JSSSJournal of Sensors and Sensor SystemsJSSSJ. Sens. Sens. Syst.2194-878XCopernicus PublicationsGöttingen, Germany10.5194/jsss-6-199-2017Development of a chopper charge amplifier for measuring the cavity pressure inside injection moulding tools and signal optimisation with a Kalman filterSchneiderManuelm.schneider@hs-sm.deJahnAlexanderGreifzuNorbertFränzelNorbertFaculty of Electrical Engineering, Schmalkalden University of Applied Sciences, Blechhammer 9, 98574 Schmalkalden, GermanyAdvanced System Technology (AST) Branch of Fraunhofer IOSB, Am Vogelherd 50, 98693 Ilmenau, GermanyManuel Schneider (m.schneider@hs-sm.de)10May20176119921012August20167April201712April2017This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://jsss.copernicus.org/articles/6/199/2017/jsss-6-199-2017.htmlThe full text article is available as a PDF file from https://jsss.copernicus.org/articles/6/199/2017/jsss-6-199-2017.pdf
This article provides insight into the development of a powerful
and low-cost chopper amplifier for piezoelectric pressure sensors and shows
its possible applications for injection moulding machines. With a power supply
of 3.3 volts and the use of standard components, a circuit is introduced
which can be connected to a commercially available microcontroller without any
additional effort. This amplifier is specialised for low frequencies and
high-pressure
environments. With the adjustment of the sample and chopper frequency by
means of software, the amplifier can easily be adapted for other applications.
This chopper amplifier is a very compact and cost-effective solution with a
small number of required components. In this contribution, it will be shown
that the amplifier has good results in various laboratory tests as well as in
the production process. Furthermore, an approach to fuse data from force and
pressure signals by using a Kalman filter will be presented. With this method,
the quality of the sensor signals can be significantly improved. This article
is an extension of our previous work in .
Introduction
Two key factors for the pricing of injection-moulded articles
are the consistent quality of the production and the production volume. Today,
production parameters are recorded and evaluated by means of machine-specific
hardware outside the injection mould. The measured data are then available for
the machine or the SCADA
System for supervisory control and data
acquisition (SCADA).
. This requires that all machines are equipped with
special hardware and that the company has the necessary infrastructure
available at the plant. Current systems keep the parameterisation data for the
production process in memory located inside the control unit of the moulding
machine or on compact discs. In the case of location changes, e.g.
installation by the tool manufacturer at the manufacturing site or a change
in the manufacturing plant, the tuned injection moulding parameters are often
lost. One possible solution could be the use of an online data management
system, but this causes a lot of other problems with data security, violating
intellectual property or company espionage.
Another possibility could be to incorporate an embedded system into the
injection moulding tool. This technology would enable the system to keep
track of all activities in the production process. Following this principle,
one can think of a system that locally stores all data related to the whole life cycle of a
moulding tool and also ensures that companies can keep
their knowledge confidential. This EDS
Embedded
diagnostics system (EDS).
enables independent quality monitoring and thus
ensures the security of the IT infrastructure. It can also be used by
companies without a SCADA system or without a connection to the World Wide
Web. This paper discusses a measurement technique that is suitable for
sampling
pressure data with low power consumption while being accurate enough to
compete with existing industrial solutions. The TLV2771 (Texas Instruments, Dallas, TX, USA) is a standard operational
amplifier for charge amplification. This IC
Integrated circuit (IC)
is only usable with a single supply when the sensors are connected to 3.3 V and to the reference
voltage. In our case, the piezoelectric sensors always have a connection to the
machine ground, and this is a problem for the amplifier. The developed
amplifier shows an alternative method of single-supply charge amplification
with a
ground connection. The contribution is structured as follows.
Sections and give an overview of the system
specifications and the basics of the developed chopper charge amplifier. In
Sect. , the focus is on the simulation of the chopper
amplifier and the verification of the simulation results. The temperature
behaviour and the amplifier quality are the main aspects in Sect. . Information on the injection moulding process and the
results of the measurement in the production process can be found in Sect. . In Sect. , the focus is on the
signal optimisation by using a Kalman filter. The conclusion is the last part
of this contribution.
System specifications
For use within injection moulding machines, two companies are
developing industrial charge amplifiers for pressure measurement. The voltage
specifications, the dimensions and the price of commercial charge amplifiers
from those companies are not within our specifications. Two examples of these
amplifiers are the 5073Axx1 and the 5050A . In
Table , some of the technical information for these two charge
amplifiers is listed.
