PRÁCTICA 2. ACCELEROMETER (2017)Pràctica Inglés
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Alba Martín, Anna Reig
INERTIAL SYSTEMS: ACCELEROMETER
Simulation with Lab View software
Implement signal processing by an inertial system
Use LabView in a more fluently way and get introduced in new LabView libraries
Learn how to use the data acquisition card KUSB-3100 from KEITHLEY
Learn how to use and how to calibrate the accelerometer MMA6270QT from Freescale
Learn how from an accelerometer through a data acquisition card it is possible to get real acceleration
Work with analogue and digital worlds at the same time
Apply mathematical equations to transform voltage data obtained from the accelerometer into
acceleration data to then integrate and compute velocity and position data
The main aim of this exercise is to experimentally develop a signal processing with signals generated by an
inertial system. The inertial system used is an accelerometer which generates analogue signals processed by
a data acquisition card (DAC). This DAC generates, in turn, digital signals readable by the computer.
The process needed for this implementation is summed up as follows. First, the specifications of the accelerometer and the DAC are needed to carry out the next steps. Once got, both devices can be connected between them without conditioning necessity. Subsequently, the adquisition card can be connected to the computer acting as a voltage generator for the sensor. Now the sensor is on and generates a voltage equivalent to the measured acceleration. Consequently, it must be converted to acceleration values making use of LabView. Then integrating them, the velocity and the position can be computed. Finally, as the sensor has systematic error as all electronic devices, the system has to be calibrated so to get accurate results.
2. Technical specifications and relevant parameters First of all, the specifications and values relatives to the accelerometer sensor and the DAC are needed to carry out all the following steps. The DAC used in the laboratory corresponds to the KUSB-3100 model from Keithley and the one concerning to the accelerometer is the MMA6270QT from Freescale.
DATA ACQUISITION CARD INPUT Number of analogic acquisition channels Input voltage range for signal acquisition Number of bits for A/D converter A/D converter resolution 1 8 channels ±10 V 12 bits 4,88mV Alba Martín, Anna Reig DATA ACQUISITION CARD OUTPUT Number of signal generation channels Output voltage range for signal generation Number of bits for D/A converter D/A converter resolution OTHERS Maximum sampling frequency Input Impedance 2 channels ±10 V 12 bits 4,88mV 50kbauds 10MΩ, 100pF Table 1 KUSB-3100 DAC characteristics  ACCELEROMETER Full scale voltage and typical voltage supply Sensibility of the characteristic equation Uncertainty of the sensibility Offset of the characteristic equation Uncertainty of the offset Output impedance 3,3V 800 mV/ g ±7,5% (±60 mV/ g) 1,65V ±10% (±0.165 V) 1kΩ, 0.1µF Table 2 MMA6270QT accelerometer characteristics  Most of the previous values have been obtained from the datasheet of already mentioned devices. However, some of them have been calculated. Let’s see how they have been got.
- A/D and D/A converter resolution 𝑉𝑚𝑎𝑥 − 𝑉min 10𝑉 − (−10𝑉) ΔR = = = 4,88𝑚𝑉 2𝑛𝑏𝑖𝑡𝑠 212 - Uncertainty of the sensibility 𝑆𝑒𝑛𝑠𝑖𝑏𝑖𝑙𝑖𝑡𝑦 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 = - 𝑉𝑚𝑎𝑥 − 𝑉𝑚𝑖𝑛 860𝑚𝑉 − 740𝑚𝑉 = · 100 = 7.5% 2 · 𝑉𝑡𝑦𝑝 2 · 800𝑚𝑉 Uncertainty of the offset 𝑂𝑓𝑓𝑠𝑒𝑡 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 = 𝑉𝑚𝑎𝑥 − 𝑉𝑚𝑖𝑛 1,815𝑉 − 1,485𝑉 = · 100 = 10% 2 · 𝑉𝑡𝑦𝑝 2 · 1,65𝑉 3. Theoretical approximation Once got all the specifications in mind and before starting connecting devices, it is important to evaluate if there is a significant load effect produced between the sensor and the DAC when connecting them without any conditioning. To do so, the following schema must be considered where Vin is the voltage given by the sensor and Vo is the voltage received by the DAC, besides R1=1kΩ and R2=1MΩ.
