IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, zyxwvutsrqpo VOL. 43, NO. 2, APRIL 1994 133 Identification of Thermoresistive Solar Radiation Sensors Antonio Marcus Norgueira Lima, zyxwvutsr Member, IEEE, Gurdip Singh Deep, Senior Member, IEEE, JosC SCrgio da Rocha Neto, Raimundo Carlos Silverio Freire, and Pi0 Caetano Lobo Abstract- An identification procedure to estimate the param- eters of a thermoresistive solar radiation sensor is presented. The proposed technique employs only electrical excitation for the sensor. The estimation algorithm is recursive and is applied to the sensor model derived from the thermodynamic equilibrium dif- ferential equations. The simulation and the experimental results demonstrate the validity of the proposed approach. I. INTRODUCTION HE principal desired characteristics of a solar radiation T sensor zyxwvutsrq are fast time response zyxwvutsrq (< 1 s) and wide wavelength spectrum (0.3pm < X < 0.5pm). zyxwvutsr A typical thermoresistive sensor responds over a broad radiation spectrum, has a long response time, and is relatively inexpensive. However, the use of this kind of sensor in an autobalanced feedback bridge circuit, enables sensor operation at a constant temperature, and consequently provides a substantial reduction in the response time of the overall bridge transducer. The output voltage of the feedback bridge circuit is a measure of the incident radiation [11-[31. The reduction of the response time, obtainable with the bridge circuit, can be determined experimentally by subjecting the sensor to a sudden change in the incident radiation and monitoring the feedback amplifier output voltage [2], [3]. The theoretical analysis of the dynamic behavior of the above bridge radiation transducer involves the thermodynamic model of the sensor and feedback circuit relations. A pre- liminary formulation of the above structure reveals that the closed-loop operation is described by nonlinear differential equations. The numerical solution of these equations requires the knowledge of the different sensor parameters such as heat transfer coefficient and thermal capacity. These parameters can be estimated using system identifica- tion methods and experimental data related to the transducer response. A preliminary technique to determine the response time of the thermoresistive sensor, employing only electrical Manuscript received May 18, 1993; revised October 25, 1993. This work was supported in part by the Conselho Nacional de Desenvolvimento Cienti fico e Tecnol6gico (CNPq), the CoordenacHo de Aperfeicoamento de Pessoal de Ensino Superior (CAPES), and the Plan0 Nacional de Desenvolvimento Cienti fico e TecnoMgico (PADCT). A.M.N. Lima, G.S. Deep, R.C.S. Freire, and P.C. Lobo are with the Department of Electrical Engineering, Federal University of Paraiba, 58 109- 970 Campina Grande, PB, Brazil. J.S.R. Neto is with the Department of Electrical Engineering, State Univer- sity of Santa Catarina, Joinville, SC, Brazil. IEEE Log Number 9215997. Fig. 1. Physical sensor dimensions. excitation, has yielded satisfactory results [l], [2]. If the electrical excitation source for heating this sensor is ade- quately chosen, it is possible to estimate correctly the sensor parameters and thus determine a model for the radiation sensor. In the following, a parameter identification or estimation procedure for a thermoresistive sensor is presented. A math- ematical model for this sensor is derived from its physical description and the thermodynamic energy conservation rela- tions with the sensor subjected to electrical excitation in the absence of incident radiation. 11. SENSOR MODELING A thermoresistive sensor, employed for the measurement of solar radiation, is sensitive to the variation of 1) the incident radiation, 2) the electric current through the sensor, and 3) the nonsolar environment. This sensitivity of the radiation sensor to the variations in the environment is an undesirable characteristic. A possible method to compensate the undesired effect of the ambient temperature in a solar radiation meter is to employ two identical sensors, one painted black (sensitive to the incident radiation, electric current, and the ambient temperature) and other painted white (sensitive to electric current and the ambient temperature). By simple algebraic manipulations of the measurement results of the two sensors, subjected to the incident radiation, it is possible to obtain the measurement of radiation, independent of the ambient temperature. In the model tested, each sensor (black or white) consists of a thin platinum film deposited on a ceramic substrate, covered with a thin protective glass coating (Fig. 1). The area of each of these sensors is approximately 20mm2, and its measured electrical resistance is 113.14 R at 27°C. zyx 00 18-9456/94$O4.O0 zyxwvutsr 0 1994 IEEE