The technical data for the 5073Axx1 and the 5050A charge amplifiers.
Characteristic5073Axx15050APhysical unitSupply voltage18–3015–30VdcMeasuring range±100…±1 000 000±5000…±100 000pCOutput voltage-10…+10VOperating temperature range0 …60 ∘CHeight64.0 mmLength115.0 mmWidth34.5 mm
The goal of this work is to propose a new charge amplifier with a low supply
voltage, a symmetrical output signal and small dimensions. The following list
contains the requirements for the development of this charge amplifier.
A regulated power supply with Vdc= 3.3 V should be used.
The output signals must be in the range of 0…3.3 V for optimal analogue-to-digital conversion.
The occupied space must be kept as small as possible.
The signal quality must be better than the indirect measurement with a force sensor.
The cost of the amplifiers must be kept low.
Basics for the chopper charge amplifier
To meet the requirements of space, power and cost
minimisation, the authors developed and evaluated different charge amplifier
concepts. In most cases, the insulation
of the PCB
Printed circuit board (PCB)
and the selected electrical
components is too low, and the charge signal is rapidly lowered to zero. The
first acceptable result has been achieved with a chopper amplifier. This
amplifier structure is developed according to . The amplifier
operates with a clocked reference voltage source at the input capacitor and
thus enables the measurement of charge changes in the positive and negative
direction with respect to the reference voltage . The
reference voltage is generated by an integrated circuit (REF3212; Texas Instruments). A CMOS
Complementary metal–oxide–semiconductor (CMOS)
switch is used to reset the electrical charge to the reference voltage on the
input capacitor. The reset frequency can be adjusted with software and is
1 kHz. The two main components of the chopper amplifier are an
instrumentation amplifier and a microcontroller. The microcontroller TM4C123G
(Texas Instruments)
has a 12-bit ADC
Analogue-to-digital converter (ADC)
input and a communication interface. The piezoelectric
signal is sampled by the ADC before every reset impulse. In Fig. , the schematic circuit diagram of the developed
chopper amplifier is shown. In this special solution, the isolation effect of
the PCBs and the cost of the PCB design could be reduced. In Fig. , the developed chopper amplifier without the
microcontroller is displayed.
A diagram of the chopper amplifier with its main components and a connected microcontroller, the piezoelectric
sensor and the timing of the electric switch.
A picture of the developed chopper amplifier with the associated board cut-out .
The components in the picture are 1. the instrumentation amplifier, 2. the reference voltage source
and 3. the electric switch.
By using a pulsed reference voltage source, the signal of interest is
approximately differentiated. Eqs. () and ()
reflect the mathematical and temporal relation at the input capacitance of
the chopper amplifier. For case (a), the voltage at the input
capacitance approaches the voltage of Uref. In case (b) when the time
t is between two resets, the voltage at the capacitance is a function of
the charge output from the piezoelectric sensor. In Eq. (), the
discharge curve during the reset interval of case (a) is described. The R is
the input resistance of the circuit. In our case, R is made up of the input
resistance of the CMOS switch and is greater than 10 MΩ. The C
is the input capacitance of the circuit additional to the cable capacitance.
In our case, the cable length is shorter than 30 cm, and thus the equation can be
simplified to C=Cin. The value of Cin is the capacitor value of
the amplifier input and has to be adjusted to the PCB design:
u(Cin)t=Ureft, case (a)QpiezotCin+Ureft, case (b)(a)n+1⋅Δt-treset<t<n+1⋅Δt(b)n⋅Δt<t<n+1⋅Δt-tresetn∈N- sample number,Qpiezot=∫t+Δt-tresett+Δtipiezotdt,for a) u(Cin)t=Uref1-e-tR⋅C+Ustart(t).
The voltage Ustart(t) from Eq. () describes the voltage
before every reset. At the first start of the chopper amplifier, the start
voltage Ustart(t) is equal to zero. At every following reset, however, the
value of U from Eq. () changes between zero and the supply
voltage. This results in a charge curve, or a discharge curve, to the reference
voltage:
Ustart(t)=Ue-tR⋅C.
