IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 5, OCTOBER 1998 1163

A Feedback -Controlled ConstantTemperature Solar Radiation Meter

Amauri Oliveira, Member, IEEE,Gurdip Singh Deep,Senior Member, IEEE,Antonio Marcus Nogueira Lima,Member, IEEE,and Raimundo Carlos Silverio Freire

Abstract—The conventional thermoresistive sensor-based feed-back constant temperature circuits have shown some perfor-mance limitations due to the input offset voltage of the amplifier.The dc analysis of this circuit has been presented to graphicallydemonstrate these limitations. Alternative feedback measurementscheme without employing the Wheatstone bridge is proposed. PIand predictive controller designs are described. Simulation resultsfor these controllers and a practical configuration are presented.

Index Terms—Constant temperature circuit, feedback control,predictive control, pulsewidth modulation, radiation measure-ment.

I. INTRODUCTION

A NEGATIVE feedback circuit configuration with a ther-moresistive sensor included in one of the arms of the

Wheatstone bridge has been employed in the measurementof fluid velocity [1], [5] and solar radiation [6], [7]. Thesensor is electrically heated to a desired temperature, and thevariation in the fluid velocity or incident radiation tends toproduce a change in the sensor temperature. This change iscompensated by changing the electrical heating due to thenegative feedback employed, and the sensor is maintained ata practically constant temperature.

In the case of measurement of fluid velocity, this configura-tion is known as a constant temperature hot-wire anemometer[2], [8]. There are other circuit configurations based on ther-moresistive sensors, e.g., constant current or constant voltage,but the so-called constant temperature configuration offers thelowest response time [8] and, for this reason, is by far themost popular in practice. In this measurement configuration,the square of the voltage across the sensor is related to thesurrounding temperature and incident thermal radiation if itexists. This nonlinear relation is quite inconvenient when thecircuit is used to measure the ambient temperature or solarradiation. A drawback of this configuration is its sensitivityto the offset voltage of the dc amplifier used in the feedbackloop. On one hand, the offset voltage is useful in preventingoscillations in closed loop, but on the other hand, it preventsthe sensor resistance from remaining strictly constant in thepresence 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 Paraıba, Campina Grande, PB,Brazil (e-mail: deep@dee.ufpb.br).

Publisher Item Identifier S 0018-9456(98)09756-3.

The dc analysis of a bridge circuit is presented to demon-strate the influence of the amplifier input offset voltage onthe measurement accuracy of the instrument and other perfor-mance limitations that it introduces. An alternative constanttemperature radiation measurement scheme based on controltheory concepts is proposed. The design of this feedbackscheme is formulated as a control problem to adjust theelectrical current through the sensor to maintain the sensortemperature constant. Two different control laws are employedfor this configuration. The performance of the proposed controllaws is evaluated by simulation, and a practical feedback con-figuration employing pulsewidth modulated current excitationfor the sensor is presented.

II. STATIC ANALYSIS OF THE BRIDGE CIRCUIT

Application of the first law of thermodynamics for the dy-namic thermal equilibrium of metallic thermoresistive sensor,with an electrical current passing through it and solar radiation

incident on it, yields the following [7]:

(1)

where is the incident solar radiation; is electricalpower dissipated in the sensor; is the sensor global heattransfer coefficient referred to its area; is the effectivetransmissivity-absorptivity product; is the sensor temper-ature; is the equivalent surrounding temperature; isthe sensor’s heat capacity; andis the time. Under staticequilibrium conditions (1) becomes

(2)

If the sensor temperature is kept constant, the variations inor may be substituted by corresponding variations in

the electrical power . This electrical power may be given asor , and thus the variation in or is directly

related to the variation in or .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 notremain really constant. Among other factors, this is caused bynonzero input offset voltage of the dc amplifier employed inthe feedback loop. On one hand, this offset voltage causes thislimitation, but on the other hand, it has a decisive influence onthe stability of the circuit [6]. In case this circuit is employedfor the measurement of solar radiation, the above offset voltage

0018–9456/98$10.00 1998 IEEE

1164 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 5, OCTOBER 1998

Fig. 1. The conventional constant temperature radiation meter.

also reduces the dynamic range of the circuit output voltage.This can be verified from the curves derived from thecombination of (2) and the circuit equations as shown below.

