. provides that magnetic metering pumps can also be used for delivering
markedly smaller amounts of fluid as the stroke movement no longer takes
place abruptly but in a regulated fashion.
In practice however it is difficult to find suitable closed-loop control
parameters. In actual fact different closed-loop control parameters are
empirically determined for various pressure portion position states and
stored in the memory means so that the pump can call up and use the
corresponding closed-loop control parameters in dependence on the
position of the pressure portion.
The operation of determining the closed-loop control parameters
however is very laborious. In addition it is heavily dependent on the
conditions in the metering chamber like for example the density and
viscosity of the delivery fluid.
Therefore the closed-loop control functions satisfactorily only when
the system approximately corresponds to the desired state. Particularly
with pressure fluctuations on the suction and/or pressure line, upon the
occurrence of cavition, upon the collection of air in the metering chamber
or however upon changes in viscosity in the delivery fluid the closed-loop
control parameters stored in the memory means are unsuitable and the
closed-loop control accuracy decreases so that the actual metering profile
differs markedly from the desired metering profile. That however is
undesirable in particular in the continuous metering of very small amounts
like for example in the chlorination of drinking water.
Taking the described state of the art as the basic starting point
therefore the object of the present invention is to provide a method of the
kind set forth in the opening part of this specification, which allows closed-
loop control of the movement of the pressure portion without previous
tabling of closed-loop control parameters even when the system is exposed
to unexpected disturbances.
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According to the invention that is attained in that a model-based
closed-loop control, in particular a non-linear model-based control, is used
for the drive of the displacer element.
In the case of a model-based control a model which is as complete
as possible of the process dynamic is developed. By means of that model,
in simplified terms, it is then possible to make a prediction as to where the
system variables will move in the next moment.
A suitable adjusting parameter can then also be calculated from that
model. A characteristic of such a model-based control is therefore ongoing
calculation of the necessary adjusting parameter on the =basis of
measurement variables using the system parameters given by the model.
Basically the fundamental physical system is approximately
mathematically described by the modeling. That mathematical description
is then used to calculate the adjusting parameter on the basis of the
measurement variables obtained. Unlike the known
metering profile
optimization methods therefore the drive is no longer viewed as a "black
box". Instead the known physical relationships are used for determining
the adjusting parameter.
In that way it is possible to achieve a markedly better closed-loop
control quality.
Even if the described method can in principle be used in improving
metering profiles of any displacement pumps, it is described in relation to
the improvement in metering profiles of electromagnetically driven
diaphragm pumps as it has been developed for same and this represents
the preferred embodiment.
In a preferred embodiment the position of the displacer element and
the current through the electromagnetic drive is measured and a state
space model is used for the model-based closed-loop control, which model
uses the position of the displacer element and the current through the
solenoid of the electromagnetic drive as measurement variables.
In a particularly preferred embodiment the state space model does
not have any further measurement variables to be detected, that is to say
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the model is so developed that it is only on the basis of the detected
pressure portion position and the detected current through the solenoid
that it makes a prediction for the immediately following movement of the
pressure portion.
Such a model-based closed-loop control can be inexpensively
implemented as for example the magnetic metering pump described in
above-mentioned EP 1 757 809 already has measuring devices for
measuring the position of the displacer element and for measuring the
current through the solenoid.
The term state space model usually signifies the physical description
of an instantaneous state of the system. For example the state parameters
can describe the energy content of the energy storage elements contained
in the system.
For example a differential equation can be established for the
displacer element as the model for the model-based closed-loop control.
For example the differential equation can be a movement equation. The
term movement equation is used to mean a mathematical equation which
describes the spatial and temporal movement of the displacer element
under the action of external influences. In that respect, in a preferred
embodiment, forces which are specific to the positive displacement pump
and which act on the pressure portion are modeled in the movement
equation. Thus for example the force exerted on the pressure portion by a
spring, or the spring constant k thereof, and/or the magnetic force exerted
on the pressure portion by the magnetic drive can be modeled. The force
exerted on the pressure portion by the delivery fluid can then be treated as
an interference variable.
A prediction for the immediately following system behaviour can then
be made by such a state space model, if the measurement variables are
detected.
If the immediately following behaviour prognosticated in that way
deviates from the desired predetermined behaviour a correcting influence is
applied to the system.