2 Alba Martín, Anna Reig SENSOR DATA ACQUISITON CARD Figure 1 Connection scheme between the sensor and the data acquisition card Theoretically, 𝑉𝑜𝑢𝑡_1 = 𝑉𝑖𝑛 In practice, 𝑉𝑜𝑢𝑡_2 = 𝑅𝑎𝑐𝑞𝑢𝑖𝑠𝑖𝑡𝑖𝑜𝑛 𝑐𝑎𝑟𝑑 10𝑀Ω · 𝑉𝑖𝑛 = · 𝑉 = 0,9999001 · 𝑉𝑖𝑛 𝑅𝑎𝑐𝑞𝑢𝑖𝑠𝑖𝑡𝑖𝑜𝑛 𝑐𝑎𝑟𝑑 + 𝑅𝑠𝑒𝑛𝑠𝑜𝑟 10𝑀Ω + 1𝑘Ω 𝑖𝑛 Consequently, the error committed can be computed as follows.
𝑉𝑜𝑢𝑡_1 − 𝑉𝑜𝑢𝑡2 = 𝑉𝑖𝑛 · (1 − 0,9999001) → 𝐸𝑟𝑟𝑜𝑟𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 = 10−4 · 𝑉𝑖𝑛 To better appreciate the magnitude of this error, let’s estimate a range of values for Vin. Thus, knowing the value of the sensibility and the offset of the characteristic equation of the accelerometer, it is possible obviously to get its equation.
𝑉𝑖𝑛 = 0,8V · 𝑋 + 1,65𝑉 As what is going to be measured is the acceleration that experiences the sensor at rest over a table in different positions, the measured acceleration will vary between -1g and 1g, that is: 𝑉𝑖𝑛𝑚𝑎𝑥 = 0,8V · 1 + 1,65𝑉 = 2,45𝑉 𝑉𝑖𝑛𝑚𝑖𝑛 = 0,8V · (−1) + 1,65𝑉 = −0,85𝑉 Therefore, the maximum absolute error takes the next value.
𝐸𝑟𝑟𝑜𝑟𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 = 10−4 · 𝑉𝑖𝑛 = 2,45 · 10−4 𝑉 Hence, to know how significant is this error, the resolution obtained when connecting the sensor directly to the DAC without previous conditioning must be calculated. If this resolution is higher than the error, the error will not be noticed by the card. Otherwise, the error will have to be considered for later computations.
𝑔𝑚𝑎𝑥 − 𝑔min 𝑉𝑜𝑢𝑡 𝑚𝑎𝑥 − 𝑉𝑜𝑢𝑡 𝑚𝑖𝑛 ΔR · sensibility = · · sensibility 2𝑛𝑏𝑖𝑡𝑠 𝑉𝑖𝑛 𝑚𝑎𝑥 − 𝑉𝑖𝑛 𝑚𝑖𝑛 1 − (−1) 10𝑉 − (−10𝑉) = · · sensibility = 2,96 · 10−3 𝑔 · sensibility 212 2,45𝑉 − (−0,85𝑉) 0,8𝑉 = 2,96 · 10−3 𝑔 · = 2,368 · 10−3 𝑉 𝑔 The obtained resolution is almost 10 times greater than the error due to the load effect, consequently, it can be neglected avoiding extra errors which will simplify a lot the next steps of the practice.
3 Alba Martín, Anna Reig 4. Initial simulations After the previous theoretical part, the practical part is composed by three different programs developed with LabView. The two first ones are introductory to the accelerometer tool to have a better understanding about how the DAC works. In these parts, the DAC is assumed to be connected to the computer with an USB.
