Self-Compensationto Build ReconfigurableMeasurement Systems

Jos Rivera-Meja, Mariano Carrillo-Romero, and Gilberto Herrera-Ruiz

Intelligent sensors are the core components of reconfig-urable measurement systems (RMS). The intelligent sensors generic functions are compensation, process-ing, communication, validation, integration and data fusion. Their design involves using self-adjustment (or compensa-tion) algorithms for eliminating or at least diminishing major types of error, such as offset, gain variation, and non-linearity, with good accuracy [1]. In addition, the design must make the readjustment process as simple as possible [2].

A methodology for designing intelligent sensors with self-compensation which can be reconfigured to measure any variable is presented in this paper. Additionally, we analyze several compensation techniques using numerical algorithms and one based on artificial neural networks theory. The meth-odology is applied to reconfigure intelligent sensors for temperature and distance measurements.

Intelligent SensorsAlthough the definitions of smart and intelligent sensors have not been widely accepted, IEEE 1451.21997 defines a smart sensor as: a sensor that provides functions beyond those nec-essary for generating a correct representation of a sensed or controlled quantity [1], [3]. Such functions typically sim-plify the sensors integration into applications in a network environment [4]. The intelligence in a sensor could be asso-ciated with functionalities performed by the sensor, such as compensation [1], [5]. This feature allows reconfiguration of an intelligent sensor to measure any variable. Accuracy will be associated with the sensing element and the compensation method.

To clarify this idea, Fig. 1 shows a block diagram of a re-configurable intelligent sensor. The sensing element is any traditional sensor with the signal conditioning necessary to obtain output voltage. This voltage, which typically is within the range 0 to 5 volts (or from 0 to 3 volts at low power con-sumption) is supplied to an analog-to-digital converter (ADC).

It does not matter if the voltage is linear or non-linear, because the intelligent part of the sensor will be able to fix such prob-lems as linearity, offset, gain, etc., using a microcontroller (C), a digital signal processor (DSP), or a field programmable gate array (FPGA). A digital-to-analog converter (DAC) is pro-vided to drive an actuator.

Some compensation methods are explained in the next sec-tion. To perform the reconfiguration and to endow the sensor with the capability of measuring any variable, compensation methods should be implemented at the sensors intelligent part.

Common Errors Affecting a Sensing ElementThe ideal response for the vast majority of sensing elements is a straight line as Fig. 2a shows. Errors occur in sensing el-ements for several reasons. It is not possible to produce large numbers of parts all having identical performance. Realiza-ble parts require some manufacturing tolerance with respect to their nominal (or ideal) behavior. The actual transfer func-tion of a realizable sensing element could be subject to any of the following errors:

Gain error. The slope of the transfer function departs from the nominal value. Within its operation range, the sensing element has incorrect sensitivity or scale factor (Fig. 2b).

Non-linearity error. The sensing elements output does not change in a linear way with respect to the input signal (Fig. 2c).

Offset error. In a linear sensor, zero input should produce zero output, called the offset error (Fig. 2d). Offset error is especially troublesome in sensors capable of dc or near dc response.

Cross sensitivity error. The output of some sensing elements responds to parameters other than the variable it was designed to measure, for example, temperature (Fig. 2e).

Acknowledgement: The authors thank the Instituto Tecnolgico de Chihuahua, Mexico, FOMIX-Chihuahua(Project No. CHIH-2009-C01-116741) and PROMEP (Project No. ITCH-EXB-001) for their financial support of this work.

10 IEEE Instrumentation & Measurement Magazine April 20131094-6969/13/$25.002013IEEE

Self-Compensationto Build ReconfigurableMeasurement Systems

Jos Rivera-Meja, Mariano Carrillo-Romero, and Gilberto Herrera-Ruiz

Hysteresis error. Hysteresis expresses the notion that the output is influenced by the previous history or path of the input signal: Typically, a sensing element with hysteresis error responds differently to low-to-high and high-to-low input transitions (Fig. 2f).

Drift error. The sensing element transfer function varies with time. Most of the time it is caused by wear in the sensor or aging (Fig. 2g).

