ME 365 EXPERIMENT 5 FIRST ORDER SYSTEM IDENTIFICATION APPLIED TO TEMPERATURE MEASUREMENT SYSTEMS

Objectives: In this two week experiment, we will gain familiarity with first order systems by using two commonly used temperature transducers. The transducers are the copper-constantan (T-Type) thermocouple and the platinum resistance temperature detector (RTD). A common step in the design process for most mechanical systems is to select appropriate sensors based on their performance characteristics. Here, we will be examining a few measures of static and dynamic performance associated with the thermocouple and RTD. If these were part of a complete design project that required temperature measurement, we could then use this information, along with factors such as cost and durability, to choose the best sensor for the job.

After completing this lab you should be able to: • Perform a static calibration on a simple temperature transducer. • Experimentally determine static performance characteristics and understand what they mean. • Use two different methods to experimentally determine the time constant of a first order system and understand the significance of the time constant.

Procedure:

Static Calibration (First Week):

We will begin our study of the static and dynamic performance characteristics of the thermocouple and RTD sensors by calibrating both instruments. You should have access to the following equipment to perform this experiment:

Copper-Constantan Thermocouple (TC) Platinum Resistance Thermometer (RTD) Glass Thermometer Hot Plate Beaker Dewar Flask 6 Volt Battery Wheatstone Bridge Patchboard 2 - 5 K• , and 1 - 124 • resistors BNC Shunt Rubber Bands Crushed Ice and Distilled Water

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Laboratory 5 First Order Systems and Temperature Measurements ME 365

Carefully bundle the TC, RTD, and thermometer together with a rubber band. Take care not to bend the TC or RTD leads when handling them. At this time, prepare an ice bath by packing the Dewar flask with ice, and adding distilled water. We won't be using the ice bath as a temperature reference for the TC, since that is being done with an integrated circuit in the ADC interface, but we will take measurements at the ice point for the calibration curve. To ensure that the RTD's output voltages lie within the specified ±20 mV ADC range, the temperature extremes must be measured. Immerse the sensor bundle in the ice bath and observe the RTD's output voltage on the DMM. Then immerse the sensor bundle in a beaker containing a small amount of boiling water and again observe the output voltage. Adjust the potentiometer on the Wheatstone Bridge so that these voltages, representing the extremes of the test, lie within the specified range. Connect the TC output to channel 1 on the ADC interface. Connect the output of the RTD/Wheatstone Bridge to channel 3. Since both of these signals are quite small (on the order of millivolts), we will correct for any bias in the ADC amplifier by subtracting off the bias voltage measured across a shorted input. Short out channel 4 with the BNC shunt to provide a measurement of the ADC bias. The VI will perform the subtraction automatically. Launch LabVIEW then load and run LOGGER.VI from the ME365 library (Desktop\ME365\me365.llb). You will be asked to specify a file name to store your calibration results under. Immerse the sensor/thermometer bundle into the beaker with a small amount of boiling water. Once the thermometer has settled at the boiling point, enter the observed temperature in the "Thermometer Reading" box and press the ENTER button 5 times on the panel to record the data point. At this point, turn off the heating element and begin gently adding chilled distilled water to slowly lower the boiling water down to freezing. The water in the beaker should be cooling down at this point. Using the VI, record the TC and RTD signals for a variety of temperatures ranging up to the boiling point. Try to capture temperatures every 10°C or so. Once again, you should attempt to make multiple recordings, at least 5 recordings, at each temperature of interest. When you have reached the freezing point, begin warming the liquid and collecting data points at the same temperatures you recorded going downscale. The VI does not actually save your data until you halt the VI properly by pressing the STOP button on the front panel. It is a good idea to save your data before proceeding.

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Repeat this procedure once more by heating the fluid from freezing to boiling then back to freezing. This concludes the experimental portion of the first laboratory session. You should spend the remainder of your lab time making sure that you have a complete set of usable data, and preparing your static performance analysis for the following week.

