=Paper= {{Paper |id=Vol-1498/HAICTA_2015_paper25 |storemode=property |title=Vacuum Regulation with a VFD Controller: Preliminary Tests and Modeling of the Vacuum System |pdfUrl=https://ceur-ws.org/Vol-1498/HAICTA_2015_paper25.pdf |volume=Vol-1498 |dblpUrl=https://dblp.org/rec/conf/haicta/RoscaCTC15 }} ==Vacuum Regulation with a VFD Controller: Preliminary Tests and Modeling of the Vacuum System== https://ceur-ws.org/Vol-1498/HAICTA_2015_paper25.pdf

Vacuum Regulation with a VFD Controller: Preliminary
Tests and Modeling of the Vacuum System

Radu Roşca1, Petru Cârlescu2, Ioan Ţenu3, Radu Ciorap4
1
Agricultural machinery Department, University of Agricultural Sciences and Veterinary
Medicine Iaşi, Romania, e-mail: rrosca@uaiasi.ro
2
Agricultural machinery Department, University of Agricultural Sciences and Veterinary
Medicine Iaşi, Romania, e-mail: pcarlescu@yahoo.com
3
Agricultural machinery Department, University of Agricultural Sciences and Veterinary
Medicine Iaşi, Romania, e-mail: itenu@uaiasi.ro
4
Bioengineering Faculty, University of Medicine and Pharmacy Iaşi, Romania, e-mail:
radu.ciorap@bioinginerie.ro

Abstract. Using a variable frequency drive (VFD) in order to drive the
vacuum pump of a milking machine allows a dramatic reduction in energy use,
while still producing equivalent vacuum stability. The VFD technology is able
to adjust the rate of air removal from the milking system by changing the speed
of the vacuum pump motor. A PID controller was developed in order to
command the electric motor driving the vacuum pump. The PID controller
used by the vacuum regulating system was tuned using the Ziegler-Nichols
tuning rules for the frequency response method. In order to proceed to a more
systematic approach a mathematical model of the vacuum system was
developed, assuming that the system consists of a single air tank, provided
with a vacuum pump port and an air-using port. In order to validate the model
and study the system’s response to vacuum variation due to a pulse air leak the
detachment (fall-off) of one teatcup was simulated; the teatcup was detached
for 10, 20 and 30 seconds respectively. During the fall-off tests the rate of air
flow into the system was measured by the means of a rotameter and the
vacuum level was recorded. The experimental results were compared with the
ones predicted by the model and it was concluded that the model accurately
describes the response of the system.

Keywords: variable frequency drive, vacuum system model, teatcup fall-off
test.

1 Introduction

The mechanical milking is achieved due to the vacuum applied to the teat, by the
means of a teatcup. In order to limit the development of congestion and edema and
provide relief to the teat from the milking vacuum, the pulsation principle is used
(Mein et al., 1987). As shown in Figure 1, vacuum is applied to the teat through the
vacuum chamber (7) created inside the liner (2). The collapse of the teatcup liner (2)

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beneath the teat is achieved when air at atmospheric pressure is admitted into the
pulsation chamber (5) of the teatcup (Fig. 1a); the liner opens, allowing the
extraction of milk, when vacuum is applied to the pulsation chamber (Fig. 1b).

a) b)

Fig 1. The principle of milk extraction (adapted from Dairy Processing handbook, 1995).
a-massage; b-milk extraction; 1-teat: 2-liner; 3-short pulse tube; 4-short milk tube; 5-pulsation
chamber; 6-shell; 7-vacuum chamber.

Figure 2 presents the layout of a typical mechanical milking system (ISO
3918:2007), which contains a vacuum pump (2), driven by an electric motor (1); the
vacuum pump creates vacuum into the vacuum pipeline (7), which is used for both
the milk extraction and the pulsation of the liner. The vacuum level is regulated by
the means of the vacuum regulator (4), placed downstream of the receiver. The
vacuum pump is permanently operated at full capacity, providing a flow of air
greater than the one entering the system through pulsators, claws, leaks. The
difference between the air extracted by the pump and the necessary flow of air during
milk extraction is compensated by the vacuum regulator, which opens to allow
supplementary air to enter into the system when working vacuum increases above the
desired level and closes when vacuum decreases below the necessary value;
according to the ISO 5707:2007 standard the working vacuum should be maintained
within ±2 kPa of the nominal vacuum.
The importance of vacuum level and stability is due to the fact that cows have a
biological limit for a positive reaction to vacuum and exceeding it may lead to
damage of the teat tissue or slipping of milking clusters off the teat, resulting in an
extended milking time and in improper milking; vacuum fluctuations generated
within the milking cluster may lead to direct bacterial penetration, thus causing
mastitis (Pařilová et al., 2011).
In order to make the vacuum pump draw only the amount of air needed to
maintain the desired vacuum level, the speed of the pump should be variable (as air
flow depends on the pump speed); in this case no conventional regulator is needed to
maintain the imposed vacuum during milking. The electric motor of vacuum pump is
controlled by the means of a variable frequency driver (VFD). This solution has the

