A feedback I/sup 2/-controlled constant temperature solar radiation meter

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A Feedback -Controlled Constant Temperature Solar Radiation Meter Amauri Oliveira, Member, IEEE, Gurdip Singh Deep, Senior Member, IEEE, Antonio Marcus Nogueira Lima, Member, IEEE, and Raimundo Carlos Silv´erio Freire

Abstract—The conventional thermoresistive sensor-based feedback constant temperature circuits have shown some performance limitations due to the input offset voltage of the amplifier. The dc analysis of this circuit has been presented to graphically demonstrate these limitations. Alternative feedback measurement scheme without employing the Wheatstone bridge is proposed. PI and predictive controller designs are described. Simulation results for these controllers and a practical configuration are presented. Index Terms—Constant temperature circuit, feedback control, predictive control, pulsewidth modulation, radiation measurement.



NEGATIVE feedback circuit configuration with a thermoresistive sensor included in one of the arms of the Wheatstone bridge has been employed in the measurement of fluid velocity [1], [5] and solar radiation [6], [7]. The sensor is electrically heated to a desired temperature, and the variation in the fluid velocity or incident radiation tends to produce a change in the sensor temperature. This change is compensated by changing the electrical heating due to the negative feedback employed, and the sensor is maintained at a practically constant temperature. In the case of measurement of fluid velocity, this configuration is known as a constant temperature hot-wire anemometer [2], [8]. There are other circuit configurations based on thermoresistive sensors, e.g., constant current or constant voltage, but the so-called constant temperature configuration offers the lowest response time [8] and, for this reason, is by far the most popular in practice. In this measurement configuration, the square of the voltage across the sensor is related to the surrounding temperature and incident thermal radiation if it exists. This nonlinear relation is quite inconvenient when the circuit is used to measure the ambient temperature or solar radiation. A drawback of this configuration is its sensitivity to the offset voltage of the dc amplifier used in the feedback loop. On one hand, the offset voltage is useful in preventing oscillations in closed loop, but on the other hand, it prevents the sensor resistance from remaining strictly constant in the presence of varying incident radiation or fluid velocity [6]. Manuscript received May 19, 1998; revised November 16, 1998. A. Oliveira is with the Department of Electrical Engineering, Federal University of Bahia, Salvador, BA, Brazil. G. S. Deep, A. M. N. Lima, and R. C. S. Freire are with the Department of Electrical Engineering, Federal University of Para´ıba, Campina Grande, PB, Brazil (e-mail: [email protected]). Publisher Item Identifier S 0018-9456(98)09756-3.

The dc analysis of a bridge circuit is presented to demonstrate the influence of the amplifier input offset voltage on the measurement accuracy of the instrument and other performance limitations that it introduces. An alternative constant temperature radiation measurement scheme based on control theory concepts is proposed. The design of this feedback scheme is formulated as a control problem to adjust the electrical current through the sensor to maintain the sensor temperature constant. Two different control laws are employed for this configuration. The performance of the proposed control laws is evaluated by simulation, and a practical feedback configuration employing pulsewidth modulated current excitation for the sensor is presented. II. STATIC ANALYSIS



Application of the first law of thermodynamics for the dynamic thermal equilibrium of metallic thermoresistive sensor, with an electrical current passing through it and solar radiation incident on it, yields the following [7]: (1) is the incident solar radiation; is electrical where is the sensor global heat power dissipated in the sensor; is the effective transfer coefficient referred to its area ; is the sensor tempertransmissivity-absorptivity product; is the equivalent surrounding temperature; is ature; the sensor’s heat capacity; and is the time. Under static (1) becomes equilibrium conditions (2) If the sensor temperature is kept constant, the variations in or may be substituted by corresponding variations in the electrical power . This electrical power may be given as or , and thus the variation in or is directly or . related to the variation in In [4], the analysis of a hot-wire anemometer bridge circuit demonstrates that in the so-called constant temperature circuit (Fig. 1), the sensor temperature and its resistance do not remain really constant. Among other factors, this is caused by nonzero input offset voltage of the dc amplifier employed in the feedback loop. On one hand, this offset voltage causes this limitation, but on the other hand, it has a decisive influence on the stability of the circuit [6]. In case this circuit is employed for the measurement of solar radiation, the above offset voltage

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Fig. 1. The conventional constant temperature radiation meter.

also reduces the dynamic range of the circuit output voltage . curves derived from the This can be verified from the combination of (2) and the circuit equations as shown below. The temperature dependence of a metallic resistance sensor ( ) is approximately given by [2]

Fig. 2. Calculated Vo Rs curves obtained from (9) with constant Ao and different values of Vos and those calculated from (6) with constant Ta and different values of SH .