So, firstly, a signal is generated with the power supply and is introduced to the DAC through an analogue input.
Then a simple code with LabView is developed so to see the value of the power supply voltage in the screen of the computer and appreciate how this output varies when changing the value of the power supply.
Subsequently, a second program is developed aiming to vary from the computer the value of the output voltage of the DAC through an analogue output. A digital multimeter is used to measure the values obtained in the output of the DAC which then are compared with the inputted values in the program so to check the correspondence in between and the validity of themselves. In practice, very similar results are get when varying the voltage value between 2,5V and 3,3V thus approving the correct performance of the system.
Once up to here, the sensor and the DAC can be connected without conditioning necessity as well as the adquisition card and the computer so to have the card on and thus acting as a power supply for the sensor.
The connections between these devices can be appreciated in the following schema.
SENSOR VDD VSS X Y Voutput 0+ Voutput ref 0+ Vground ref Vinput 1 Vinput 0 DATA ACQUISITION CARD USB Figure 2 Schema of the connections between the devices interacting in the practice After making the previous connections, the third program is developped which, from the computer, controls the voltage output of the DAC which supplies 3,3V to the sensor. Now the sensor is on and it generates a voltage equivalent to the measured acceleration. So, to be able to interpret correctly this voltage, it must be converted to acceleration in m/s2. This conversion is executed by the software with voltage values obtained from the sensor, acquired by the DAC (Vinput_0 and Vinput_1), sent to the computer to then been plotted.
Hence, the acceleration can be computed by means of an easy conversion.
𝑉 − 1,65 𝑎𝑋,𝑌 = 9,8 · [𝑚/𝑠 2 ] 0,8 This equation has been obtained from the parameters mentioned in section 2, where; - 1,65 V is the typical offset value for a 3,3V input voltage - 0,8 V/g is the sensitivity for a 1,5g full scale - 9,8 m/s2 is the conversion factor from gm/s2 In this first version of the accelerometer, the user has the possibility of changing the input voltage given by the computer to the DAC which corresponds to the output voltage of the DAC. This initial approach is necessary to consolidate all the data computed so far and to verify that the idea initially conceived is correct.
4 Alba Martín, Anna Reig 5. Acceleration, velocity and position computations The main objective of this project is to develop a useful system for air navigation where acceleration is not enough to meet the necessary requirements. As the basic resource used is the accelerometer sensor, it is relatively simple to link up all the constraints. From physics, the velocity can be extracted integrating once the acceleration, and finally integrating twice in order to get the position.
𝑣𝑋 = ∫ 𝑎𝑋 · 𝑑𝑋 , 𝑣𝑌 = ∫ 𝑎𝑌 · 𝑑𝑌 𝑋 = ∫ 𝑣𝑋 · 𝑑𝑋, 𝑌 = ∫ 𝑣𝑌 · 𝑑𝑌 Applied to the case at hand, the characteristic equation would finally be: 𝑣𝑥𝑖 = 𝑎𝑥𝑖−1 · 𝑡 + 𝑣𝑥𝑖−1 𝑣𝑦𝑖 = 𝑎𝑦𝑖−1 · 𝑡 + 𝑣𝑦𝑖−1 𝑥𝑖 = 𝑣𝑥𝑖−1 · 𝑡 + 𝑥𝑖−1 𝑦𝑖 = 𝑣𝑦𝑖−1 · 𝑡 + 𝑦𝑖−1 6. Calibration Up to here, the program carries out all the functionalities required initially within a single drawback, it is not calibrated. Nowadays, all devices not calibrated are devices without a valid initial reference, consequently the measured values are not accurate and have a considerable error which oscillates between the expected values.
If one wants accurate measures, devices measuring directly parameters as for instance a sensor must be calibrated. This process can be performed by modifying the characteristic equation of the sensor in such a way that the typical values of sensibility and offset are removed and replaced by the measured and calculated ones since known sensor positions.