Because of these errors, measurement systems should be indi-vidually calibrated to maintain and guarantee accuracy.

Fig. 1. Reconfigurable intelligent sensor architecture.

Fig. 2. Possible errors in the transfer function of the sensing element. (a) Ideal response of the sensing element. (b) Gain error. (c) Non-linearity error. (d) Offset error. (e) Cross sensitivity error. (f) Hysteresis error. (g) Drift error by aging of the sensing element.

April 2013 IEEE Instrumentation & Measurement Magazine 11April 2013 IEEE Instrumentation & Measurement Magazine 11

These types of systematic errors are present from the design phase. As an example, Fig. 3a shows a temperature sens-ing element composed of a negative temperature coefficient thermistor. In this case, the thermistor is part of a voltage di-vider in which the output voltage V0 is defined by:

(1)

where Vcc is the voltage power supply, R1 is the resistance con-nected in series with the thermistor RT, R0 is the resistance of the thermistor at temperature T0, and T is the temperature we wish to measure. The thermistor features are R0 = 10,000 at T0 = 25 C and = 4,100 10%. Fig. 3b shows the output volt-age of the voltage divider evaluated by Monte Carlo simulation assuming a sample of 1000 circuits in which the sensing element is at 50 C, the resistor R1 = 6,200 5% and Vcc = 5 V 1%. Note that the output voltage has a variation from 3.1 to 3.35 V. This example presents two errors: first, non-linearity due to the thermistors response (Fig. 3a), and second, the offest error due to manufacture tolerance of the thermistor R and the power supply, (note the possible variation of V0 due to the offset er-ror (Fig. 3b). The following section will explain algorithms to fix these problems and how to build a reconfigurable sensor.

The Compensation ProcessBefore studying compensation methods, we present a com-pensation process which can be used to build reconfigurable intelligent sensors. The output voltage in response to a mea-sured variable of the sensing element can be defined as:

(2)

where qi is the variable to be measured, and V0 is the output voltage of the sensing element, which is a function of qi. Nor-malization is recommended to simplify and generalize the process of information handling for any variable and any mea-surement range. Normalization is performed on the input

variables qi and the sensing elements output voltage V0, pref-erably in the range [0,1], using the following equations:

(3)

and

(4)

After normalization, (2) can be rewritten as: v = f(x). Now, the desired output signal is a straight line with unitary slope. This is the goal of the compensation process. The reference sig-nal is defined by [5] as:

(5)

Now, the sensor signal is ready to apply to any compen-sation algorithm. Fig. 4 shows the compensation process; the output signal of the compensation algorithm is the function y, and it is defined in [6] as:

(6)

Finally, to evaluate the compensation process, the non-lin-earity relative error (NLE) can define how straight the function y is. It is evaluated by:

(7)

The maximum acceptable value of r is 1% using a mini-mum quantity of readjustment points.

Techniques or Algorithms for CompensationCompensation is based on linearization techniques used to fix problems like offset, gain, non-linearity and drift errors. When the compensation method is chosen, it is important to consider the number of readjustment points N and the

Fig. 3. A simple temperature sensors output. (a) Thermistor in a voltage divider and the dividers output voltage at temperatures from 0 C to 100 C. (b) Output voltage simulated from 1000 circuits at 50 C.

,

12 IEEE Instrumentation & Measurement Magazine April 2013

maximum acceptable NLE as in (7). Maintenance of the measurement system will be less expensive if the compen-sation method requires few readjustment points to reach a NLE less than 1%.

Later, we present the quantitative comparison between four compensation algorithms. Three of these algorithms are considered numerical methods: piecewise linear interpola-tion, the polynomial progressive method [7] and [8], and an improved polynomial progressive method [5]. The other is an artificial neural network method (ANNM) [9]. The four methods were simulated and a quantitative evaluation of its performance was executed. Using the generated information and two different sensors, the compensation methods were selected and programmed in a microcontroller for real mea-surement of two variables.

