Analysis of an Improved Temperature Management Concept forSAR System Calibration Transponders

Sebastian Raab, German Aerospace Center (DLR), sebastian.raab@dlr.de, GermanyBjörn J. Döring, German Aerospace Center (DLR), bjoern.doering@dlr.de, GermanyDaniel Rudolf, German Aerospace Center (DLR), daniel.rudolf@dlr.de, GermanyJens Reimann, German Aerospace Center (DLR), jens.reimann@dlr.de,m GermanyMarco Schwerdt, German Aerospace Center (DLR), marco.schwerdt@dlr.de, Germany

AbstractFor the radiometric calibration of spaceborne synthetic aperture radar systems, active targets with known backscatter,so called transponders, are used. These serve as an external absolute reference, and the quality of the derived calibra-tion parameters depends on the quality of the deployed transponders. Due to the temperature dependent behavior ofthe implemented active radio frequency components the transponder radar cross section is sensitive to the temperatureof the components. This effect requires the implementation of a reliable and precise temperature management systemto stabilize the temperature of the radio frequency components to a constant value under all relevant environmentalconditions. In order to fulfill the increasing requirements for future transponders towards radiometric accuracy tem-perature control concepts must be further developed. For this purpose, an existing temperature management systemsis analyzed and a control design concept is investigated. Finally the functionality of the implemented temperaturemanagement system is verified with measurements of the complete transponder system in a climatic chamber.

1 Introduction

For the radiometric calibration of a spaceborne syn-thetic aperture radar (SAR) system point targets with wellknown backscatter properties, e. g. corner reflectors andtransponders, are used [1]. Those act as an absolute refer-ence and the quality of the derived calibration parametersinherently depends on the quality of the deployed targets.Any uncertainty in their reflectivity, e. g. caused by ther-mal variations, influences the calibration of the SAR in-strument and consequently the quality of the calibratedSAR images.

A transponder is an active device with a known radarcross section (RCS), determined during an external cal-ibration process [2] [3]. With its implemented RF loop areceived signal is amplified, possibly recorded and modi-fied before it is retransmitted to the radar system. The re-flectivity is temperature sensitive due to the temperature-dependent behavior of the RF components installed in thetransponder. To minimize the corresponding gain drift ef-fects a temperature management system is typically in-tegrated in the transponder which maintains the inter-nal temperature during operation at an almost constantvalue. This is an important feature in order to ensure thethermal stability of the transponder at different environ-mental conditions. Together with an accurate knowledgeof the backscattering characteristics the stability of thetransponder is a prerequisite for an accurate and reliablecalibration of a spaceborne SAR system.

2 Thermal DesignThe DLR Microwaves and Radar Institute has designed,developed and manufactured new C-band transponders[4] [5], shown in Figure 1, which have been successfullyoperated for ESA’s Sentinel-1A mission since April 2014[6] [7].

Figure 1: DLR Kalibri transponder with cover removed.

These Kalibri transponders are equipped with a well in-sulated housing and a heat exchanger. For thermal con-trol the heat loss of the active sub-components, e. g. thedigital-sub-system (DSS), is used. The thermal trans-fer is regulated by several fans installed inside the heatexchanger. Figure 2 shows simulations of the thermalflow inside the transponder. The air-flow follows an S-pattern through the device. By reading out several sen-sors the temperature within the housing can be monitored

and controlled.

Figure 2: Thermal simulation for the Kalibri transponderthermal design.

3 Gain Drift Compensation and De-pendence on Temperature

Serving as reference, the transponder impulse responsemust be stable after determination of its RCS by an exter-nal calibration [2] [3]. For this purpose, a gain drift com-pensation "facility" is implemented within the Kalibritransponder to minimize gain and phase changes of theradar signal path over time. This compensation is imple-mented in two steps: monitoring and correction. There-fore a calibration signal is generated by the DSS, fed intothe transmitting path, then routed through a gain compen-sation loop by two radio frequency (RF) switches, andfinally recorded again by the analog-to-digital-converter(ADC) of the DSS, shown in Figure 3.