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In order to calculate how a suitable influencing looks the influence of
the available adjusting parameters on the closed-loop control variable can
be simulated in the same model. The instantaneously best control strategy
can then be adaptively selected by means of known optimization methods.
As an alternative thereto it is also possible on the basis of the model to
determine a control strategy as a one-off and then to apply same in
dependence on the detected measurement variables.
In a preferred embodiment therefore a non-linear state space model
is selected as the state space model and the non-linear closed-loop control
is effected either by way of control-Lyapunov functions, by way of flatness-
based closed-loop control methods with flatness-based precontrol, by way
of integrator backstepping methods, by way of sliding mode methods or by
way of predictive closed-loop control, In that case non-linear closed-loop
control by way of control-Lyapunov functions is preferred.
All five methods are known from mathematics and are therefore not
discussed in greater detail here.
Control-Lyapunov functions are for example a generalized description
of Lyapunov functions. Suitably selected control-Lyapunov functions lead
to a stable behaviour in the context of the model.
In other words, a correction function is calculated, which in the
underlying model leads to a stable solution to the model.
In general there are a multiplicity of control options which have the
result that the difference between actual profile and target profile becomes
smaller in the underlying model.
In a preferred embodiment the model which forms the basis for the
model-based closed-loop control is used for formulating an optimization
problem in which as a secondary condition in respect of optimization, the
electrical voltage at the electric motor and thus the energy supplied to the
metering pump become as small as possible, but at the same time an
approximation of the actual profile to the target profile which is as fast as
possible and which has little overshoot is achieved. In addition it may be
advantageous if the measured signals are subjected to low-pass filtering
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prior to processing in the fundamental model in order to reduce the
influence of noise.
In a further particularly preferred embodiment it is provided that
during a suction-pressure cycle the difference between the detected actual
position profile of the displacer element and a desired target position
profile
of the displacer element is detected and a target position profile
corresponding to the desired target position profile reduced by the
difference is used for the next suction-pressure cycle.
Basically a self-learning system is implemented here. Admittedly the
model-based closed-loop control according to the invention has already led
to a marked improvement in the control characteristic, nonetheless there
can be deviations between the target profile and the actual profile. That is
not to be avoided in particular in the energy-minimizing selection of the
control intervention. In order further to reduce that deviation at least for
following cycles the deviation during a cycle is detected and the detected
deviation is at least in part subtracted from the desired target position
profile in the next cycle.
In other words, a "false" target value profile is intentionally
predetermined for a following pressure-suction cycle, wherein the "false"
target value profile is calculated from the experience acquired in the
preceding cycle. If more specifically the following suction-pressure cycle
entails exactly the same deviation between actual and target profile as in
the preceding cycle, the use of the "false" target value profile has the
result
that the actually desired target value profile is achieved as a consequence,
Admittedly it is basically possible and by virtue of the periodic
behaviour of the system in some applications also sufficient for the
described self-learning step to be performed only once, that is to say for
the difference to be measured in the first cycle and for the target value
profile to be appropriately corrected as from the second and in all further
cycles. It is particularly preferred however if the difference between actual
and target profile is determined at regular intervals, best in each cycle, and
is correspondingly taken into account in the following cycle.
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It will be appreciated that it is also possible to use only a fraction of
the detected difference as profile correction for the following cycle or
cycles. That can be advantageous in particular in situations in which the
detected difference is very great in order not to produce instability of the
system due to the sudden change in target value.
In addition it is possible to determine the magnitude of the fraction
of the detected difference, which is used as profile correction, on the basis
of the currently prevailing difference between the target and the actual
profiles.
It is also possible for the difference between the actual and the
target profiles to be measured over a plurality of cycles, for example 2, and
for a mean difference to be calculated therefrom, which is then at least in
part subtracted from the target profile of the following cycles.
In a further alternative embodiment any function dependent on the
detected difference can be used for correction of the next target position
profile.
The modeling according to the invention can be used in a further
preferred embodiment to determine a physical variable in the displacement
pump. The fluid pressure for example in the metering chamber can be
determined in that way.
The movement equation of the displacer element takes account of all
forces acting on the displacer element. Besides the force applied to the
displacer element by the drive that is also the counteracting force applied
to the diaphragm and thus to the displacer element by the fluid pressure in
the metering chamber.
Therefore if the force applied to the displacer element by the drive is
known conclusions about the fluid pressure in the metering head can be
drawn from the position of the displacer element or from the speed, which
can be deduced therefrom, or acceleration, of the displacer element.