This charging takes place in finite time. That means that during the reset
time,
the accumulated charge signal cannot be measured, thus leading to
incorrect measurements of the charge signal. To keep the information loss as
low as possible, treset should be much smaller than the sample time
Δt. However, this time depends on the input capacitor, the PCB isolation
and the leakage current of the other electrical components on the PCB. According to
, a value of 100 pF requires 400 ns for a complete
discharge from URef to ground by using the ADG612 (Analog Devices, Massachusetts, USA)
analogue switch. In this
case, it could be used as a benchmark for the reset time of the chopper
amplifier. Fig. shows one result of the charge and
discharge curve of such a 100 pF capacitor. The orange line is the 400 ns
charge impulse and the blue line describes the charge and discharge curve of
the input capacity.
The result of the shortest switching pulse from the analogue switch ADG612. A pulse of 400 ns (orange curve)
is enough to load the capacitor from zero to the reference voltage. After the pulse, the voltage returns to zero
in a time of approximately 4 milliseconds (blue curve; ).
The discharge time depends on the measurement set-up with the oscilloscope and
the analogue switch. In this experiment, the shortest switching pulse of the
analogue switch is determined. In the next section, the operation of the
chopper amplifier is verified by a simulation.
Simulation of the chopper charge amplifierBasics of the chopper simulation
To illustrate the operation of this amplifier, a simulation script in
SCILAB
SCILAB is an open-source software for numerical computation;
http://www.scilab.org.
has been written. The basis of this simulation
is a periodic signal, which is passed as a voltage signal to the input of the
chopper amplifier. For the simulation, a signal with two constant derivation
values was chosen. The simplest signal with these characteristics is the
triangular wave. The advantages of this signal are the two different
derivation values and the numbers of different Fourier frequencies. In Eq. (), the analytical expression of this test signal
in the time interval from t=t0=0 s to t=T (T is the sampling interval of
the signal) is shown. The SCILAB plot in Fig. shows
the triangular signal. Another method to generate a triangular test signal is
the
development of a Fourier series. In Eq. (), the result of the
Fourier series development for the periodic test signal is displayed. The
variable u^/2 stands for the maximum value of the set voltage. Both
equations represent the functional relationship between voltage and time. The
variable ω0 represents the radian frequency of each oscillation. The
result of the superposition of this Fourier function is the same as shown in
Fig. and Eq. (). For this simulation,
u^ is set to π:
ut=2⋅u^T⋅t, case (a) 0≤t≤T2-2⋅u^T⋅t+u^, case (b) T2≤t<T,
ut=u^2-16⋅u^ω0T2cos1ω0t12+cos3ω0t32+⋯.
A representation of the triangular test signal with an interval of T= 1 s. The line shows the input signal, and the
same signal is the result of the integration of the digital sampled chopper signal from Fig. .
In Fig. , the operation of the chopper amplifier is
illustrated. The capacitor voltage is periodically set to zero (here
T= 10 ms). This results in the characteristic chopped signal, which is
amplified further. It can be seen that the chopper amplifier generates an
approximation of the derivative of the input signal. To reduce the number of
plotting lines in the simulation, the chopper frequency is set to 100 Hz.
The blue signal illustrates the simulated chopper output signal with a sampling frequency of 100 Hz.
The red line illustrates the sampled values of the blue time signal.
This signal is sensed and converted into digital values. The optimal result of the derivative triangular signal is a
rectangular signal. In order to restore the input signal from the digital values, the digitised samples must be integrated.
Through the integration of the chopper signal, the test signal (triangular signal) is formed again. The result is the same
curve from Fig. . These simulation results are also verified with the developed chopper amplifier.
Verification of the simulation results
The peak-to-peak amplitude of the laboratory triangular test signal is set to
120 mV and the frequency is 1 Hz. This test signal was generated by an
function generator. The sampled, chopped and
amplified triangular test signal is shown in Fig. . The expected rectangular oscillation
is not clearly visible.
The distortion is mainly caused by the 50 Hz power grid frequency. In this
experiment, the chopper frequency is set to 1 kHz. This resulted in a lower
amplitude of the chopper signal, but with the gain value of 50 the signal
could be measured. The effective voltage over 500 ms segments is
calculated with ≈±12 mV. The main information of the test signal
is smaller than the noise level.
Display of the chopped input triangular signal after the amplifier (recording time 10 s; peak-to-peak
amplitude u^ at the signal generator 120 mV; time period T= 1 s; amplifier gain 50).
To produce the original test signal, different mathematical operations have to
be performed. The first is the subtraction of the reference voltage. The next step is
the integration of the time signal, and the last is the division of the
amplifier gain value. The result of the first two operations is displayed in
Fig. . As can be seen in the illustration, the peaks
in the signal increase with time. There is drift in the data. The reason
could be an integration error or the interference signals of the chopper
signal from Fig. . Another possible reason for the drift
could be an unstable reference voltage. For long measurement times, an offset in
the reference voltage results in a drift in the positive or negative direction.
