Download Simulation of Self Calibrated Linear Variable Differential

IJECT Vol. 6, Issue 1, Spl-1 Jan - March 2015
ISSN : 2230-7109 (Online) | ISSN : 2230-9543 (Print)
Simulation of Self Calibrated Linear Variable Differential
Transformer (LVDT) using PIC Micro-controller
1
Koushik Pyne, 2Vishwanath Gupta
Director, G.E Motors PVT. LTD, Sheoraphully, India
Assistant Professor, Dept. of EE, SKFGI, Mankundu, WB, India
1
2
Abstract
In this proposed work a Linear Variable Differential Transformer
(LVDT) is self calibrated with the help of a PIC18F458
(Programmable Inter-phase Controller) microcontroller based on
the regression equation which is derived by the method of least
squares. The proposed work is simulated based on experimental
data obtained from LVDT trainer kit by using the software Proteus
Design Suite ISIS Professional v7.7SP2 which incorporates
PIC18F458. However, the standard data obtained are digital which
need to be converted to analog form for real time applications.
(digital) is given at the input port of the microcontroller and the
corresponding error is calculated using interpolation technique (as
the error varied linearly between two consecutive test data) and
then the corresponding standard data is obtained and displayed
at the output port. This digital data can then be converted to
corresponding analog data with the help of Digital to Analog
converter and used as control signals for various applications.
The scheme of the proposed work can be explained with the help
of the schematic diagram shown in fig. 1.
Keywords
Self-Calibration; Regression; Microcontroller
I. Introduction
In the present scenario of technological advancement, sensors are
playing a very important part. They are part of almost all major
upcoming technologies. Sensors have found various applications
in our day to day life and their use is increasing to a rapid extent.
They are the heart and soul of almost every automation circuit of
present day. Various sensors like temperature sensors, magnetic
sensors, position sensors etc. have already found immense
applications in recent technological advancements. But, most
of the sensors that are being used are not standard. In order to
make the sensors standard, they have to be calibrated with the
help standard sensors or they can be self calibrated as has been
discussed in the proposed work. In this proposed work a Linear
Variable Differential Transformer (LVDT) is self calibrated
with the help of a PIC (Programmable Interphase Controller)
microcontroller based on basic statistical methods. The proposed
work if found to give acceptable results will help to calibrate most
of the modern day sensors whose standard data follow specific
mathematical functions. This will help us to remove the various
inherent instrumental errors and make our calculations more
accurate. Although the standard values could have been obtained
by writing simple programs in C or MATLAB but, then these
standard values could not be used as control signals as they are not
actually obtained at the sensor output. In order to make the standard
values available as control signals an additional interface has been
created via PIC microcontroller. The self calibrated sensor will
be more accurate and the output can be post processed with more
accuracy and applied to various control circuits which control
particular processes. This will enhance the credibility of the system
in which the self-calibrated sensor is used.
Fig. 1: Schematic Diagram
The proposed work is simulated by using the simulated model
of PIC18F458 present in Proteus Design Suite ISIS Professional
v7.7SP2 software which has a wide range of electrical and
electronics simulation models including microcontrollers and
gives real time results on the oscilloscope. In order to simulate
the model in Proteus Design Suite ISIS Professional v7.7SP2 the
algorithm for the regression equation needs to be written in C and
converted into corresponding .hex file which is to be burnt on the
simulated model of PIC18F458.
III. PIC18F458 Microcontroller
The PIC18F family of microcontroller is one of the most
advanced and highest performing family among the 8 bit PIC
microcontrollers. The fact that PIC18F458 is available in 18 to
80 pin packages make it an ideal choice for new designs because
it allows easy migration to more powerful versions of the chip
without losing software compatibility. The block diagram of the
PIC18F is shown in fig. 2.
II. Methodology
In the first stage laboratory experiment is performed for obtaining
the test data (analog) for LVDT. Then this analog data is converted
into digital data with the help of microcontroller PIC18F458 and
this data is then used as test data to obtain the best fit curve (straight
line in case of LVDT) by the method of regression. This best fit
curve data is taken as the standard data for the particular LVDT.