Static Calibration Deliverables:

The following should be submitted at the beginning of the next laboratory session:

• Plots of your calibration curves, • Calibration equations for the TC and RTD using linear regression analysis, • A table summarizing the static performance characteristics for the two sensors including: sensitivity, bias, maximum nonlinearity (% FSD), maximum hysteresis (%FSD), R2 , 99% confidence interval of the slope and intercept (from calibration equation), and input resolution.

* Note that the ADC input range used by Logger.VI is ±.02 Volts

• and the answers to the following questions.

Q1) Based on the results of your static performance and linear regression analyses, is a linear calibration curve appropriate for the RTD? Is it appropriate for the TC? Why or why not?

Q2) Based on the static performance characteristics you've identified, which sensor would you select for accurate measurement of slowly varying temperatures? Why?

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Dynamic Response (Second Week):

During the second lab session, we will evaluate the dynamic performance characteristics of the TC and RTD sensors. Set up the equipment as you did in the previous laboratory, and load the multichannel scan VI used at the end of Lab 3. Bring the beaker of water to a boil in preparation for step response testing, that is, carefully plunging the sensor into the beaker of boiling water. An ice bath will be helpful for cooling the sensor before repeating the step response test. You will need to experiment with the VI panel settings (i.e. sample rate, number of samples, input range, etc.) to determine which are best for capturing the dynamic response of the two sensors. It is suggested that you first try sample rates of 30 and 3000 samples per second for both the RTD and thermocouple. When you are confident that you have produced a useful step response, click on the file switch to record the step response data. Save step response curves for both the RTD and TC.

Dynamic Response Deliverables: Prepare plots of your step response curves for both sensors. You will need to apply the calibration equation you calculated in the previous week to produce a plot using proper engineering units. Use the techniques for identifying first order system parameters presented in the lecture notes to find the time constants of the RTD and TC. Present both of your plots and calculations along with well thought answers to the following questions:

Q3) Based on the results of your system identification analysis, are the RTD dynamics described by a 1st order system? How about the TC dynamics? Why or why not?

Q4) Based on the dynamic performance characteristics you've identified, which sensor would you select for accurate measurement of quickly varying temperatures? Why?

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Q5) Briefly discuss any discrepancies between Q2 and Q4.

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Appendix A: Temperature Measurement Devices

We will be studying two types of temperature measuring devices in this laboratory, the T-type thermocouple and the platinum resistance temperature detector (RTD). Keep in mind that there are many other useful devices for obtaining practical engineering temperature measurements, for example, the thermistor. This appendix describes the basic principles which govern the behavior of thermocouple and RTD sensors.

The Thermocouple

In 1821, Thomas Seebeck made the discovery that when two wires composed of dissimilar metals are joined at both ends and one of the ends is heated a continuous current will flow through the wires [1]. If this thermo-electric circuit is broken, the net open circuit voltage is a function of the junction temperature and the composition of the two wires. This potential is the Seebeck voltage, and it is the underlying physical principle used to make thermocouple based temperature measurements.

Three basic laws govern the behavior of thermocouples [2]. They are: 1. The law of homogeneous metals states that a thermo-electric current cannot be sustained in a circuit of a single homogeneous material, by the application of heat alone. At least two different materials are required for a thermoelectric circuit.

2. The law of intermediate metals states that the algebraic sum of the thermo-electric voltages in a circuit composed of any number of dissimilar materials is zero if all of the circuit is at a uniform temperature. A consequence of this is that thermocouple wires may be joined by soldering, welding, or clamping without affecting the thermoelectric output as long as the junction is isothermal.

3. The law of intermediate temperature tells us that if two dissimilar metals produce a thermal EMF of E1 when the junctions are at temperatures T1 and T2, and a thermal EMF of E2 when the junctions are at T2 and T3, then the EMF produced when the junctions are at T1 and T3, will be E1 + E2.

A thermocouple based temperature measurement is always a measurement of the electrical potential developed by the thermocouple circuit when the two junctions of the thermocouple are at temperatures T1 and Tref. T1 is the temperature of the measurement junction and Tref is the temperature of the second junction. This second junction is thermally fixed at a known, reference, temperature, often the ice point of water. Figure 1 illustrates a typical thermocouple circuit.