The integration result of the noisy test signal from Fig. .
As can be clearly seen, the amplified voltage level is approximately 6 V
and the time period is 1 s. With the division of the gain value, the result is
approximately 120 mV.
In Sect. , a solution for the drift problem with long
measurement times will be proposed.
Measurement of the amplifier qualityLaboratory set-up for the resolution measurement
For the study of the resolution measurement and the
temperature behaviour of the amplifier, a test set-up using a temperature
controlled chamber, a signal generator and a computer system was developed.
The computer system automatically controls the experiment properties of the
HMF2525 signal generator (ROHDE & SCHWARZ, Münich, Germany)
and measures the signals from the chopper amplifier
inside the climatic chamber. In Fig. , the measurement
set-up is displayed.
A schematic representation of a fully automated measurement set-up with a signal generator,
amplifier circuit and data analysis with laptop and SCILAB.
For the evaluation, two typical temperatures were chosen that represent the
expected conditions inside the mounted EDS. The set of ambient temperatures in
the chamber were 25 and 50 ∘C. The computer sends the configuration
for the HMF2525 signal generator via the standard SCPI
Standard Commands for Programmable Instruments (SCPI)
interface and
simultaneously receives the converted values of the AD converter. The
recorded data are used to determine the temperature-dependent signal-to-noise
ratio and the threshold assessment of the amplifier structure.
In order to determine the signal-to-noise ratio and the sensitivity of the
developed charge amplifier, the fully automatic measurement set-up, as shown
in Fig. , was used. Due to the fact that it is not
typical to specify a signal-to-noise ratio in commercial charge amplifiers,
additional information for this special amplifier is provided in this
section. A number of sine waves with different frequencies were used as test signals. The series of measurements started at a frequency of f= 1 Hz and
was performed in 19 steps up to f= 20 Hz. The calculated values of the spectral
coefficients of the input signal are divided by the sum of all the frequency
components that are independent of the input signal to respectively
calculate the signal-to-noise ratio. The mathematical relation for this is shown
in .
The threshold assessment allows for a qualitative and
quantitative assessment of the quality of the proposed charge amplifier. The
threshold value of the circuit is the smallest measurable change in
charge (in pC) that produces a change in the least significant bit (LSB) of
the sampled voltage signal. A rectangular oscillation voltage at the input
of the amplifier is applied for this measurement. This rectangular oscillation
passes the chopper amplifier and results in an alternating periodic needle
pulse similar to Dirac pulses. In Sect. , the
results of these measurements are described.
Signal quality results of the chopper amplifier
For the measurement of the signal-to-noise ratio, different
sine waves with frequencies of 1 to 20 Hz were used. The calculated
signal-to-noise ratio (SNR) is on average around 31.49 dB at T1 = 25 ∘C
and around 30.96 dB at T2 = 50 ∘C. The results of the noise measurements
for different input frequencies are shown in Fig. . As can be
seen in this measurement, there are three runaways at different frequencies.
The reason could be the climatic chamber itself. There are some engines and
electronics that disturb the measurement at varying times. At these times, the
frequency disturbances in other frequency ranges increase and result
in negative peaks in the measurements.
The measurement results for the signal-to-noise ratio subject to the input frequency
and the ambient temperature as described in .
A solution for this problem can be a delayed start of the measurement after a
settling time for the climatic chamber. The results of the threshold
assessment measurement can be seen in Figs. and . In this case, there is a linear relationship between the input
signals and the measured output values. In both figures, the level of
interference at different ambient temperatures is nearly constant.
The threshold assessment (intersection point of the graphs at approximately 0.1 pC)
of the circuit at 25 ∘C . The blue dashed line shows the peak voltage in the measurement data at a corresponding input
charge. The red dotted line shows an increase in the calculated amplifier noise by 3 times, similar to .
The threshold assessment (intersection of the graphs at approximately 0.12 pC) of the circuit
at 50 ∘C of ambient temperature. The blue dashed line shows the swing in the measurement data at a
corresponding input charge. The red dotted line shows a threefold increase in the calculated amplifier noise, similar to .