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potential to significantly reduce the energy consumption of the milking system; in a
study conducted by Pazzona et al. (2003) energy savings between 24 and 87% were
reported. It was concluded that, if the VFD controller is adjusted properly, it can
meet or even exceed the vacuum stability recorded by the systems equipped with
conventional regulators (Pazzona et al., 2003; Reinemann, 2005), the target being a
receiver vacuum within ±2 kPa of the vacuum set point during normal milking (ISO
5707:2007).

Fig. 2. Layout of a mechanical milking system.
1-electric motor; 2-vacuum pump; 3-interceptor; 4-vacuum regulator; 5-sanitary trap; 6-
vacuum gauge; 7-permanent vacuum pipeline; 8-milk pipeline; 9-pulsator; 10-teatcup
assembly; 11-claw; 12-long milk tube; 13-long pulse tube; 14-receiver; 15-milk pump.

The first stage of the study was aimed to validate the principle of the vacuum
regulation by the means of the VFD controlled vacuum pump. In order to proceed to
a more systematic approach of the problem in the second part of the paper a
mathematical model of the vacuum system was developed and tested, based on the
system’s response to vacuum variation due to a pulse air leak - detachment (fall-off)
of one teatcup.

2 Materials and Methods

A bucket type milking machine was tested and modeled; Fig. 3 presents the
diagram of the milking system. The original system was equipped with a valve and
spring type of vacuum regulator, placed on the pipeline connecting the interceptor (I)
to the bucket (B); the electric motor (M) driving the vacuum pump (VP) was
connected to the three phase power grid. A BRK pneumatic pulsator (P) was used to
achieve the liner pulsation; the machine was equipped with four Boumatic R-1CX
type teatcups. Artificial teats, manufactured according to the ISO 6690:2007
standard, were inserted into the teatcups. The vacuum pump provided an airflow
q=4.69·10-3 m3 s-1 at a speed of 1350 min-1.
In order to use the VFD controller for driving the vacuum pump a Smartec
SPD015AAsil absolute pressure sensor (T, fig. 3) was used to monitor the vacuum in

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the permanent vacuum line, providing the pressure signal for the VFD controller. The
electric signal from the pressure sensor was fed to the data acquisition (DAQ) board
by the means of a signal conditioning unit (SC).

Fig. 3. Schematics of the tested milking system
DAQ-data aquision board; SC-signal conditioning unit; I-interceptor; VP-vacuum pump; M-
electric motor; B-bucket; P-pulsator; SMT-short milk tube; SPT-short pulse tube; T-absolute
pressure transducer; C-claw.

The data aquision board was USB 6009 (National Instruments), with a sample rate
of 48 ksamples/s, four differential analog input channels and two analog output
channels.
Based on the software running on the computer the entire system (DAQ board,
VFD controller and computer) acts as a PID regulator for the vacuum level, for
which the set point (SP) is the desired vacuum level and the process variable (PV) is
the actual vacuum level in the vacuum pipeline. The controller calculates the output
signal u(t), which is then used to command the VFD and adjust the running speed of
the electric motor and vacuum pump. The PID controller output is given by the
relation (Aström and Murray, 2008):

⎡ 1 de( t ) ⎤
u ( t ) = K p ⋅ ⎢e( t ) + ⋅ ∫ e( t ) ⋅ dt + Td ⋅ ⎥ , (1)
⎣ Ti dt ⎦

where the error signal is e(t) = SP-PV; KP is the proportional gain, TI is the integral
time and Td is the derivative time.
The PID controller was built with the help of the PID control toolbox from
LabVIEW 7.1 and a virtual instrument was created in order to provide the control
signal to the VFD. The control panel of the virtual instrument (Fig. 4) allowed the
adjustment of the desired vacuum level (vacuum set point) and of the PID gains:
proportional gain, integral time [min] and derivative time [min].
The output range of the PID controller was 0…5V, due to the characteristics of the
data aquision board; an additional signal conditioning unit (not shown in Fig. 3) was
used to obtain the 0…10V range imposed by the variable frequency drive.
An oscilloscope display allowed the visualization of the vacuum set point, system
vacuum and output signal of the PID controller.