(3) is the sensor resistance at 0 C, is its temperature where is the sensor temperature. coefficient, and and as follows: From (3) we can write (4) and (5) Substituting (4), (5), and we have

in (2),

(6) For the circuit in Fig. 1, we have (7)

Fig. 3. Generalized representation of a measurement system.

two curves. It is thus easy to visualize that, for different values of the measurand, the sensor resistance and consequently its temperature varies. The variation of the output voltage , for incident radiation is more when the input offset voltage varying from zero to mV. is 1 mV than when The nonlinear relation between the circuit output voltage and the measurand need more elaborate and complex compensation schemes for cancelling the effects of variation . In the following, an of the surrounding temperature alternative feedback circuit configuration is presented in which the sensor resistance is also maintained constant and output variable representing the measurand (i.e., incident radiation) is made directly proportional to . This output variable also varies linearly with the ambient temperature.

and (8) Combining these two equations we have (9) curves calculated from (6) for three values of The ( ; 0.5 and , where is the electrical power dissipated in the sensor at the static operating point) curves calculated from (9) are plotted in Fig. 2. The constant at 10 and equal to 1, 2, and considering 5 mV, are also shown in the same figure. The static circuit operating point under different operating conditions and circuit parameters is the point of intersection of the corresponding

III. ALTERNATIVE FEEDBACK MEASUREMENT SCHEMES Based on the recent representations of the measurement process [9]–[11], the thermoresistive sensor can be considered to be an input block of the overall measurement scheme for the present application. The sensor is subjected to the desired and an auxiliary adjustable electrical excitation measurand (electrical power , Fig. 3). The objective is to monitor the variation in the sensor resistance which can be quantified or . The functional blocks and in terms of represent the implementation of (1) and (3), respectively. The results from the auxiliary excitation and electrical power can be expressed in terms of and . the value of The proposed constant temperature measurement configuration employs feedback to maintain the sensor resistance value




Fig. 4. A feedback control scheme with u(t) Is2 and y (t) Rs .

constant. This proposition is formulated as a control problem (Fig. 4) and in the conventional configuration (Fig. 1), this control occurs in an implicit form. and the system output The input excitation variable are defined as follows: variable (10) and (11) where and are the proportionality constants. Fig. 4 shows a generic feedback scheme based on these ideas. In this configuration, the dc gain of the controller should be may be considered to remain pracsufficiently high so that tically constant under static thermal equilibrium conditions. represents the measurand . Further, and substituting (10) in (2), we have Assuming

Fig. 5. Calculated u(t) time response curves for step changes in the incident radiation SH = 0:1; 0:2; 0:4; 1 1 1, 1:0Pe0 .


Considering a PI controller with transfer function given by (14)

(12) implies As mentioned before, constant sensor resistance constant sensor temperature . The variation in is linearly or . As the variation can be related to variation in compensated by the use of another sensor not subjected to , and if the measurand but exposed only to variation in the measured variable of the compensating sensor is linearly variation, this compensation amounts to a related with simple subtraction operation. Two different controllers have been designed for use with a thin film platinum sensor [12] employed for the measurement of incident solar radiation. The design criteria and simulation results of the controller performance are given as follows. A. PI Control Scheme We may employ a procedure similar to the one used for the small signal analysis of a thermoresistive sensorbased feedback anemometer circuit [2], [6], for the analysis of a radiation measurement circuit. The dynamic thermal equilibrium equation (1) of the sensor is linearized around , (or ), , a quiescent operating point with . Using Laplace transformation we get [13] and

and using the pole–zero cancellation technique, i.e., , the transfer function of the feedback scheme has a pole at implying a time constant of . The time constant and the gain depend upon the electrical current through the sensor. By choosing an operating point for the sensor with , however, we can choose the value of . The dynamic performance of the designed system should not be significantly affected by the presence of incident radiation. This can be verified from the simulation runs and is described as follows. The thin film platinum sensor described in [5] has the W/ C, following parameters: J/ C, ( C) , and . C and With no radiation incident on the sensor and mA, we have: s, , /A , and W. The choice and using pole–zero cancellation yields of A s and A . for In Fig. 5, the calculated time response of step changes in the incident radiation for and are shown. It is interesting to observe that the circuit time constant does not depend on the amplitude of the incident radiation.