The temperature dependence of a metallic resistance sensor( ) is approximately given by [2]

(3)

where is the sensor resistance at 0C, is its temperaturecoefficient, and is the sensor temperature.

From (3) we can write and as follows:

(4)

and

(5)

Substituting (4), (5), and in (2),we have

(6)

For the circuit in Fig. 1, we have

(7)

and

(8)

Combining these two equations we have

(9)

The curves calculated from (6) for three values of( ; 0.5 and , where is the electrical

power dissipated in the sensor at the static operating point)are plotted in Fig. 2. The curves calculated from (9)considering constant at 10 and equal to 1, 2, and5 mV, are also shown in the same figure. The static circuitoperating point under different operating conditions and circuitparameters is the point of intersection of the corresponding

Fig. 2. CalculatedVo �Rs curves obtained from (9) with constantAo anddifferent values ofVos and those calculated from (6) with constantTa anddifferent values of�SH.

Fig. 3. Generalized representation of a measurement system.

two curves. It is thus easy to visualize that, fordifferent values of the measurand, the sensor resistance andconsequently its temperature varies.

The variation of the output voltage , for incident radiationvarying from zero to is more when the input offset voltageis 1 mV than when mV.

The nonlinear relation between the circuit output voltageand the measurand need more elaborate and complex

compensation schemes for cancelling the effects of variationof the surrounding temperature . In the following, analternative feedback circuit configuration is presented in whichthe sensor resistance is also maintained constant and outputvariable representing the measurand (i.e., incident radiation)is made directly proportional to . This output variable alsovaries linearly with the ambient temperature.

III. A LTERNATIVE FEEDBACK MEASUREMENT SCHEMES

Based on the recent representations of the measurementprocess [9]–[11], the thermoresistive sensor can be consideredto be an input block of the overall measurement scheme forthe present application. The sensor is subjected to the desiredmeasurand and an auxiliary adjustable electrical excitation(electrical power , Fig. 3). The objective is to monitor thevariation in the sensor resistance which can be quantifiedin terms of or . The functional blocks andrepresent the implementation of (1) and (3), respectively. Theelectrical power results from the auxiliary excitation andthe value of can be expressed in terms of and .

The proposed constant temperature measurement configura-tion employs feedback to maintain the sensor resistance value

OLIVEIRA et al.: FEEDBACK -CONTROLLED CONSTANT TEMPERATURE SOLAR RADIATION METER 1165

Fig. 4. A feedback control scheme withu(t)�I2s

andy(t)�Rs.

constant. This proposition is formulated as a control problem(Fig. 4) and in the conventional configuration (Fig. 1), thiscontrol occurs in an implicit form.

The input excitation variable and the system outputvariable are defined as follows:

(10)

and

(11)

where and are the proportionality constants. Fig. 4 showsa generic feedback scheme based on these ideas.

In this configuration, the dc gain of the controller should besufficiently high so that may be considered to remain prac-tically constant under static thermal equilibrium conditions.Further, represents the measurand .

Assuming and substituting (10) in (2), we have

(12)

As mentioned before, constant sensor resistanceimpliesconstant sensor temperature. The variation in is linearlyrelated to variation in or . As the variation can becompensated by the use of another sensor not subjected tothe measurand but exposed only to variation in, and ifthe measured variable of the compensating sensor is linearlyrelated with variation, this compensation amounts to asimple subtraction operation.

Two different controllers have been designed for use with athin film platinum sensor [12] employed for the measurementof incident solar radiation. The design criteria and simulationresults of the controller performance are given as follows.

A. PI Control Scheme

We may employ a procedure similar to the one usedfor the small signal analysis of a thermoresistive sensor-based feedback anemometer circuit [2], [6], for the analysisof a radiation measurement circuit. The dynamic thermalequilibrium equation (1) of the sensor is linearized arounda quiescent operating point with , (or ), ,and . Using Laplace transformation we get [13]

(13)

where

Fig. 5. Calculatedu(t) time response curves for step changes in the incidentradiation�SH = 0:1; 0:2; 0:4; � � �, 1:0Pe0.

and

Considering a PI controller with transfer functiongiven by

(14)

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 constantand 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 besignificantly affected by the presence of incident radiation.This can be verified from the simulation runs and is describedas follows.