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Fig. 4. The control panel of the virtual instrument

The variable frequency drive unit was VFD 007M43B (0.7 kW maximum power
of the electric motor); the output frequency range was set to 0...60 Hz for a range of
the analog comand signal comprised between 0 and 10V.
In order to establish the working parameters of the milking process (pulsation rate
and ratio, duration of the phases), two additional Smartec SPD015Aasil absolute
pressure sensors (not shown on the diagram in Fig. 3) were attached to the short
pulse tube (SPT, Fig. 3) and short milk tube (SMT). The pulsation ratio was defined
according to the specifications of the ISO 5707:2007 standard.
The Ziegler-Nichols tuning rules for the frequency response method were used;
the disturbance was induced by changing the set point. After that the permanent
vacuum values were recorded in a series of dry tests, performed for three vacuum
levels: 0.35 bar, 0.40 bar and 0.45 bar (35, 40 and 45 kPa). In order to asses vacuum
stability the results were compared, using the average value of the vacuum, the
standard deviation and the standard error of the mean. Three tests were performed
for each vacuum level and vacuum regulation method and the mean, standard error
and standard error of the mean were calculated.
In order to evaluate whether there was a significant difference between the two
pairs of data (the permanent vacuum levels recorded for two regulation methods) a
statistical analysis was performed. The Kolmogorov-Smirnov test proved that data
distribution was not normal; as a result, the Man Whitney rank sum test was
performed; this test is a substitute for the two-sample t test when the samples are not
normally-distributed populations (Panik, 2005). The analysis was performed with a
demo version of the SigmaPlot 12.5 software.
The mathematical model of the vacuum system was developed assuming that the
system is composed of a single air tank, provided with a vacuum pump port and an
air-using port (Tan, 1992; Tan et al., 1993), as shown in Fig. 5, where m ! 1 represents
the mass airflow rate of the vacuum pump and m ! 2 is the mass airflow rate into the
system.

206
Fig. 5. Schematics of the milking
system [5]

! 2 -mass air flow rate
! 1, m
m

The following equations may be written [6]:

dM M ,
! 2 −m
=m !1 =m
! 2 −q⋅ (2)
dt V
M ,
p = R ⋅T⋅ (3)
V
where M is the mass of air in the air tank, V is the tank volume, q is the volumetric
flow rate of the vacuum pump, R is the gas constant for air (R=287 J⋅kg-1⋅K-1) and T
is the air temperature [K].
Using equations (2) and (3) the transfer function of the system is (Tan et al.,
1995):

p(s) R ⋅T/q .
G (s) = = (4)
! 2 (s) 1 + s ⋅ V / q
m

Fig. 6 presents the system response when the air flow rate increases due to the
detachment of one teatcup: when the mass flow rate m ! increases by m ! p , the
absolute system pressure pn increases by pp.

Fig. 6. Model response to mass
airflow rate variation (Tan et al.,
1993)

p-absolute pressure; t1-detachment
duration.

! p is (Tan et al., 1993):
The mass flow rate resulting from the pulse air leak m

!p
m !p
m
! (s) =
m − ⋅ e − t 1 ⋅s . (5)
s s

207
Introducing equation (5) into equation (4) and applying the inverse Fourier
transform finally leads to:

R ⋅T
p( t ) =
q
⋅m [ ]
! p ⋅ Φ ( t ) − Φ ( t − t1 ) − e − q ⋅ t / V + Φ ( t − t1 ) ⋅ e − q ⋅( t − t 1 ) / V , (6)

where Φ(t) is the step function, defined as follows:

0, if t < 0 .
Φ( t ) = { (7)
1, if t ≥ 0

For the milking system taken into account the singe tank volume (which includes
the interceptor volume and the bucket volume) was V=3.5⋅10-2 m3 and the air
temperature was T=293 K.
In order to validate the model and study the system’s response to vacuum
variation due to a pulse air leak the detachment (fall-off) of one teatcup was
performed; the teatcup was detached for 10, 20 and 30 seconds respectively. During
the fall-off tests the rate of air flow into the system was measured by the means of a
rotameter and the evolution of the vacuum level was recorded using the pressure
sensor (T, Fig. 3).
The air flow rate into the system during the fall-off test was m ! p =7.6⋅10-5 kg⋅s-1
(average value).
The steady state gain K of the model and the time constant τ were calculated with
the relations (Tan et al., 1993):