Based on the adjustment process of measuring systems described in the Vocabulary International of Metrology (ISO IEC (VIM), 9:2007) [10], N readjustment points from the measurement range of the sensor are chosen and called the readjustment vector, qi. The readjustment vector is supplied to the sensing element, and the output signal is recorded to generate the vector V0. Using (3) and (4), the signals are nor-malized in the range of [0,1] to get x(i) = [x1,x2,,xN] and v(i) = [v1,v2,,vN] for i = 1 to N. The ideal output for each point is de-fined by (5), t(i) = [t1,t2,, tN]. The x, v, and t vectors will be used for the compensation methods.

In the case of the artificial neural network topology, the size of the matrix depends on the neural network topology and is independent of the number of readjustment points used to train the neural network.

Evaluating Compensation EfficiencySelecting the best compensation method is a challenging task which has generated a large body of literature. We have found little quantitative information after reviewing the literature, and procedures to select the optimal readjustment points necessary to reach the desired accuracy are not well established. To select the best compensation method, we follow this process [6]:

1. Simulate the sensing element response. The most impor-tant information needed for this step is to define or determine the maximum percentage of non-linearity rela-tive error (MPNRE) of the sensing element. The MPNRE is the maximum value obtained by comparison of the output sensing element with the straight line, which is divided by the measurement range. The MPNRE could be obtained from the data sheet sensor or by a practical way. For example, a K type thermocouple in the range from 0 to 1000 C has 0.6% MPNRE. The MPNRE of thermistors

with from 3575 to 4500 C, is between 13% and 23%, as Fig. 3 shows. The Sharp GP2Y0A02YK infrared sensor, which measures the distance to an object, has 46.7% of MPNRE.

2. Use the following equation to simulate the sensing element response:

(8) whereV0 is the simulated output voltage of the sensing element, qi is the input variable of the sensing element, and m is the variable to control the non-linearity grade of (8) in computing the MPNRE of V0. For example, with values of qi between 1 and 100 and m between 1 and 95, the MPNRE of V0 will be between 94.3% and 12%, as Fig. 5 shows.

3. Evaluate the method response using different quantities of readjustment points.

4. Taking into consideration the computational demand, the MPNRE, and the number of readjustment points, compare the results, and choose the most advantageous method.

The performance comparison between the piecewise lin-ear interpolation method, polynomial progressive method, improved polynomial progressive method (IPPM), and the ANNM was computed using N = 5, 6, 7, and 8 readjustment points and Fig. 6 shows the results. The x-axis represents the maximum non-linearity of the sensing element and the y-axis represents the maximum non-linearity in the output of the compensation methods. For example, in Fig. 6a, using five re-adjustment points, the piecewise method can fix non-linearity problems under 15% with error less than 0.01.

Table 1 summarizes the quantitative comparison between these compensation methods. This helps the designer select the best compensation method for any particular situation. As mentioned above, the user needs to know only the MPNRE in the sensing element. The method providing the greatest range meeting the 1% MPNRE target is seen to be the ANNM because it can fix problems of maximum non-linearity up to 56.6%, (shown on the x-axis with the input as the maximum

Fig. 4. The compensation process.

Fig. 5. Simulation response of (8).

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nonlinearity of the uncorrected sensor) and improve its per-formance if the number of readjustment points increases, but it would take time to train and program the reconfigurable part. The training can be done off line.

The improved polynomial progressive method with seven readjustment points can fix problems of maximum non-linear-ity up to 45.5%, but a special process to choose the best order of readjustment points is required.

The piecewise and polynomial methods have similar performance with N = 5, 6, and 7 readjustment points, as can be noted in Table 1. The piecewise method has better performance compared to the polynomial method if eight readjustment points are used. The polynomial method is not recommended with more than seven readjustment points because oscillations are present around the solution. Some authors call this the over fitting effect [5].

It is recommended to use the algorithm with the lowest quantity of readjustment points be-cause its calibration cost will be computationally less expensive.