For example if the actual fluid pressure reaches or exceeds a
predetermined maximum value a warning signal can be output and the
warning signal can be sent to an automatic shut-down arrangement which
shuts down the metering pump in response to reception of the warning
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signal. If therefore for any reason a valve should not open or the pressure
on the pressure line should rise greatly, that can be ascertained by the
method according to the invention without using a pressure sensor and the
pump can be shut down for the sake of safety. Basically the displacer
element with the associated drive additionally performs the function of the
pressure sensor.
In a further preferred embodiment of the method for a movement
cycle of the displacer element a target fluid pressure curve, a target
position curve of the displacer element and/or the target current pattern
through the electromagnetic drive is stored. In that case the actual fluid
pressure can be compared to the target fluid pressure, the actual position
of the displacer element can be compared to the target position of the
displacer element and/or the actual current through the electromagnetic
drive can be compared to a target current through the electromagnetic
drive and a warning signal can be output if the differences between the
actual and target values satisfy a predetermined criterion.
That method step is based on the notion that given events like for
example gas bubbles in the hydraulic system or cavitation in the pump
head cause a recognizable change in the fluid pressure to be expected and
therefore conclusions about said events can be drawn from the operation of
determining the fluid pressure.
The warning signal can activate for example an optical display or an
acoustic display. Alternatively or in combination therewith however the
warning signal can also be made available directly to a control unit which
performs suitable measures in response to reception of the warning signal.
In the simplest case the difference between the actual and the target
values is determined for one or more of the measured or given variables
and a warning signal is output if one of the differences exceeds a
predetermined value.
In order however not only to detect the possible fault events like for
example gas bubbles in the metering chamber or the occurrence of
cavitation but also to distinguish them from each other it is possible to
define a dedicated criterion for each fault event.
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In a preferred embodiment a weighted sum of the relative deviations
from the target value can be determined and the criterion can be so
selected that a warning signal is output if the weighted sum exceeds a
predetermined value,
Different weighting coefficients can be associated with the different
fault events. In the ideal case, upon the occurrence of a fault event,
precisely one criterion is met so that the fault event can be diagnosed.
Therefore the operation of determining the pressure in the metering
head is possible by the described method without having recourse to a
pressure sensor and conclusions about given states in the metering head
can be drawn from the pressure determined in that way, and they can then
in turn trigger the initiation of given measures.
Pressure variations can be very precisely determined with the
method according to the invention.
In a further embodiment therefore the time gradient of a measured
or given variable is ascertained and, if it exceeds a predetermined limit
value, valve opening or valve closure is diagnosed.
In .an alternative embodiment the mass m of the displacer element,
the spring constant k of the spring which prestresses the displacer element,
the damping d and/or the electrical resistance Ro, of the electromagnetic
drive are determined as a physical variable.
In a particularly preferred embodiment even all of the stated
variables are determined. That can be
effected for example by a
minimization calculation. All the specified variables with the exception of
the pressure in the metering chamber represent constants which can be
determined by experiment and which generally do not change in pump
operation. Nonetheless fatigue phenomena in respect of the different
elements can occur, which change the value of the constants. For example
the measured pressure-travel relationship can be compared to an expected
pressure-travel relationship. The difference integrated over a cycle from
both relationships can be minimized by a variation in the constant
parameters. If in that case it is established for example that the spring
constant has changed a defective spring can be diagnosed.
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Such a minimization operation can also be carried out in the
pressure-less condition, that is to say when there is no fluid in the metering
chamber.
As was already stated in the opening part of this specification the
closed-loop control is markedly influenced by the density and the viscosity
of the delivery fluid. The closed-loop control accuracy can be improved for
example by the density and/or viscosity of the delivery fluid being
measured and the measurement result being used for dimensioning of the
closed-loop control parameters. However such a measurement operation
necessitates at least one additional sensor which would increase the selling
price of the displacement pump and is also in need of maintenance and
repair. Therefore hitherto changes in density and viscosity are not taken
into consideration in the closed-loop control.
In a further particularly preferred embodiment it is therefore
provided that a physical model with hydraulic parameters is also set up for
the hydraulic system and at least one hydraulic parameter is calculated by
means of an optimization calculation.
The term hydraulic parameters is used to mean any parameter of the
hydraulic system - apart from the position of the displacer element - that
influences the flow of the delivery fluid through the metering chamber.