D

DA

RXantenna

TXantenna

Gain compensationloop

RX chain (includingactive components)

TX chain (includingactive components)

Digital sub-system

- Digital delay- Signal recording- Gain correction

A

D

D

A

Figure 3: Schematic block diagram of a transponder in-cluding a gain compensation loop.

Assuming a constant attenuation in the gain compensa-tion path, variations of the calibration signal must becaused by the receiving or transmitting path. They canbe compensated by adjusting the variable attenuator inthe transmitting path and by modifying the signal in theDSS. This procedure runs repeatedly and finishes whenthe gain setting has reached its nominal value, determinedduring external calibration of the transponder.

4 Temperature Management

Current temperature management systems of SAR cali-bration transponders are commonly based on a closed-loop control, shown in Figure 4. In case of the Kalibritransponders the speed of the fans, integrated in the heatexchanger, is regulated by the controller.

Temperaturecontrol unit

Internal transpondertemperatures

Temperaturesensor

Heat exchangerwith integratedfans

Fans

Transpondertemperature

Fanspeed

Controller

Plant

-

Desiredtranspondertemperature

Feedback loop

Figure 4: Block diagram of a closed loop temperaturecontroller for a transponder.

In addition to the selection of suitable hardware compo-nents for the transponder temperature stabilization (e. g.properties of insulating material , sufficient capacity ofthe heat exchanger) the design and implementation of aconvenient controller algorithm is one of the main chal-lenges. When it comes to erratic environment changes,e. g. caused by extreme weather changes, an unadaptedcontroller can only react inadequately slowly. This canlead to significant RCS changes of the transponder. Anexample of the gain and temperature drift recorded bya Kalibri transponder is shown in Figure 5. Due to un-stable temperature conditions (lower diagram) the imple-mented gain compensation procedure is not able to sta-bilize the loop gain (upper plot). With a efficient tem-perature management system the transponder RCS canbe stabilized with a precision of 0.01 to 0.02 dB. Theshown uncertainty of 0.2 dB at unstable thermal con-ditions (Figure 5, upper diagram) leads to relevant de-viation in the transponder RCS. It can be seen that thegain variation correlates with the transponder tempera-ture. This fact underlines the need of an efficient temper-ature management system because the gain drift compen-sation is not able to ensure a constant transponder reflec-tivity under erratic environmental changes.

Figure 5: Example for temperature-dependent RCS driftbased on data recorded during test measurements.

4.1 Concept for Controller Design

In control engineering the main procedure for analysisand design of a controller are based on an adequate mod-eling of the controlled section, so called plant. Figure 6.shows the fundamental procedure for controller develop-ment. From the nominated model equations of the con-trolled system an adequate control law is derived whichin turn is the basis of the realization of the suitable con-troller [9].

Controlledsystem Controller

Controller tuning methods

Fuzzy control logic

or

Process domain

Fuzzy control logic

Model ofplant

Control design Control law

Model domain

Modeling Realization

Figure 6: Fundamental procedure for the solution of con-trol tasks according to [9].

In case of the transponder temperature management therealization of the controller design in the model domaincan be a difficult matter so that considerable effort has tospent for analysis, simulations, and tests of the transpon-ders thermal behavior. Capturing all influences fromall transponder sub-components to a sufficient thermalmodel can only be reached by operating much effort (i. e.people, facilities for thermal tests, time) to this challenge.

A simpler process to find a suitable controller is a di-rect design in the process domain. As shown in Figure 6the two strategies of controller tuning methods and fuzzycontrol logicl are available for this purpose. Both meth-ods are promising an adequate control design in orderto find a sufficient control algorithm for the transpondertemperature management system.