The thin film platinum sensor described in [5] has thefollowing parameters: W/ C,

J/ C, ( C) , and .With no radiation incident on the sensor and C and

mA, we have: s, ,/A , and W. The choice

of and using pole–zero cancellation yieldsA s and A .

In Fig. 5, the calculated time response of forstep changes in the incident radiation for

and are shown. It is interestingto observe that the circuit time constant does not depend onthe amplitude of the incident radiation.

B. Predictive Control Scheme

Assuming in (10) and (11), and combiningthese with (4) and (1), we have

(15)

1166 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 5, OCTOBER 1998

The above equation can be discretized employing Euler’sfirst-order approximation [12] and may be written as

(16)

where 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 con-trol equation can be written as follows: Given thatis the desired value of the sensor resistance,seconds later,we calculate the value of which should be applied to thesensor at instant, using

(18)

where , , and are the estimated values of, , andand is the estimated value of [i.e., the value

of for the sensor which is shielded from the radiation].variation results in variation in , which in turn is

used in the estimation of .In Fig. 6 the plots of and , for three different

step changes in the incident radiation, have been calculatedusing the sensor characteristic equation (16) and the predictivecontrol law equation (18). We observe that the variationin the sensor resistance due to the change in the incidentradiation is really very small even for andthus the measurement configuration can be considered to bea practically constant temperature one and the is linearlyrelated with .

C. A Practical Configuration

The schematic feedback control configuration shown inFig. 4 can be practically implemented in various ways em-ploying analog-to-digital and digital-to-analog converters, anda digital signal processor. can be obtained from the sensorvoltage and current. The control law and the transformation ofvariables can be implemented in software with a digital signalprocessor or a microcontroller.

In Fig. 7, the sensor is excited with a pulsed current, isthe modulating signal for the pulsewidth modulator, andis the amplitude of the pulsed voltage across the sensor. Therms value of the sensor pulsed current waveform is given as

(19)

where is the current amplitude, is the pulsewidth, andis the repetition period.Equation (2) with replaced by or can

be rewritten as

(20)

(a)

(b)

Fig. 6. Calculatedu(t) and y(t) time response curves for step changes inthe incident radiation�SH = 0:1; 0:5; and1:0Pe0.

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

If the sensor resistance and its temperature are maintainedconstant, the estimate of the measurand is contained in thechange in value of the pulsewidth which can be readilyobtained in the digital form. From (19), can be written as

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 analogcomparators.

IV. CONCLUSIONS

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

OLIVEIRA et al.: FEEDBACK -CONTROLLED CONSTANT TEMPERATURE SOLAR RADIATION METER 1167

performance limitations. For example, the nonlinear relationbetween measurand and the electrical quantity actually mon-itored and the presence of dc amplifier input offset voltagedetermine the dynamic range of the output voltage. Theresistors used in the bridge circuit imply additional powerloss and larger bridge excitation voltage is required, whichimplies high values of supply voltage for the circuit. Thisconstitutes additional restrictions in the design of this circuitin the integrated circuit form.

In the proposed measurement configuration, the sensor isalso maintained at a practically constant temperature, usingfeedback control employing the measured variable namely

. This makes the change in the measured variable directlyproportional to the quantity to be estimated (i.e., radiationpower) and also to ambient temperature whose influence onthe measurement needs to be compensated.

With the use of pulsewidth modulated current for sensorexcitation, the pulsewidth becomes the monitored variableand is directly proportional to the incident radiation (i.e., mea-surand). The pulsewidth is measured using digital techniqueswith relative ease, and we obtain the desired measurement inthe digital form without the use of conventional analog-to-digital converter block. Absence of resistors in series with thesensor should permit the use of lower supply voltage which isan 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.NewYork: McGraw-Hill, 1976.

[3] K. Okamoto, T. Ohhashi, M. Asakura, and K. Watanabe, “A digitalanemometer,” inProc. IMTC/93—Instrumentation and MeasurementTechnology Conf.,1993, pp. 59–63.

[4] A. E. Perry and G. L. Morrison, “A study of the constant-temperaturehot-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 digitalanemometer with PWM excitation,” inProc. 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 thermoresistiveelectrical substitution pyrometer,” inProc. Solar Energy EngineeringConf., 1995, vol. 2, pp. 751–756.