Step by step, the user will calibrate the sensor with 2 simple movements. In LabView, the software has been developed by a Flat Sequence Structure that allows to divide the software and thus the calibration in different steps as shown.
- First calibration: The user is asked to place the sensor in the table steadily. In this position, the acceleration in X and Y axis is equal to zero. Before the countdown achieves zero, the program takes the voltage measured by the sensor. Once it achieves zero, the mean is done for the array of measured voltage values in X axis and in Y axis.
These means are then assumed to be the offset value of the characteristic equation of the sensor for X and Y axis respectively.
Figure 3 Calibration 1 - Second calibration: The user must place the sensor at 90º until the countdown arrives at 0, as before. In this position, the acceleration in X axis equal to 9,8 m/s2 and the acceleration in Y is null. Before the countdown achieves zero, the program takes the voltage measured by the sensor and gets the sensibility by applying: 𝑉𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑𝑥 − 𝑉𝑜𝑓𝑓𝑠𝑒𝑡 𝑥 𝑆𝑒𝑛𝑠𝑖𝑏𝑖𝑙𝑖𝑡𝑦 = 1𝑔𝑥 5 Figure 4 Calibration 2 Alba Martín, Anna Reig Once the countdown achieves zero, the mean is done for the array of measured sensibility values in X axis. This mean is then assumed to be the sensibility value of the characteristic equation of the sensor for X axis.
- Third calibration: The user has to place the sensor with the shorter part on the table and wait for the countdown to be at zero. In this position, the acceleration in Y axis equal to 9,8 m/s2 and the acceleration in X is null. Before the countdown achieves zero, the program takes the voltage measured by the sensor and gets the sensibility by applying: 𝑉𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑𝑦 − 𝑉𝑜𝑓𝑓𝑠𝑒𝑡 𝑦 𝑆𝑒𝑛𝑠𝑖𝑏𝑖𝑙𝑖𝑡𝑦 = 1𝑔𝑦 Figure 5 Calibration 3 Once the countdown achieves zero, the mean is done for the array of measured sensibility values in Y axis. This mean is then assumed to be the sensibility value of the characteristic equation of the sensor for Y axis.
The whole application developed through this project can be seen in the following figure where the current acceleration, velocity and position are plotted as a function of time for X and Y axis, calculated from every given voltage output of the sensor for both axis. In the first column of plots, the behaviour of acceleration can be appreciated after having placed the sensor in the four basic positions, at rest and within acceleration positive and negative in X axis and then in Y axis. In the second column, for both axis, the velocity increase and decreases when turning the sensor to the next position when going from g to -g. Finally, the position cannot be well determined as it is very relative to the initial reference; it varies a lot due to the fact that the random error of the system increases exponentially when integrating a measured value. This is because the sensor used is not really accurate and it is pretty old and used.
6 Figure 6 Accelerometer tool 3.0 Alba Martín, Anna Reig 7. Conclusions The main objective of this project was to develop an accelerometer sensor in order to be conscious about all the processes needed to carry out any avionics system that is to be used in an aircraft.
On the beginning is very important to have a good knowledge of the parameters involved in the whole process.
Once the concerning information has been extracted from the datasheets, some calculations have been done that have helped to adapt all the devices correctly as well as to be aware of possible errors or possible variations on the devices.
The key and basic step is in well performing the changes between acceleration, velocity and position which are the possibilities offered by the tool developed. Even though, this is not enough if a reliable sensor wants to be developed.
Finally, as a necessity appears the calibration. Although the variation in the measurements were initially considered as known, all devices have a tolerance that determines the difference between a good sensor and a useless for aviation. For some determined positions, the values measured in those positions have been considered as an offset and substituted by zero. It could be said that we have managed to fulfil all the objectives initially marked, which included developing with ease in the libraries of LabView.
8. References . KUSB-3100 User’s Manual. KUSB3100-900-01 Rev. A, January 2005.
. MMA6270QT Rev 4, April 2008. Freescale Semiconductor. Technical Data.