As a basis for the calculation of the amplifier noise, the mean square of the
noise is multiplied by a factor of 3 p. 57. The threshold of the
charge amplifier can be read at the intersection between the measured
value (blue) and the amplifier noise (red). It is about 0.1 pC/LSB; the
optimisation of the resolution is part of further work. According to
, commercial charge amplifiers have a threshold of 1 fC. The
next section gives an overview of the measurement in the production process.
Measurement during the production processInformation about the injection moulding process
The purpose of this chopper amplifier is the measurement of pressure sensor
signals inside the cavity during the injection moulding process. To get a
better understanding of the injection moulding tool, it is necessary to give
some information about it. The application for our sensor system is a two-component injection moulding tool. The tool produces a two-component
multipurpose test specimen
The multipurpose test specimen is also
referred to as a tensile bar or test piece.
as specified in . Additional
information for the topic of polymer testing can be found in
p.15 and . For the measurement of the
production quality of the tensile bar, a range of sensors within the
injection moulding tool is accommodated. The sensor positions and different
sensor types are illustrated in Fig. .
A 3-D model of the investigated tool with the different sensor types and their respective positions.
The red points show the positions of the thermocouple sensors. The yellow points are the piezoresistive
force sensors, also called load cells. The blue points are the piezoelectric pressure sensors, which are
used for the measurement of the injection pressure of the molten plastics. A view of the cut through the plane
is displayed in Fig. .
For the temperature measurement of the flowing plastics, four thermocouples are
inserted inside the cavity. Furthermore, two thermocouples are applied inside
each tool half to measure the tool temperature. Four piezoelectric pressure
sensors are inserted inside the cavity of the injection tool. They measure
the injection pressure of the flowing plastics melt. The two load cells are
placed between the ejector pins and the ejector plate. They record the
ejection force of the produced tensile bar after the cooling phase of the
process. The secondary effect of this kind of sensor is an indirect injection
pressure measurement. Figure shows the produced test piece;
on the right side is a cut through the moulding tool at the ejection step of the
final product.
On the left side is a sketch of the produced two-component tensile bar. On the right side is a
cross-section of the moulding tool to show the ejector and the sensor position.
In Fig. , the injection moulding tool with mounted embedded
measurement hardware (EDS) is shown.
A photograph of the moving side of the two-component injection moulding tool. In the middle
of the picture is the embedded measurement hardware (EDS; ).
Measurement results during the manufacturing process
In this section, the measurement results during the
manufacturing process are described. The signal from the chopper amplifier is
shown in Fig. . The recording time was limited to 50 s, which is the interval time for the manufacturing process of the
produced tensile bar in the injection mould.
The sampled chopper signal positive pressure changes result in a downward-facing peak relative to
the reference voltage (resulting pressure gradient at Priamus 6001A).
The negative modulation in the charge curve in Fig. is due to the mechanical structure of the piezoelectric
sensor. A inversion of the signal around the reference voltage can be
achieved with software. With the mathematical operations described in Sects. and , the pressure signal can be reconstructed. In
Fig. , the results of the calculations and integration of the
chopper signal are displayed. It illustrates one injection moulding process
with a very low noise level.
The results of the absolute value of the integrated chopper signal after the mathematical operations.
It is the reconstructed injection pressure of the plastics melt into the cavity.
For the validation of the pressure signal, a second sensor can be used. As
shown in Fig. , the force sensors are in a good position to
perform an indirect measurement of the injection pressure. The measured force
signal of the same production cycle as in the previous pictures is displayed
in Fig. .
A diagram of the pressure curve at the KM26 force sensor.
Both measurement results from Figs. and have a similar shape. A major difference lies in the
recorded noise levels of these sensors. The interference level from the force sensor is greater than that of the integrated pressure signal.
Furthermore, a significant temporal difference between the sensor signals can be observed after 40 s. The reason for that can be the
different measurement positions of each sensor in the moulding tool. The greatest difference can be found in the drift of the integrated
chopper signal. The reasons for that are described in Sect. .
In Fig. , the 25 piezoelectric pressure curves of
the chopper charging amplifier are shown.
The 25 production intervals measured by the chopper charging
amplifier;
the interval time is 50 s.
As can be seen, the waveform of the chopper amplifier has a drift in the
pressure data. These differences are clearly visible at the end of the
measurement. Due to the parallel recording of the force signals, the
measurements can be compared directly.
The 25 production intervals measured through the force sensors; the interval time is also 50 s.
These production cycles are the same as in Fig. .
In Fig. , no drifts in the force signals could be found.