R ⋅T V .
K= , τ= (8)
q q

For the milking system taken into account the following values were obtained:
• K=1.79⋅105 kPa⋅s⋅kg-1;
• τ=7.47 s.
Using the experimental data the system steady state gain Ks and the time constant
τs were evaluated. The system steady-state gain was calculated with the formula:

Δp ,
Ks = (9)
!p
m

where Δp is the vacuum drop when the teatcup is detached.
The time constant τs was considered to be the time required for the output
vacuum to reach 63.2% of the final value when the teatcup was detached.

208
3 Results and Discussion

3.1 Vacuum stability

In order to tune the PID controller using the Ziegler-Nichols tuning rules for the
frequency response method, the integral time was set at 10000 and the derivative
time was set to 0; the proportional gain was adjusted until the oscillations were
sustained and had a constant amplitude. Finally, the critical gain was Kc = 68. The
critical period Tc was measured using the recorded vacuum signal; it was established
that the critical period was Tc = 7.53±0.46 s. The PID gains were then calculated
using the formula presented in Table 1 (Aström and Murray, 2008).

Table 1. Controller parameters for the Ziegler-Nichols frequency response method

Controller type KP Ti Td
P 0.5·Kc - -
PI 0.4·Kc 0.8·Tc -
PID 0.6·Kc 0.5·Tc 0.125·Tc

For the case of the PID controller, the following gains were obtained: KP = 40, Ti
= 4.76 s (0.062 min), Td = 0.941 s (0.015 min).
The results referring to the working parameters of the system and vacuum stability
are shown in Tables 2 and 3.

Table 2. Working parameters of the milking system

Regulati Vacuum level [kPa]
Item
on method 35 40 45
Pulsation rate
48.4±0.231 51.9±0.266 55.9±0.200
[cycles/min]
Pulsation ratio [%] 55.1/44.9 53.7/46.3 53.3/46.7
Vacuum
Duration of b
regulator 44.9±0.137 41.98±0.362 39.74±0.270
phase* [%]
Duration of d
0.42±0.005 0.387±0.003 0.343±0.003
phase** [s]
Pulsation rate 48.9±0.352 52.2±0.500 56.4±0.167
[cycles/min]
Pulsation ratio [%] 54.6/45.4 53.8/46.2 53.2/46.8
PID
Duration of b
controller 44.02±0.352 41.21±0.405 39.40±0.113
phase [%]
Duration of d
0.42±0.006 0.387±0.012 0.337±0.003
phase [s]
* **
Notes: at least 30% of the cycle duration; at least 0.15 s.

The results presented in Table 2 show that the working parameters of the system
(pulsation rate and ratio, duration of the cycle phases) did not change significantly
when passing from the classical method for vacuum regulation (based on the use of a

209
valve type regulator) to the new one, based on the adjustment of the vacuum pump
speed. A slight increase of the pulsation rate was however noticed when the second
method was used, but the differences did not exceed 1%; the slightly higher pulsation
rate resulted in a shorter b phase when the PID controller was used for vacuum
regulation, but the requirements of the ISO 5707 standard were fulfilled.
An analysis of the individual values of the permanent vacuum showed that, for the
both methods, the working vacuum was maintained within ±2 of the nominal vacuum
kPa, in accordance with the requirements of the ISO 5707 standard.
The results presented in Table 3 show that the use of the PID controller method
for vacuum regulation led to lower standard deviations and standard errors of the
mean than the ones recorded when the classical vacuum regulator was used, proving
a better vacuum stability.
The statistical analysis of the results, performed by the means of the Man Whitney
rank sum test (SigmaPlot ver. 12.5, demo), confirmed that, for each set value of the
vacuum level (35, 40 and 45 kPa, respectively) there were significant differences
between the two sets of data.