(13) B. Predictive Control Scheme where

in (10) and (11), and combining Assuming these with (4) and (1), we have (15)



The above equation can be discretized employing Euler’s first-order approximation [12] and may be written as (16) is the sampling interval, , , , ; ; ; , and . The predictive control law can be developed by rewriting the discretized sensor model of (16), as follows:


(17) Based on this equation, the one-step-ahead predictive control equation can be written as follows: Given that is the desired value of the sensor resistance, seconds later, which should be applied to the we calculate the value of sensor at instant , using


(18) are the estimated values of , , and where , , and and is the estimated value of [i.e., the value for the sensor which is shielded from the radiation]. of variation results in variation in , which in turn is . used in the estimation of and , for three different In Fig. 6 the plots of step changes in the incident radiation, have been calculated using the sensor characteristic equation (16) and the predictive control law equation (18). We observe that the variation in the sensor resistance due to the change in the incident and radiation is really very small even for thus the measurement configuration can be considered to be is linearly a practically constant temperature one and the . related with

(b) Fig. 6. Calculated u(t) and y (t) time response curves for step changes in the incident radiation SH = 0:1; 0:5; and 1:0Pe0 .

C. A Practical Configuration The schematic feedback control configuration shown in Fig. 4 can be practically implemented in various ways employing analog-to-digital and digital-to-analog converters, and can be obtained from the sensor a digital signal processor. voltage and current. The control law and the transformation of variables can be implemented in software with a digital signal processor or a microcontroller. is In Fig. 7, the sensor is excited with a pulsed current, the modulating signal for the pulsewidth modulator, and is the amplitude of the pulsed voltage across the sensor. The rms value of the sensor pulsed current waveform is given as (19) is the current amplitude, where is the repetition period. replaced by Equation (2) with be rewritten as

is the pulsewidth, and or


Fig. 7. The feedback measurement scheme with sensor supplied with pulsewidth modulated current.

If the sensor resistance and its temperature are maintained constant, the estimate of the measurand is contained in the which can be readily change in value of the pulsewidth can be written as obtained in the digital form. From (19), and if is chosen to be , then from (10), can be written as . The amplitude of the . pulsed voltage across the sensor is given as . From (9), we have In this configuration, we can use a PI controller and analog comparators. IV. CONCLUSIONS


The dc analysis of a conventional constant temperature thermoresistive sensor-based radiation meter has shown some



performance limitations. For example, the nonlinear relation between measurand and the electrical quantity actually monitored and the presence of dc amplifier input offset voltage determine the dynamic range of the output voltage. The resistors used in the bridge circuit imply additional power loss and larger bridge excitation voltage is required, which implies high values of supply voltage for the circuit. This constitutes additional restrictions in the design of this circuit in the integrated circuit form. In the proposed measurement configuration, the sensor is also maintained at a practically constant temperature, using feedback control employing the measured variable namely . This makes the change in the measured variable directly proportional to the quantity to be estimated (i.e., radiation power) and also to ambient temperature whose influence on the measurement needs to be compensated. With the use of pulsewidth modulated current for sensor becomes the monitored variable excitation, the pulsewidth and is directly proportional to the incident radiation (i.e., measurand). The pulsewidth is measured using digital techniques with relative ease, and we obtain the desired measurement in the digital form without the use of conventional analog-todigital converter block. Absence of resistors in series with the sensor should permit the use of lower supply voltage which is an actual tendency in the design of integrated circuits. REFERENCES [1] C. G. Lomas, Fundamentals of Hot Wire Anemometry. New York: Cambridge Univ. Press, 1986. [2] E. O. Doebelin, Measurement System Application and Design. New York: McGraw-Hill, 1976. [3] K. Okamoto, T. Ohhashi, M. Asakura, and K. Watanabe, “A digital anemometer,” in Proc. IMTC/93—Instrumentation and Measurement Technology Conf., 1993, pp. 59–63. [4] A. E. Perry and G. L. Morrison, “A study of the constant-temperature hot-wire anemometer,” J. Fluid Mech., vol. 47, pt. 3, pp. 577–599, 1971. [5] A. Oliveira, R. C. S. Freire, G. S. Deep, and P. C. Lobo, “A digital anemometer with PWM excitation,” in Proc. IECON’95—Int. Conf. Industrial Electronic, Control and Instrumentation, 1995, pp. 893–897. [6] A. Oliveira, P. C. Lobo, G. S. Deep, R. C. S. Freire, and J. S. R. Neto, “Frequency domain analysis of a constant temperature radiation meter,” in Proc. Solar Energy Engineering Conf., Washington, DC, Apr. 1997, pp. 155–161. [7] P. C. Lobo, G. S. Deep, R. C. S. Freire, J. S. da Rocha Neto, and A. M. N. Lima, “Dynamic response of an electronic feedback thermoresistive electrical substitution pyrometer,” in Proc. Solar Energy Engineering Conf., 1995, vol. 2, pp. 751–756. [8] G. R. Sarma, “Analysis of a constant voltage anemometer circuit,” in Proc. IMTC’93—Instrumentation and Measurement Technology Conf., 1993, pp. 731–736. [9] P. K. Stein, “The unified approach to the engineering of measurement systems for test & evaluation—A brief survey,” in Proc. IMTC’96—Instrumentation and Measurement Technology Conf., 1996, pp. 1–28. [10] R. Z. Morawski, “Unified approach to measurand reconstruction,” in Proc. IMTC’94—Instrumentation and Measurement Technology Conf., 1994, pp. 226–231. [11] A. Barwicz, “System approach to electrical measurements,” in Proc. IMTC’93—Instrumentation and Measurement Technology Conf., 1993, pp. 397–402. [12] A. M. N. Lima, G. S. Deep, J. S. R. Neto, R. C. S. Freire, and P. C. Lobo, “Identification of thermoresistive solar radiation sensor,” IEEE Trans. Instrum. Meas., vol. 43, pp. 133–138, Apr. 1994. [13] A. Oliveira, “Sensores termo-resistivos em configura¸co˜ es realimentadas,” Ph.D. dissertation, Universidade Federal da Para´ıba, DEE/COPELE, Campina Grande, PB, Brazil, 1997.