In both Figs. and , it can be seen that
some production intervals have a different shape. This is an indication
of non-optimal production parameters for these test pieces. The automatic
classification of production quality is part of the work of
and . In the following section,
the signal fusion with a Kalman filter is described.
Signal optimisation with a Kalman filterTheory of the Kalman pressure estimation
Various software filters were investigated in order to improve the signals.
One opportunity for the signal optimisation is the Kalman filter. It is
assumed here that the chopped pressure signals are applied to the input of
the model and transferred into the force signals through the behaviour of the
system. This is a kind of real-time data fusion from one pressure and one
force signal. For a better understanding, a
sketch of this system with the simplified mathematical operations is shown in Fig. .
The Δ block in the figure describes the differentiation of the sampled
chopper signal. This operation eliminates the reference voltage in this data
series. The next block (-1) inverts the signal. The two Δ-1
blocks describe the two-time integration of the signal to generate the
force signal.
A sketch of the system model with the pressure signal as input and the system, measurement
noise and the measured force signal as output.
The prerequisite for the calculation of the Kalman filter is the state-space
representation for the system. Eqs. () and () are
used here as the basic equations for the discrete state-space model similar
to , .
xn+1=Ad⋅xn+Bd⋅un+wn;n∈N,yn=Cd⋅xn+vn.
The matrices for Eqs. () and () are simplified and
optimised for implementation in an embedded system for integer
calculations and higher accuracy:
Ad=1101 ; Bd=01 ; Cd=10.
The internal states xn+1 of the system depend only on the
last state from the past x and the input variables un.
The index n is the sample number. The system noise wn and
the measurement noise vn are shown in Fig. . Both
can be calculated as the standard deviation of the respective signal and were
used to model the uncertainty of the system and the measurement.
A detailed sketch of the filter design with the addition of the recursive
Kalman filter in the lower part .
An illustration of the transient phenomenon of the filter
coefficients k1 and k2 of the Kalman filter.
As Eqs. () and () show, the reference voltage is
still contained in the measured value. One possibility for the removal of the
reference voltage is illustrated in Fig. . The
quantity calculated with Eqs. () and ()
represents the input value un of the state-space model:
In order to transfer the input variable un into vector form, it is
multiplied by the input matrix Bd. The system matrix
Ad describes the double integration of the system model, as can
be seen in Fig. . Thus, it should be possible to
reconstruct from un the force progression yn. The two downstream
elements in the system model perform these mathematical operations (see Fig. ). The Kalman filter created with these assumptions works
here as a state observer. It tries to approach the internal states of the
system based on an estimate u^n. The filter is represented as a
parallel structure of the real system. In Fig. , the filter
design is displayed. So that the filter can respond to deviations in the
system range, the output yn will be constantly compared to the output
y^n of the filter. The difference between these values is used as a
correction value for the estimated states x^n of the
filter:
Kn=k1k2.
The correction values act through matrix K on the state vector of
the filter. The values k1 and k2 are the filter coefficients and
are adjusted after each iteration of the filter calculation based on the
error between yn and y^n. With Eqs. () and (), the required covariance matrix Q of the system
noise ω and the covariance matrix R of the
measurement noise v can be calculated. In this special case, the matrix
R is only a scalar:
Q=Bd⋅σsys2⋅BdT,R=σmeas2.
With the predetermined values, the recursive algorithm can determine the
covariance matrices Pn- and Pn for the
calculation of the estimation error vectors e- and e
according to , :
en-=xn-x^n-,en=xn-x^n.
Matrices and variables with superscript minus are designated as a priori
estimations. The a posteriori values are denoted without a minus. The
following calculation steps run in parallel to the actual filtering process
and illustrate the adaptation of the filter coefficients:
A representation of the force signal (light blue), the piezoelectric signal (blue) and the
result of the Kalman filter (red) for one injection moulding cycle.
These operations enable the calculation of the internal states
x^n of the filters. The state vector is multiplied by
the output matrix C, and as a result the output size y^n
of the filter is created. Figure shows the expanded
configuration of the filter design with the addition of the recursive
algorithm.
The results of the developed Kalman filter are described in the next section.
Results with application of a Kalman filter
The Kalman filter requires a certain time to settle before it provides useful
results from the data fusion. The time needed is approximately 10 s. In Fig. , the curve of the filter coefficients during the settling
phase is illustrated.