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Figure 1: A Thermocouple Circuit with Ice Point Reference

As one might suspect, it is not always convenient to have a reference ice bath on the lab bench when running a test with a thermocouple. In fact, it would be quite annoying to keep dropping ice cubes into the bath to maintain a constant reference during a long experiment! Fortunately, the ice bath may be replaced with an integrated circuit which produces an equivalent Seebeck voltage. Most modern temperature measurement systems, including our laboratory, make use of an integrated circuit ice point reference.

The Resistance Temperature Detector

The platinum resistance temperature detector (RTD) is perhaps one of the most important temperature measurement devices because of its use in the establishment of reference temperature scales [4]. RTD's began to see widespread use as precision temperature sensors in 1887 when H. L. Callander reported that platinum resistance thermometers exhibited "prerequisite stability and reproducibility if they were properly constructed and treated with sufficient care. [5]" All practical temperature scales since 1927 have been based in part on measurements made with the standard platinum resistance thermometer (SPRT) [6].

The classical construction of an RTD consists of a helical coil of platinum wound around a mica structure with the entire assembly enclosed in a glass tube as shown in Figure 2 [7]. Changes in temperature cause the platinum coil to expand or contract resulting in a resistance change. This construction is quite fragile, and is generally not useable in industrial environments.

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Figure 2: Cross Section of RTD Construction

A more durable RTD construction consists of a platinum coil wound on a glass or ceramic bobbin, which is then sealed with a coating of molten glass. The sealing process assures that the RTD will maintain its integrity under extreme vibration; however, this also limits the expansion of the platinum wire at high temperatures. Unless the thermal expansion coefficients of the bobbin match that of the wire, strain induced resistance changes in the wire can corrupt the temperature measurement.

Resistance measurements are not immediately usable by most computer data acquisition systems, rather, changes in resistance must be converted to equivalent changes in voltage. One common way in which finely varying resistances may be converted into usable voltages involves a circuit called the Wheatstone Bridge, shown in Figure 3. We will be studying and using the Wheatstone Bridge again later in the semester.

Figure 3: A Wheatstone Bridge Circuit for Making RTD Measurements

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Manufacturers' Calibration Data

Standard calibration tables for thermocouples and RTDs are readily available from the ASTM and sensor manufacturers [3]. It is important to note, however, that these calibration results have been obtained in a carefully controlled environment with certain operating assumptions, i.e. a specific reference temperature for a thermocouple. In practice, your experimental setup may be quite different, so there is no good reason to assume that the calibration for your sensor will be the same.

In order to make accurate measurements, and to satisfy yourself that your measurement system is working properly, it is important to get in the habit of preparing your own sensor calibrations before performing an experiment, or at the very least, verifying a few data points from the manufacturer's calibration. It is also a good idea to verify the calibration data at the end of the experiment to make sure that the performance of your setup has not degraded during testing.

REFERENCES

[1] Seebeck, T. J., "Magnetische Polarisation der Metalle und Erze durch Temperatur Differenz," Abh. Koenigl, Akad. Wiss. Berlin, p. 265, 1822- 1833.

[2] American Society for Testing and Materials, "STP-470 - Manual on the Use of Thermocouples in Temperature Measurements," ASTM, Philadelphia, 1970.

[3] "Practical Temperature Measurements," Omega Engineering, Inc. Catalog v. 26, pp. T34-T85, 1988.

[4] "The International Practical Temperature Scale of 1968," Adopted by the Comite' des Poids et Mesures, Metrologia, v. 5 n. 2, pp. 35-44, 1969.

[5] Callendar, H. L., "On the Practical Measurement of Temperature: Experiments Made at the Cavendish Laboratory, Cambridge," Phil. Trans., v. 178, pp. 161-230, 1887.

[6] Burgess, G. F., "The International Temperature Scale," J. Res. Nat. Bur. Stand. RP22, v. 1, pp. 635-640, 1928.

[7] Meyers, C. H., "Coiled Filament Resistance Thermometers," NBS Journal of Research, v. 9, 1932.

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