Hydraulic parameters are therefore for example the density of the
delivery fluid in the metering chamber and the viscosity of the fluid in that
chamber. Further hydraulic parameters are for example hose or pipe
lengths and diameters of hoses and pipes which are at least temporarily
connected to the metering chamber.
That measure makes it possible to determine hydraulic parameters
without having to provide an additional sensor.
An inherent property of the positive displacement pump is that the
hydraulic system markedly changes whenever one of the valves, by way of
which the metering chamber is connected to the suction and pressure lines,
is opened or closed.
The system is simplest to model for the situation where the valve to
the suction line is opened and the valve to the pressure line is closed. More
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specifically a flexible hose is frequently fitted to the valve to the suction
line, and that hose ends in a supply container which is under ambient
pressure.
That state occurs during the so-called suction stroke movement, that
is to say while the displacer element is moving from the second position
into the first position. That hydraulic system could be described for
example by means of the non-linear Navier-Stokes equation, having regard
to laminar and turbulent flows. Besides density
and viscosity of the
delivery fluid the diameter of the hose connecting the suction valve to the
supply container, the length of the hose and the difference in height that
the fluid in the hose has to overcome are then also to be considered as
hydraulic parameters.
Depending on the respective system used further meaningful
assumptions can be made. By means of an optimization calculation which
can be effected for example by way of the known gradient method or
Levenberg-Marquardt algorithms it is possible to determine the hydraulic
parameters which are contained in the physical model and which best
describe the pressure variation in the metering head and the movement or
the speed and acceleration derived therefrom of the pressure portion.
In principle the determining method according to the invention could
be effected solely by repeated analysis of the suction stroke performance.
As an alternative thereto however it is also possible to consider the
physical model of the hydraulic system for the situation where the valve to
the suction line is closed and the valve to the pressure line is open. As
however the pump manufacturer initially does not generally know in what
environment the metering pump is used and therefore also does not know
the pipe system connected to the pressure valve connecting the pressure
line to the metering chamber, only a generalized assumption can be made
here. Therefore without knowledge of the pipe system connected to the
pressure valve the physical model set up cannot be set up with the
accuracy, as is generally possible for the hydraulic system during the
suction stroke.
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In a particularly preferred embodiment physical models are used for
both described hydraulic systems and then the valve opening times are
measured or determined and the respectively correct physical model is
selected in dependence on the result of determining the valve opening
time. Basically then the method according to the invention is carried out
separately for the suction stroke and the pressure stroke. In both cases
values which in practice are not exactly the same are obtained for the
hydraulic parameters like for example the density and viscosity of the
delivery fluid. In principle it would therefore be possible to average the
different values, in which case here it is under some circumstances
necessary to take account of the fact that, by virtue of the better
description of the actual situation by the physical model during the suction
stroke, the value obtained during the suction stroke is weighted more
greatly in the averaging operation, than the value ascertained during the
pressure stroke.
After the hydraulic parameters have been determined in the manner
according to the invention the physical model set up can be used with the
hydraulic parameters determined in that way in order in turn to determine
the pressure in the metering chamber. That knowledge can be used in turn
to improve the movement regulation of the pressure portion insofar as the
force exerted on the pressure portion by the fluid is modeled by the
hydraulic parameters determined in that way.
According to one aspect of the invention, there is provided a method of
optimizing metering profiles of electromagnetically driven metering
pumps, in which a moveable displacer element delimits a metering
chamber which is connected by way of valves to a suction line and a
pressure line so that delivery fluid can alternately be sucked into the
metering chamber by way of the suction line and urged out of the
metering chamber by way of the pressure line by an oscillating
movement of the displacer element, wherein the delivery fluid flow into
the pressure line represents the metering profile and there is provided
an electromagnetic drive for the oscillating movement of the displacer
element, wherein a model-based closed-loop control is used for the
electromagnetic drive, wherein position of the displacer element,
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Date recue /Date received 2021-11-08
current through the electromagnetic drive, or both, is measured and a
state space model is used for the model-based closed-loop control,
which state space model uses the position of the displacer element, the
current through the electromagnetic drive, or both, as measurement
variables.