Amauri Oliveira (M’88) was born on March 21, 1954, in Rui Barbosa-BA, Brazil. He received the Bachelor’s degree in electrical engineering from Federal University of Bahia, Brazil, in 1979 and the Master’s degree in electrical engineering from COPPE—Federal University of Rio de Janeiro in 1982. He completed his doctoral work at Federal University of Para´ıba (UFPB), Campina Grande, Para´ıba, Brazil, in 1997. He has been on the teaching faculty of UFBA since 1983. His research interests include electronic instrumentation and sensors.

Gurdip Singh Deep (M’76–SM’84) was born on December 12, 1937. He received the B.Tech. (Hons.) degree in electrical engineering from Indian Institute of Technology (I.I.T.), Kharagpur, India, in 1959, the M.E. degree in power engineering (electrical) from the Indian Institute of Science, Bangalore, India, in 1961, and the Ph.D. degree in electrical engineering from I.I.T. Kanpur, India, in 1971. From 1961 to 1965, he worked as an Assistant Professor in Guru Nanak Engineering College Ludhiana, and from 1965 to 1972, he was with the I.I.T., Kanpur, as a Lecturer/Assistant Professor. Since July 1972, he has been a titular Professor at the Centre of Science and Technology of Federal University of Para´ıba in Campina Grande, Brazil. Presently, he is the Coordinator of the Electronic Instrumentation and Control Laboratory of the University. He has been a consultant for Encardio-rite Electronics (Pvt) Ltd., India, during 1969–1970. His research interests are electronic instrumentation and microcomputer-based process control.

Antonio Marcus Nogueira Lima (S’79–M’93) was born in Recife, Pernambuco, Brazil, in 1958. He received the Bachelor’s and Master’s degrees in electrical engineering from Federal University of Para´ıba, Campina Grande, Para´ıba, Brazil, in 1982 and 1985, respectively, and the doctoral degree in 1989 from Institut National Polytechnique de Toulouse, Toulouse, France. He was with the Escola T´ecnica Redentorista, Campina Grande, Para´ıba, Brazil, from 1977 to 1982 and was a Project Engineer at Sul-Am´erica Philips, Recife, Pernambuco, Brazil, from 1982 to 1983. Since September 1983, he has been with the Electrical Engineering Department of Federal University of Para´ıba where he is now Professor of Electrical Engineering. His research interests are in the fields of electrical machines and drives, electronic instrumentation, control systems, and system identification.

Raimundo Carlos Silv´erio Freire was born on October 10, 1954, in Po¸co de Pedra-RN, Brazil. He received the Bachelor’s degree in electrical engineering from Federal University of Maranh˜ao, Brazil, in 1980, and the Master’s degree in electrical engineering from Federal University of Para´ıba, Campina Grande, Para´ıba, Brazil, in 1982. He received the doctoral degree in electronics, automation, and measurements at National Polytechnical Institute of Lorraine in Nancy, France, in 1988. He worked as an Electrical Engineer for Maranh˜ao Educational Television, in Brazil, from 1980 to 1983. He was a Professor of Electrical Engineering at Federal University of Maranh˜ao from 1982 to 1985. Since December 1989, he has been on the faculty of the Electrical Engineering Department of the Federal University of Para´ıba. His research interests include electronic instrumentation and sensors, and microcomputer-based process control.

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