Example of the Selection and Use of Compensation AlgorithmsTo show the selection and use of compensation al-gorithms based on the information presented in Fig. 7a, the simulation of (8) is shown with qi in the range of 0 to 100 and m = 50. The V0 is nonlinear

Table 1 Comparison results of compensation methods

Quantity of readjustment points (N)

MPNRE that can be fixed by the compensation method

Piecewise PolynomialImproved Polynomial

Artificial Neural Network

N = 5 15.4% 21.4% 25.0% 33.8%N = 6 23.3% 25.5% 37.4% 42.9%N = 7 33.0% 30.1% 45.5% 53.1%N = 8 38.4% 32.2% 35.5% 56.6%

MPN

RE

100

101

10-1

10-2

100

101

10-1

MPN

RE

15 20 25 30 35 40 45 50 55

15 20 25 30 35 40 45 50 55

15 20 25 30 35 40 45 50 55

15 20 25 30 35 40 45 50 55 60 65

Maximum % of non-linearity error of the input

100

101

10-1

10-2

Maximum % of non-linearity error of the input

10-3

100

101

10-1

10-2

Compensation results using N=7 Compensation results using N=8

Compensation results using N=5 Compensation results using N=6

PiecewisePolynomialIPPMANNM

PiecewisePolynomialIPPMANNM

PiecewisePolynomialIPPMANNM

PiecewisePolynomialIPPMANNM

(a) (b)

(c) (d)

Fig. 6. Results of quantitative evaluation using different amounts of readjustment points in the compensation methods. (a) N = 5, (b) N = 6, (c) N = 7, and (d) N = 8.

14 IEEE Instrumentation & Measurement Magazine April 2013

and if its response is compared with a straight line, the MPNRE is 23.51%. Using (3) and (4), the response is normalized. Five points were selected to make the compensation and are denoted by an asterisk in Fig. 7a. Normalization yields the following ma-trices: x(i) = [0, 0.25, 0.5, 0.75, 1.0], v(i) = [0, 0.442, 0.724, 0.896, 1.0], and the ideal output t(i) = [0, 0.25, 0.5, 0.75, 1.0]. Fig. 7b shows the results.

The relative error that will be obtained after the compen-sation algorithms can be seen in Fig. 6. If the piecewise or polynomial progressive method is used, the error obtained will be more than 1%, but if the IPPM or ANNM is used, the er-ror will be less than 1%.

Fig. 8 shows the output of the compensation algorithms. The output of the four algorithms is almost a straight line. The relative error is computed using (6) and Fig. 8b shows its re-sult. As previously anticipated, error below 1% was reached with IPPM and ANNM. Using the straight line equation, the real measured values can be recovered. The output of the com-pensation algorithms approximate to a straight line as shown

in Fig. 8a. For this example, the real measured values can be re-covered by multiplying the x- and y-axes by 100.

Example of Reconfigurable Measurement SystemsSince the principles or bases needed to build reconfigurable systems have been established, some application examples are discussed next. Real applications sometimes require only measurement or monitoring of the process variables. In this case, the topology shown in Fig. 9a could be used. On the other hand, the topology shown in Fig. 9b would be used for many closed-loop measurement and control processes.

The ADC will be selected according to the required reso-lution. If a microcontroller is used in the reconfigurable part, many options are available because microcontrollers with eight and ten bits ADC can be found easily. If greater resolution is required, it often will be necessary to use an external ADC.

Another important item is the selection of a communi-cation protocol to provide network connection capability.

Fig. 7. An example of a compensation signal. (a) The sensors signal simulated with (8). (b) Nonlinearity evaluated with (7).

Fig. 8. Output of the compensation algorithms. (a) The signal compensated y. (b) The percent of relative error.

April 2013 IEEE Instrumentation & Measurement Magazine 15

Today, intelligent sensors can be interconnected by wires or wirelessly, and suitable devices are available for network pro-tocols such as: J1850, Control Area Network, LongTalkTM, Ethernet, etc. Table 2 shows some examples of some of these semiconductors.

Fig. 10 shows an example of reconfigurable measurement system network using Control Area Network (CAN) as the communication protocol. This reconfigurable measurement system can be monitored by a computer using CAN to a Uni-versal Series Bus converter, CAN to an Ethernet converter, or CAN to a Wi-Fi converter.