So corresponding to each test data we get a standard data and
therefore an error for each test data. In the next stage, a test data
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International Journal of Electronics & Communication Technology 115
ISSN : 2230-7109 (Online) | ISSN : 2230-9543 (Print)
IJECT Vol. 6, Issue 1, Spl- 1 Jan - March 2015
(2)
Equation (1) is known as Regression equation of y on x, and
equation (2) as Regression equation of x on y. The coefficient
byx appearing in the regression equation of y on x is known as
the regression coefficient of y on x. Similarly, bxy is called the
regression coefficient of x on y. The geometrical representation of
the linear regression equation (1) and (2) are known as regression
lines. These lines are “best fitting” straight lines obtained by the
method of least squares [7].
The value of regression coefficient of y on x is given by
(3)
Where, Ryx is the correlation coefficient between x and y
Sy is the standard deviation of y
Sx is the standard deviation of x
The value of correlation coefficient between x and y is given by
Fig. 2: Block Diagram of PIC18
IV. Self-calibration of LVDT
For obtaining the test data for our experiment, the LVDT trainer kit
at the Sensor and Transducer Laboratory of Supreme Knowledge
Foundation Group of Institutions is used as shown in fig. 3.
The value of standard deviation of x is given by
(4)
and the value of standard deviation of y is given by
(5)
(6)
By using the above equations, we can obtain the predicted values
(here the standard data) of the output (voltage) for the corresponding
values of input (displacement) provided in Table 1.
Table 1: Obtained Test Data and Predicted Standard Data
Input Displacement
(mm)
4.22
5
5.5
6
7
7.5
8
Experimental Test
Data (volts)
0
0.63
1.18
1.37
2.1
2.69
3.03
Predicted Standard
Data (volts)
0.03
0.64
1.04
1.43
2.22
2.62
3.01
From the above data, the characteristics (with test data and standard
data) of the LVDT under test were obtained using Matlab 7.1. The
characteristics are shown in Fig. 4 and Fig. 5.
Fig. 3: The LVDT Trainer Kit
From the obtained data, the best fit curve was done using linear
regression equation. In linear regression (or simple regression)
the relationship between the variables is assumed to be linear. The
estimate of y (say y’) is obtained from an equation of the form
(1)
and the estimate of x ( say x’) from another equation (usually
different from the former) of the form
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International Journal of Electronics & Communication Technology
Fig. 4: Experimental Test Data
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ISSN : 2230-7109 (Online) | ISSN : 2230-9543 (Print)
Fig. 5: Predicted Standard Test Data
The algorithm in C language for the prediction of standard result
is now converted to its corresponding .hex file, with the help of
C 18 Tool Suite in MICROCHIP’S MPLAB IDE v8.92.
The .hex file is burnt on the simulated model of PIC18F458 in
Proteus Design Suite ISIS Professional v7.7SP2 and real time
results are obtained. The standard output voltage in digital form
for 8mm displacement is shown in fig. 6.
IJECT Vol. 6, Issue 1, Spl-1 Jan - March 2015
1988.
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Fig. 6: Simulated Result when input is 3.03V
V. Conclusion
From the results obtained it can be concluded that the “.hex” file
generation by MPLAB software is successful. Self calibration of
the LVDT under test is done satisfactorily for LVDT whose output
is in the range of 0-5V. The DAC could not be incorporated in
the model due to its unavailability in the simulation software, but
the digital output is used manually to calculate the corresponding
analog output. The proposed model can be designed in future so
that it can incorporate input values greater than 5V. The proposed
scheme for self calibrating LVDT can also be extended for other
sensors having characteristics different from LVDT.
VI. Acknowledgement
The authors would like to extend their gratitude to the Department
of AEIE, Supreme Knowledge Group of Institutions for providing
the permission of conducting the experiment to obtain test data from
LVDT trainer kit in their Sensors and Transducers laboratory.
References
[1] Patranabis, Ghosh, Bakshi,“Linearizing Transducer
Characteristics”, Vol. 37, No. 1, IEEE Xplore, March,
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