It shows that the coefficient k1 only affected the estimates. The value
k2 has no effect on the state estimations. In order to obtain stable
filter coefficients, it is necessary to conduct an offline training of the
Kalman algorithm. The precomputed coefficients enable the usage without a
settling phase. This is a great advantage for implementation in the EDS.
The light blue graph in Fig. shows the recorded force signal
without filtering. The red curve is the result of the combined sensor signals
with the Kalman filter. As one can see, the merged signal has almost no
interference and shows good adaptation to the force curve.
The Kalman filter provides good results by reducing the interference level
and the offset at the beginning of the force signal. The second point is the
elimination of the drift error in the piezoelectric pressure signal. The last
feature of the data fusion is the filter phase delay of zero. However, the
quality of the data fusion depends on the sensor position and the geometry of the
tool cavity. In our case, the data fusion is useful for both force sensors in
the ejector.
Conclusions
Two major advantages of this chopper amplifier
are the ground connection of the sensor and the single power supply. The ground
connection of the amplifier input results in better shielding of the sensor
signals in industrial environments. In special cases, the amplifier can be used
with only one cable connection to the piezoelectric sensor. The contact to
the ground could be achieved through the tool connection with the metal case of the
chopper amplifier.
As can be seen from the results in Sect. , the interference
of the 50 Hz power grid frequency could be eliminated through the
integration of the signal. This voltage drift is likely due to an integration
error caused by the interference voltages, an error in the reference voltage and the
short “reset” phases during the chopping of the input signal. This error varies
in every measurement and depends on the interferences in the chopper
amplifier and the chopper signal. The developed chopper amplifier is very
robust against external noise. The disturbances during the determination of
the signal-to-noise ratio coincide temporally with the start of a permanently
installed fan in the climate chamber. The fan motors generate a
disturbance peak in another spectral section, which can worsen the SNR by
up to 4 dB. In further work, this effect is reduced with better
electrical shielding of the electronics.
The calculated threshold of 0.1 pC in Sect. is approximately
100 times worse than in commercial charge amplifiers. However, they have
considerably larger dimensions and a significantly higher supply voltage;
most of the piezoelectric sensors have an accuracy of 10 pC bar-1. For this
reason, the question arises of whether it is useful to use high-precision amplifier
technology in injection moulding. However, a task for future work is to
improve the sensitivity of the chopper amplifier. With dimensions of
approximatively 2 to 3 cm, a small PCB design could be achieved, but it
would still need to be optimised.
The amplifier was able to be tested for functionality with the
measurements in the current manufacturing process. The differences described
in Sect. between the pressure and force signals over time may be
due to the different position of the sensors in the cavity
or the ejection mechanism mounted on the force sensor as described in
Sect. . The developed charge amplifier provides robust and
clean results at a sufficient resolution during the production process. With
the aid of a Kalman filter, it could be shown that a data fusion between
force and pressure signals is possible, and an improvement in the signal
quality can be achieved. The noise of the force signal can be reduced. The
previously measured drift phenomena in the pressure signal can be eliminated
by the data fusion. Furthermore, an advantage of the Kalman filter is that
the phase delay of the digital filter is zero.
The result of this investigation is a reduction in the equipment costs for
pressure measurement inside an injection moulding tool. With this chopper
amplifier and the software filtering of the force and pressure signals, the
prices for sensor equipment can be reduced. It could also be a suitable
solution for multi-cavity tools. The points on the requirement list from
Sect. could be achieved. Data fusion
for injection moulding processes is still the subject of current research.
With this contribution, it could be shown that the developed amplifier for
measuring the charge transfer of piezoelectric sensors has good properties
and can be used in embedded systems.
The data and results presented in this contribution are part of further research project and special for
the used injection moulding machine and tool. Furthermore, the data series itself does not carry any relevants besides
demonstrating the chopper charge amplifier and the signal optimisation. Therefore, the data series are not available
online, but the authors can provide sample data upon request.
Manuel Schneider and Alexander Jahn designed the schematic circuit diagram, the test environment and
the construction of the prototype chopper amplifier. The data analyses, software development and filter design were
accomplished by Norbert Greifzu, Manuel Schneider and Norbert Fränzel.
The authors declare that they have no conflict of interest.