[8] G. R. Sarma, “Analysis of a constant voltage anemometer circuit,” inProc. IMTC’93—Instrumentation and Measurement Technology Conf.,1993, pp. 731–736.

[9] P. K. Stein, “The unified approach to the engineering of mea-surement systems for test & evaluation—A brief survey,” inProc.IMTC’96—Instrumentation and Measurement Technology Conf.,1996,pp. 1–28.

[10] R. Z. Morawski, “Unified approach to measurand reconstruction,” inProc. IMTC’94—Instrumentation and Measurement Technology Conf.,1994, pp. 226–231.

[11] A. Barwicz, “System approach to electrical measurements,” inProc.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,”IEEETrans. Instrum. Meas.,vol. 43, pp. 133–138, Apr. 1994.

[13] A. Oliveira, “Sensores termo-resistivos em configura¸coes reali-mentadas,” Ph.D. dissertation, Universidade Federal da Paraıba,DEE/COPELE, Campina Grande, PB, Brazil, 1997.

Amauri Oliveira (M’88) was born on March 21,1954, in Rui Barbosa-BA, Brazil. He received theBachelor’s degree in electrical engineering fromFederal University of Bahia, Brazil, in 1979 andthe Master’s degree in electrical engineering fromCOPPE—Federal University of Rio de Janeiro in1982. He completed his doctoral work at FederalUniversity of Paraıba (UFPB), Campina Grande,Para´ıba, Brazil, in 1997.

He has been on the teaching faculty of UFBAsince 1983. His research interests include electronicinstrumentation and sensors.

Gurdip Singh Deep (M’76–SM’84) was bornon December 12, 1937. He received the B.Tech.(Hons.) degree in electrical engineering from IndianInstitute 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 inelectrical engineering from I.I.T. Kanpur, India, in1971.

From 1961 to 1965, he worked as an AssistantProfessor in Guru Nanak Engineering College

Ludhiana, and from 1965 to 1972, he was with the I.I.T., Kanpur, as aLecturer/Assistant Professor. Since July 1972, he has been a titular Professorat the Centre of Science and Technology of Federal University of Paraıba inCampina Grande, Brazil. Presently, he is the Coordinator of the ElectronicInstrumentation and Control Laboratory of the University. He has been aconsultant for Encardio-rite Electronics (Pvt) Ltd., India, during 1969–1970.His research interests are electronic instrumentation and microcomputer-basedprocess control.

Antonio Marcus Nogueira Lima (S’79–M’93) wasborn in Recife, Pernambuco, Brazil, in 1958. Hereceived the Bachelor’s and Master’s degrees inelectrical engineering from Federal University ofParaıba, Campina Grande, Paraıba, Brazil, in 1982and 1985, respectively, and the doctoral degreein 1989 from Institut National Polytechnique deToulouse, Toulouse, France.

He was with the Escola Tecnica Redentorista,Campina Grande, Para´ıba, Brazil, from 1977 to1982 and was a Project Engineer at Sul-America

Philips, Recife, Pernambuco, Brazil, from 1982 to 1983. Since September1983, he has been with the Electrical Engineering Department of FederalUniversity of Paraıba where he is now Professor of Electrical Engineering. Hisresearch interests are in the fields of electrical machines and drives, electronicinstrumentation, control systems, and system identification.

Raimundo Carlos Silverio Freire was bornon October 10, 1954, in Po¸co de Pedra-RN,Brazil. He received the Bachelor’s degree inelectrical engineering from Federal Universityof Maranhao, Brazil, in 1980, and the Master’sdegree in electrical engineering from FederalUniversity of Paraıba, Campina Grande, Paraıba,Brazil, in 1982. He received the doctoral degreein electronics, automation, and measurements atNational Polytechnical Institute of Lorraine inNancy, France, in 1988.

He worked as an Electrical Engineer for Maranhao Educational Television,in Brazil, from 1980 to 1983. He was a Professor of Electrical Engineeringat Federal University of Maranhao from 1982 to 1985. Since December1989, he has been on the faculty of the Electrical Engineering Departmentof the Federal University of Paraıba. His research interests include electronicinstrumentation and sensors, and microcomputer-based process control.