Table 3. Results regarding vacuum stability

Regulation Vacuum level (SP) [kPa]
Item
method 35 40 45
mean vacuum level, x [kPa] ♣ 34.417 39.462 44.398
standard deviation, S [kPa] 0.202 0.230 0.226
Vacuum regultor
standard error of the mean, S x ♣♣

0.0142 0.0162 0.0159
[kPa]
mean vacuum level, x [kPa] 34.514 39.381 44.580
standard deviation, S [kPa]
♣ 0.172 0.194 0.186
PID controller
standard error of the mean, S x ♣♣

0.0121 0.0137 0.0131
[kPa]
Notes: for 200 recorded values; S x = S / n
♣ ♣♣

3.2. Vacuum system model

Fig. 7 presents the experimental results of the fall-off tests; the model data
(“model”) and data from three experimental replicates (“experiment 1”, “experiment
2”, “experiment 3”) are shown on each chart, with the ±2.5% y errors bars superposed
over the model curve.
The tests clearly show that there are only small differences between model and
experimental data and that the curves corresponding to the experimental data follow
closely the theoretical curves predicted by the model, the majority of the experimental
data being within the ±2.5% variation domain.
Table 4 presents the results concerning the steady-state gain and time constant
obtained from the experimental results; the experimental steady-state gain is with 9%
lower than the value given by the model and the time constant of the system is with

210
20% lower than the value predicted by the model.

43.00 43.00

41.00 41.00

39.00 39.00

37.00 37.00

vacuum [kPa]
vacuum [kPa]

35.00 model 35.00
model
experiment1
33.00 33.00 experiment1
experiment2
31.00 31.00 experiment2
experiment3
experiment3
29.00 29.00

27.00 27.00

25.00 25.00
0 10 20 30 40 50 60 0 10 20 30 40 50 60
tim e [s] tim e [s]

a) b)
43.00

41.00

39.00

37.00
vacuum [kPa]

35.00 Fig. 7. Experimental and model data
model
33.00 experiment1

31.00 experiment2 a) 10 s detachment of the teatcup;
29.00
experiment3
b) 20 s detachment of the teatcup;
27.00 c) 30 s detachment of the teatcup.
25.00
0 10 20 30 40 50 60 70
tim e [s]

Table 4. Experimental results for the time constant and steady-state gain

Item
Teatcup detachment time [s]
Ks⋅10-5 [kPa⋅s/kg] τs [s]
10 1.34 4.72
20 1.72 5.7
30 1.82 7.6
Average 1.63±0.146 6.00±0.845

The inaccuracy of the predicted time constant may be due to the assumptions that
air is a perfect gas and that the system is isothermal, with only small variations of the
air temperature (Tan, 1992; Tan et al., 1993). If the process is considered adiabatic
(Tan et al., 1993; Tan et al., 1995), the time constant is calculated with the
relationship:

V ,
(10) τ=
γ ⋅q
where γ=1.4 is the heat capacity ratio of air.
As a result the time constant of the model becomes τ=5.33 s, a value which is

211
much closer to the average value of 6 s given by the experiments (12,5% lower).

4 Conclusions

The permanent vacuum level in a bucket milking machine was adjusted by the
means of a PID regulator, using a variable frequency driver in order to power the
electrical motor driving the vacuum pump. The PID regulator, implemented using
the NI LabView capabilities, was aimed to maintain a constant vacuum level.
The PID regulator was tuned in order to establish the PID gains using the Ziegler-
Nichols frequency response method.
A series of dry tests were performed, at different vacuum levels, in order to
compare the two methods of vacuum regulation (using a mechanical vacuum
regulator and a PID regulator, respectively); the tests proved that vacuum regulation
by the means of the PID controller has the potential to replace the classical method of
regulation as it did not adversely affect the working parameters of the system, while
achieving better results regarding the stability of the permanent vacuum.
As the principle of the vacuum regulation by controlling the vacuum pump speed
was confirmed the next step was to develop a mathematic model of the milking
system in order to proceed to a more rigourous analysis of the system. As a first step
a simplified physical model was adopted, considering the mechanical milking system
as first order dynamic system with a single air tank, provided with a vacuum pump port
and an air-using port.
In order to validate the model and study the system’s response to vacuum variation
due to a pulse air leak the detachment (fall-off) of one teatcup was simulated; the teatcup
was detached for 10, 20 and 30 seconds respectively. During the fall-off tests the rate of
air flow into the system was measured by the means of a rotameter and the vacuum level
was recorded.
As a result of the tests it was concluded that the developed model is accurate, the
majority of the experimental values being comprised within the ±2.5% range of the
model.
However, the assumption that the process is isothermal led to a relatively high
difference between the predicted value of the time constant and the value obtained during
the experiments. This difference diminished if the adiabatic hypothesis was considered.
Developing a more complex model of the milking system is taken into account for a
future work, aiming to obtain more accurate predictions.

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