Further advantages, features and possible uses of the present
invention will be apparent from the description hereinafter of a preferred
embodiment and the accompanying Figures in which:
Figure 1 shows a diagrammatic view of an ideal movement profile,
Figure 2 shows a diagrammatic view of the self-learning function,
Figure 3 shows a diagrammatic view of a pressure-travel graph and a
travel-time graph for the normal condition,
Figure 4 shows a diagrammatic view of a pressure-travel graph and a
travel-time graph for a condition with gas bubbles in the metering
chamber,
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Date recue /Date received 2021-11-08
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Figure 5 shows a diagrammatic view of the suction line connected to
the positive displacement pump, and
Figures 6a ¨ 6e show examples of hydraulic parameters and their
time-dependent development.
The method according to the invention has been developed in
connection with a magnetic metering pump. In a preferred embodiment
such a metering pump has a moveable pressure portion with a thrust rod
fixedly connected thereto. The pressure portion is supported axially
moveably along the longitudinal axis in a magnet casing fixedly anchored in
the pump housing so that the pressure portion with thrust rod is pulled into
a bore in the magnet casing upon electrical actuation of the magnetic coil in
the magnet casing, against the force of a compression spring, and the
pressure portion reverts to the initial position due to the compression
spring after deactivation of the solenoid. The consequence of this is that
the pressure portion and a diaphragm actuated thereby, upon continued
activation and deactivation of the magnetic coil, performs an oscillating
movement which in the metering head arranged in the longitudinal axis, in
conjunction with an outlet and inlet valve, leads to a pump stroke (pressure
stroke) and an intake stroke (suction stroke). Activation of the magnetic
coil is effected by applying a voltage to the coil. The movement of the
pressure portion can thus be determined by the time pattern of the voltage
at the coil.
It will be appreciated that the pressure stroke and the suction stroke
do not necessarily have to last for the same period of time. As no metering
is effected during the suction stroke but the metering chamber is only re-
filled with delivery fluid, it is in contrast advantageous for the suction
stroke in any case to be performed as quickly as possible, in which respect
however care is to be taken to ensure that no cavitation occurs in the
pressure chamber.
In contrast the pressure stroke can last very long, in particular in
situations of use in which only very small amounts of fluid are to be
metered. The result of this is that the pressure portion only gradually
moves in the direction of the metering chamber. To achieve a movement
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of the pressure portion as is shown in idealized form in Figure 1 the
movement of the pressure portion must be subjected to closed-loop
control. In that case only the position of the pressure portion and the
= magnitude of the current through the magnetic coil are usually available
as
the measurement variable.
According to the invention therefore a (non-linear) model is
developed, which describes the condition of the magnetic system.
The following model applies to a preferred embodiment:
*= = ¨1 (-d.Z - kx - + Fp + K1 (8)0.2)
_ R (8p(D)
____________________ \-1?0,
/Y1 N,
wherein
m: mass of the pressure portion
(1): magnetic flux
IC,(8)02 : magnetic force
NI: number of turns
u: voltage
d: damping
k: spring constant
Fvpr: force on pressure portion due to spring prestressing
Fp: force on pressure portion due to fluid pressure in the delivery
chamber
Riõõ(6,0) : magnetic reluctance
Rcu: ohmic resistance of the coil
x: position of the pressure portion
: gap size between armature and magnet
CA 02922313 2016-02-24
That is a non-linear differential equation system which makes it
possible to provide a prediction about the immediately following behaviour
of the system, starting from a starting point.
It is therefore possible by means of that model to identify future or
actually already existing deviations between the target curve and the actual
curve. The model can also be used to calculate the probable influence of a
control intervention.
In real time therefore measurement of the current strength and the
position of the pressure portion determines how the system will probably
develop. It is also possible to calculate the control intervention, that is to
say the change in voltage at the magnetic coil, by which the system can be
moved in the desired direction again.
It will be appreciated that there are a multiplicity of possible ways of
intervening in the system for closed-loop control. It is therefore possible at
any moment in time to seek stable solutions for the dynamic system. That
computing step is repeated continuously, that is to say as frequently as the
available computing power allows, to achieve optimum closed-loop control.
With the model proposed here it is generally not necessary to
determine new stable solutions of the dynamic system at every moment in
time. In general it is sufficient for the suitable correction function to be
determined once in dependence on the measurement variables, that is to
say in dependence on the position of the pressure portion and the voltage
at the magnet drive, and to use that correction function thereafter for the
closed-loop control.
In spite of that closed-loop control there will inevitably be deviations
between target and actual values as the selected model always represents
an idealization. In addition the detected measurement variables are always
error-afflicted (noise).