Acknowledgements
The authors would like to thank the Thüringer Aufbaubank as a project
sponsor for this research. The results of the underlying work were
funded by the State of Thuringia and the European Union (ESF), project number
2013 FRG 0130.
Edited by: E. Starke
Reviewed by: two anonymous referees
ReferencesChoi, K.: Measuring of dynamic figures: SNR, THD, SFDR, Department of Computer
Science and Engineering, Pennsylvania State University,
available at: http://www.cse.psu.edu/~chip/course/analog/lecture/SFDR1.pdf (last access: 6 May 2017),
2006.Enz, C. C. and Temes, G. C.: Circuit techniques for reducing the effects of
op-amp imperfections:autozeroing, correlated double sampling, and chopper
stabilization, P. IEEE 84.11, 10.1109/5.542410, 1996.
Gautschi, G.: Piezoelectric Sensorics – Force Strain, Pressure, Acceleration
and Acoustic Emission Sensors Materials, 978-3-662-04732-3, Springer, 2002.
Greifzu, N.: Entwicklung von Hard- und Software zur Messung von Kraft-, Druck-
und Temperatursignalen in Kunststoffspritzgussmaschinen, Master's thesis,
University of Applied Sciences Schmalkalden, 2015.Grellmann, W. and Seidler, S.: Polymer Testing, vol. 2, Carl Hanser Verlag,
10.3139/9781569905494, 2013.Higgins, W. T. J.: A Comparison of Complementary and Kalman Filtering, IEEE Transaction on Aerospace and Electronic Systems, 11.3, 321–325,
10.1109/TAES.1975.308081, 1974.
ISO 294-1: Plastics – Injection moulding of test specimens of thermoplastic
materials, Beuth Verlag GmbH, 1996.
Jahn, A.: Konzeption, Umsetzung und Test einer analogen
Signalaufbereitungsschaltung für piezoelektrische Drucksensoren, Bachelor's
thesis, University of Applied Sciences Schmalkalden, 2015.Kistler Group: Industrial Charge Amplifier for Applications in
Manufacturing Type 5073A,
available at: https://kistler-embedded.partcommunity.com/3d-cad-models/FileService/File/kistler/07_electronics/01_charge_amplifiers/02_industrial/5073a_english.pdf (last access: 6 May 2017),
2012.
Priamus System Technologies GmbH: PRIAMUS Easy Ladungsverstärker Typ en
5050A/5050A-M01/5050A-M02/5050A-M03,
available at: http://www.priamus.com/index.php?option=com_jdownloads&Itemid=245&view=finish&cid=335&catid=143&m=0&lang=de (last access: 6 May 2017),
2015.Schneider, M. and Wenzel, A.: Entwurf eines Eingebetteten Diagnosesystems zur
Überwachung von Prozessparametern bei Spritzgießen, in: Tag der Forschung,
University of Applied Sciences Schmalkalden, 10.13140/RG.2.1.4739.5441,
2014.Schneider, M., Jahn, A., Greifzu, N., and Fränzel, N.: Entwicklung eines
unipolaren differentiellen Ladungsverstärkers für die Anwendung in
eingebetteten Diagnoseseystemen zur Druckmessung in Spritzgussmaschinen, in:
18. GMA/ITG-Fachtagung Sensoren und Messsysteme, 782–789,
10.5162/sensoren2016/P9.2, 2016a.Schneider, M., Jahn, R., and Wenzel, A.: Erprobung eines echtzeitfähigen
Auswertungsalgorithmus zu Bewertung der Fertigungsqualität beim
Spritzgießen mit Hilfe eines eingebetteten Diagnosesystems, in: 17.
Nachwuchswissenschaftlerkonferenz, University of Applied Sciences
Schmalkalden, 10.13140/RG.2.1.3829.2887/1, 2016b.Schneider, M., Walther, C., and Wenzel, A.: Classification of Production
Quality in Injection Moulding with an Embedded Diagnostic System Using a
Fuzzy Inference System, 26. Workshop Computational Intelligence, 193–203, 10.5445/KSP/1000060007, 2016c.Seefried, A. and Drummer, D.: Prüf- und Probekörperwerkzeuge am Lehrstuhl
für Kunststofftechnik, Friedrich-Alexander Universität Erlangen-Nürnberg,
available at: http://www.lkt.uni-erlangen.de/laboratorien-technika/fertigungseinrichtungen/Pruef-und Probekoerperwerkzeuge.pdf (last access: 6 May 2017),
2015.
Unbehauen, H.: Regelungstechnik II: Zustandsregelungen, digitale und
nichtlineare Regelsysteme, vol. 9, Vieweg+Teubner Verlag, 2009.
Welch, G. and Bishop, G.: An Introduction to the Kalman Filter, University of
North Carolina, Department of Computer Science TR 95-041, 2000.