Fig. 11 shows an example of a measurement system with one or more reconfigurable intelligent sensors with a wireless interconnection. Communication can be established between all of the elements, and a remote converter-to-network can be used. The required converter is determined by the protocol used by the network to USB or Ethernet or Wi-Fi. Communi-cation between the reconfigurable intelligent sensors could be made with Bluetooth or ZigBee protocols. Many options are available for Bluetooth, such as converters from serial-to-Bluetooth and Bluetooth-to-USB. Wireless networks, can be

built using many commercially available modules like XBZA-ACI-001 from Digi International Inc. with ZigBee protocol that can be easily incorporated with any microcontroller, DSP or FPGA, and will provide wireless interconnection capabil-ity. Clearly, the trend is to use wireless interconnections and more hardware, which makes the development of measure-ment systems easier.

The architectures that have been presented are for general reconfigurable measurement systems with appropriate sensing elements to monitor any variable. Fig. 12 shows N intelligent sensors interconnected across CAN for general cases. The sen-sors are monitored by personal computer connected by wire or Wi-Fi to the Internet, and the variables can be monitored with any device with Ethernet connection. In the next section, we will give some specific measurement examples.

Examples of Reconfigurable Measurement SensorsFig. 13 shows the reconfigurable intelligent sensor topology using the compensation functionality of intelligent sensors. We now describe how the measurement system with the proper sensing element is reconfigured to measure temper-ature or distance. The reconfigurable part was built with C part number PIC18F2680, whose main features are: eight 10-bit

Fig. 9. An intelligent sensor to build reconfigurable measurement systems. (a) A reconfigurable measurement system. (b) A reconfigurable measurement and control system.

Fig. 10. Reconfigurable measurement system with CAN 2.0B.

Table 2 Some semiconductors with protocols that provide wired or wireless

network interconnection

Part No Manufacturer Protocol

MC68HC705V8 FreescaleTM J1850M68HC05/MC68HC05X16

FreescaleTM CAN 2.0B

MC143150/MC1431120

FreescaleTM LonTalkTM

MPC555 FreescaleTM CAN 2.0B68HC08AS32A FreescaleTM J1850ATmega32c1 Atmel CAN 2.0B

DS80C410 MaximEthernet y CAN

2.0BPIC18F2680 Microchip CAN 2.0BPIC18f2480 Microchip CAN 2.0BdsPIC32FJ256GP710 Microchip CAN 2.0BPIC18F97J60 Microchip Ethernet

16 IEEE Instrumentation & Measurement Magazine April 2013

ADC channels, 40 MHz of maximum frequency clock, 64 KB flash memory, and CAN2.0B communication.

Temperature MeasuringSemiconductors, thermocouples, resistance temperature detectors (RTDs), and thermistors are the most common de-vices used to measure temperature. The proper device will be selected depending on the measurement range. Compen-sation of semiconductors, thermocouples, and RTDs can be implemented with any compensation method using less

than five readjustment points. To illustrate the capability of compensation methods, temperature will be measured by a thermistor.

This device is very inexpensive and there are different sizes. It is widely used, although it has high non-linearity from 13% to 23% for from 3575 to 4500 C. In this design, a thermistor was used as the sensing element to measure temperature from 0 C to 100 C, as Fig. 3a shows with features of = 4500 10% and R0 = 10,000 at 25 C. The MPNRE is 23%. Reviewing the information from Table 1, compensation can be accom-plished by any of the compensation methods. Six readjustment points will be required for most of the techniques already dis-cussed, but only five readjustment points will be required if the ANNM is selected. The qi selected with six readjustments points was qi = [0, 20, 40, 60, 80, 100], and the output voltage of sensing element was V0 = [1.31, 2.50, 3.52, 4.16, 4.55, 4.69].

The ANNM in [9] was used, and after training the compen-sation algorithm using the neuron models purelin and logsig it is:

The performance of the piecewise linear interpola-tion method, the polynomial progressive method, IPPM, and ANNM were compared with the target straight line,

Fig. 11. A reconfigurable measurement system with a wireless interconnection.

Fig. 12. Reconfigurable measurement system with CAN connected to the Internet and monitored from any device with a wire or wireless Ethernet connection.