To further reduce the difference between actual and target profiles
that difference is measured during a pressure-suction cycle and the sum of
the measured difference and the desired target profile is used as the target
profile for the following cycle. In other words, use is made of the fact that
the pressure-stroke cycle is repeated. Thus in the following cycle there is
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predetermined a target value profile which deviates in relation to the target
value profile that is actually wanted.
That self-regulating principle is diagrammatically shown in Figure 2
for clarification purposes. This shows the position of the pressure portion
on the Y-axis and time on the X-axis.
In the first cycle, a target profile used for the closed-loop control is
illustrated in a broken line. That target profile corresponds to the desired
target profile which is reproduced for comparison in the third cycle as the
reference profile. In spite of the model-based closed-loop control according
to the invention the actual profile will deviate from the target profile. In
the first cycle in Figure 2 therefore by way of example an actual profile is
shown in solid line. In that case the deviations between the actual and
target profiles are shown more pronounced for clarity than they occur in
practice.
In the second cycle the difference between the actual profile of the
first cycle and the reference profile is then subtracted from the target
profile used for the first cycle and the difference is used as the target
profile for closed-loop control during the second cycle. The target profile
obtained in that way is shown in broken line in the second cycle.
In the ideal case in the second cycle the actual profile deviates to the
same extent from the target profile used, as was observed in the first cycle.
As a result there is an actual profile (shown in solid line in the second
cycle), that corresponds to the reference profile.
By virtue of measuring the position of the pressure portion and the
current through the magnetic drive Fp, that is to say the force on the
pressure portion due to the fluid pressure in the delivery chamber, is the
sole unknown variable. Therefore, using that model, it is possible to
determine the force acting on the pressure portion due to the fluid pressure
in the delivery chamber. As the area of the pressure portion subjected to
the fluid pressure is known the fluid pressure can be calculated from the
force.
The described drafting of a non-linear system description for the
electromagnetic metering pump system makes it possible to use model-
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based diagnosis methods. For that purpose the state parameters of the
system models are evaluated and the pressure in the pump head of the
electromagnetic metering pump is determined. The necessary current and
position sensors are in that case already installed in the pump system for
.. control purposes so that the information is already available without the
structure of the metering pump having to be supplemented. The diagnosis
algorithms can then be performed on the basis of the time variation in the
state parameters and the pressure in the metering head of the pump.
Thus for example the model-based diagnosis of process-side
overpressure and the automated pump shut-down can be implemented.
Recognition of the valve opening and valve closing times can be
effected for example by way of determining and evaluating time gradients
of linked state parameters of the system model. A situation involving
exceeding or falling below the state gradients can be detected by means of
predetermined limits, which leads to a identification of the valve opening
and valve closing times.
Alternatively thereto it is also possible to determine the pressure in
dependence on the position of the pressure portion and to deduce the valve
opening and valve closing times from an evaluation operation. A
corresponding pressure-travel graph is shown at the left in Figure 1. The
associated travel-time graph is shown at the right in Figure 1. The travel-
time graph shows the time-dependent movement of the pressure portion.
It will be seen that the pressure portion firstly moves forwardly from a
starting position 1 (x=0 mm) and reduces the volume of the metering
chamber (pressure phase). At time 3 the pressure portion passes through
a maximum and then moves back into the starting position again (suction
phase).
The associated pressure-travel graph is shown at the left in Figure 3.
It is traveled in the clockwise direction, beginning at the coordinate origin
.. at which the pressure portion is in position 1. During the pressure phase
the pressure in the metering chamber will initially rise steeply until the
pressure is in a position of opening the valve to the pressure line. As soon
as the pressure valve is opened the pressure in the metering chamber
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remains substantially constant. The opening point is identified by reference
2. From that moment in time which is also shown at the right in Figure 3 a
metering action takes place. With each further movement of the pressure
portion metering fluid is pumped into the pressure line. As soon as the
pressure portion has reached the maximum position (time 3) the
movement of the pressure portion reverses, the pressure valve
immediately closes and the pressure in the metering chamber falls again.
As soon as a minimum pressure is reached (time 4) the suction valve
opens, connecting the metering chamber to the suction line, and metering
fluid is sucked into the metering chamber until the starting position is
regained.