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and Fig. 14 shows the results. From the four methods, the MPNRE is less than 1%. Any of those four methods could be used to build a reconfigurable intelligent sensor to measure temperature using a thermistor as the sensing element with any value and regardless of a temperature coefficient that is either positive or negative. The compensation algorithm will fix these errors.

Distance MeasuringTo illustrate how the reconfigurable intelligent sensor can be used to measure distance, the sensing element was re-placed by an infrared device, GP2Y0A02YK manufactured by Sharp, to measure the distance to an object. The range was 20 cm to 150 cm, and it produced a dc voltage between 2.6 and 0.4 V, and has a MPNRE of about 46.7%. Reviewing the information on Table 1, the methods that can solve this error are the IPPM and the ANNM with seven readjustments points. The qi selected was: qi = [20, 42, 63, 85, 106, 128, 150] to build a distance meter from 20 cm to 150 cm. The output voltage of the sensing element was: V0 = [2.73, 1.29, 0.86, 0.63, 0.51, 0.47, 0.36].

The ANNM from [9] was used and after training was:

The outputs of the IPPM and ANNM were compared with the target straight line, and Fig. 15 shows the results. The MPNRE from the two methods is less than 1%, and either of them can be used to build a reconfigurable intelligent sensor.

As these two examples demonstrate, the end user is only re-quired to select one of several possible compensation methods according to the maximum permissible non-linearity percent-age error as measured at the sensor output.

ConclusionThis paper presented a methodology based on compensa-tion methods to build reconfigurable measurement systems. The quantitative comparison of several popular methods

Fig. 14. Results of non-linearity error compensation methods for reconfigurable intelligent sensor to measure temperature.

Fig. 15. Results of IPPM and ANNM non-linearity error compensation of a reconfigurable intelligent sensor to measure distance.

Fig. 13. Example of reconfigurable intelligent sensor for measurement of temperature or distance.

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was shown to illustrate the selection of a computationally efficient compensation method. Using the methodology de-scribed here, the user only needs to know the maximum percentage of non-linearity in the sensing element and the desired amount of non-linearity error that can be tolerated in the intelligent sensors output signal. This information al-lows selection of the compensation method and the number of readjustment points. With this approach, a critical part of the intelligent sensor is reusable and may be used in wired or wireless reconfigurable measurement systems.

AcknowledgmentThe authors thank the students of the Instituto Tecnolgico de Chihuahua instrumentation and control laboratory in 2011 for their help.

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Jos Rivera-Meja (jrivera@itchihuahua.edu.mx) received the M.S. degree from the Instituto Tecnolgico de Chihuahua, Mexico in 1979 and the Dr. Eng. Degree from the Universidad Autnoma de Quertaro, Mexico in 2008. From 1985 to 1994, he worked as Superintendent of Technical Support at Zenith el. Corp. and since 1994, he has been a professor and a researcher at the Postgraduate Department of the Instituto Tecnolgico de Chihuahua. His research interests include intelligent sen-sors, measurement systems, metrology and reliability. He is a member of the National Researchers System in Mexico, holds a Dr. Eng. Degree, and is an IEEE member. Dr. Rivera-Mejias dissertation was recognized by the Universidad Autnoma de Quertaro as the best thesis in 2008. He has published more than 45 papers and two books.

Mariano Carrillo-Romero received the M.S. Degree in electronic engineering from the Instituto Tecnologico de Chi-huahua in 2007. His research interests include instrumentation systems, smart sensors, neural networks and fuzzy logic applications.

Gilberto Herrera-Ruiz received the Ph.D. degree in mechan-ical engineering from the Technical University of Budapest, Hungary, in 1992, and the Post-Doctoral degree from the Me-chanical Engineering Laborabory (MEL), Tsukuba, Japan, in 1994. He is a Researcher with the Consejo Nacional de Cien-cia y Tecnologa of Mxico and is currently a Head Professor in the School of Engineering, in Quertaro State University, Mexico. He has been an adviser for more than fifty theses and a coauthor on more than forty technical papers published in international journals and conferences. His fields of interest include motion control, hardware signal processing, and man-ufacturing processes.

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