The valve closing times can be determined from the travel-time
graph as they are on the travel maxima of the pressure portion. The times
2 and 4, that is to say the valve opening times, are not so easy to
determine, especially as in practice the pressure-travel graph has rounded-
off "corners". Therefore for example, starting from position 1 in the
pressure-travel graph, upon reaching 90% of the pressure maximum
(known from position 3) the travel can be read off and the gradient of the
pressure-travel graph between points 1 and 2 can be determined. The
90% curve is shown in dotted line. The resulting straight line intersects the
curve p=pm,õ at the valve opening time. The time 4 can
also be
determined in the same way. That determining operation can be effected
in each cycle and the result used for a later cycle. In that way changes in
the opening times are also detected.
Gas bubbles in the hydraulic system, cavitation in the pump head of
the metering unit and/or valve opening and valve closing times of the
metering units can be diagnosed by comparison of the target and actual
trajectories of the individual state parameters. Particularly when
a
predetermined fault limit is exceeded between the target and actual
trajectories that can trigger a warning signal and corresponding measures.
An example is shown in Figure 4. Here too the pressure-travel graph
is shown at the left and the travel-time graph at the right. The right-hand
Figure is identical to the corresponding graph in Figure 3. If there are gas
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bubbles which are compressible in the hydraulic system that can have the
result that the pressure valve opens only at the time 2' and the suction
valve opens only at the time 4'. A marked shift in the valve opening times
can therefore be used to diagnose the state "air in the metering chamber".
In the case of cavitation only the valve opening time 4' but not the valve
opening time 2 is shifted so that such a behaviour can be used to diagnose
the state "cavitation".
The model-based method presented, by virtue of analysis of the
individual linked system state parameters, permits a substantially more
extensive and higher-grade diagnosis than was previously implemented.
In addition that can be achieved with low sensor system costs and a
high level of reliability and certainty. The higher quality of diagnosis means
that the area of use of electromagnetic metering pump systems can be
enhanced under some circumstances as now the metering accuracy can be
extremely improved.
By virtue of the design of a physical model, in particular a non-linear
system description of the hydraulic process in the metering chamber or in
the line connected to the metering chamber of an electromagnetic metering
pump system, it is possible to use model-based identification methods in
real time. For that purpose the hydraulic parameters, that is to say the
state parameters of the hydraulic models, are evaluated and the system
dynamic as well as the parameters of the hydraulic process are determined.
The position of the displacer element or the speed and acceleration
which can be deduced therefrom of the displacer element and the pressure
in the metering chamber which can be determined by way of the force
exerted on the delivery fluid by the diaphragm serve as measurement
variables or external variables to be determined.
As generally in the specified positive displacement pumps the suction
line comprises a hose connecting the suction valve to a supply container
the hydraulic system can be described in simplified form for the suction
stroke, that is to say while the pressure valve is closed and the suction
valve is opened, as is shown in Figure 5. The suction line comprises a hose
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of a diameter Ds and a hose length L. The hose bridges over a height
difference Z.
The non-linear Navier-Stokes equations can be simplified if it is
assumed that the suction line is of a constant diameter and is not
stretchable and that an incompressible fluid is used.
By means of known optimization methods like for example the
gradient method or the Levenberg-Marquardt algorithms, the 'hydraulic
parameters are now determined, which on the basis of the model can best
describe the measured or determined position of the pressure portion and
the measured or determined pressure in the metering chamber.
Figures 6a through 6e, using the example of glycerin as the delivery
fluid, here each show a hydraulic parameter (dotted line) and the values
from the method according to the invention (solid line) in relation to time.
Thus for example Figure 6a shows the density of the delivery fluid.
That is about 1260 kg/m3 (dotted line). It will be seen that the method
according to the invention is in a position to determine the density within
about 100 seconds. Admittedly, at the time t = 0 seconds the given value
is still markedly below the actual value. By virtue of ongoing optimization
however the value determined by the method according to the invention for
density very rapidly approaches the true value (solid line).
The same applies to the hose length L (see Figure 6b), the height
difference Z (see Figure 6c), the hose diameter (see Figure 6d) and
viscosity (see Figure 6e).
The parameters determined by the method according to the
invention can then in turn be used together with the physical model
produced to determine the force exerted on the pressure portion by the
hydraulic system.
That information can be used for the closed-loop control according to
the invention. Thus the hydraulic model developed can physically
reproduce the influence of the hydraulic system and take account of same
in the form of a disturbance variable intrusion.
That yet once again markedly improves the pump operation of
electromagnetic metering pump systems.
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