By using a controller tuning method for the design ofthe transponder temperature controller the properties ofthe transponders thermal behavior is identified throughfew experiments with the complete transponder only. Nothermal analysis of the transponders sub-components arenecessary in order to find the right controller. This is abig advantage with respect to the required effort in com-parison to the plant modeling approach described above.The second eligible method is based on the usage offuzzy logic. Therefore a controller is designed by usingthe already known knowledge about the thermal behav-ior of the transponder. All informations are implementedas so called fuzzy rules and processed within a definedlogic method to an overall controller [10]. In compari-son to the model domain approach this strategy promiseslower efforts in order to model the thermal behavior ofthe transponder. On the other side the efficiency of thismethod depends on the knowledge about the thermal ef-fects of the transponders sub-components [10]. In com-parison to the controller tuning strategy additional effortin characterizations of the overall thermal transponderenvironment with several sub-component test measure-ments is expectable because the fuzzy logic needs infor-mation of the thermal behavior on sub-components level.At the controller tuning method in contrast few exper-iments with the complete transponder system are suffi-cient promising the design of a comparable controller.For this reason the controller tuning strategy is appliedfor the design of the temperature management concept ofthe SAR system calibration transponder.

4.2 Identification of Thermal TransponderSystem

As described in Section 2 the heat loss of the active sub-components combined with a heat exchanger is used forthermal control of the transponder. By regulating thespeed of the fans, installed in the heat exchanger, thethermal transfer is regulated. Figure 7 shows the cor-responding hardware setup. According to Figure 4 thefan speed defines the actuating signal of the control sys-tem. This means the control algorithm computes thecurrent speed which is given as a pulswidth modulated(PWM) signal to the fans. Hereby the thermal transferbetween the transponder and outdoor environment is reg-ulated through the heat exchanger.

Figure 7: Heat exchanger sub-component with four in-stalled fans.

The performance of a heat exchanger can be approxi-mated as a nonlinear system of first order with time delay[11] [12]. This model can be used for the application ofa controller tuning method. The corresponding transferfunction is defined as [9]

G(s) =K

Ts+ 1· e−sτ (1)

where K is defined as the gain, T as the time constant,and τ as the time delay. In Figure 8 the step response isshown.

0,63 K

K

TTime

τ

InputOutput

Figure 8: Step response of a nonlinear system of first or-der with time delay. The system parameters K,T , andτ can be derived from graphical analysis, shown in thisFigure.

By measuring the step response the parametersK, T , andτ of such a system can be determined with graphical anal-ysis, shown in Figure 8. In case of the transponder thestep response can be determined by setting the fan speedon a constant value and measure the temperature to becontrolled.

4.3 Controller Design

The proportional plus integral plus derivative (PID) con-trol function is one of the commonest used controller inpractical applications. Dependent on the used parametersthis algorithm promises a fast regulation of the controlledvariable to the desired value without any relevant over-shoot [9] [11]. The transfer function of a PID controllerist given by [9]

KPID(s) = KP (1 +1

TIs+ TDs) (2)

where the controller gain KP , the integral time TI , andthe derivative time TD are the parameters to be deter-mined during controller design. The performance of thecontroller depends on the quality of this controller param-eters.With a measured step response of the controlled sectionand the resulting plant parameters K, T , and τ , the pa-rameters for a adequate PID controller can be derived[9]. Therefore several algorithm are available. A com-mon used strategy is the so called Ziegler-Nichols tuningmethod [9]. According to this method the parameters fora PID controller can be derived from the following rela-tions

KP =1, 2 · TK · τ

, TI = 2 · T, TD = 0, 5 · τ . (3)

Together with the controller transfer function, shown inEquation 2, a software PID controller can be realized andimplemented to the temperature management system ofthe transponder. According to Figure 4 the controller de-termines the fan speed from the difference between de-sired and measured temperature. In a closed loop systemthis process is repeated continuously. When the desiredtemperature is reached and the system stays in a thermalequilibrium the fan speed is set to a nearly constant value.Without any disturbances (e. g. by sun illumination orrapid changes in the outdoor temperature) no changes areexpected.The step response of the thermal transponder behaviorwas measured in a climatic chamber at a constant tem-perature of 17◦ C. The fan speed was set to a constantvalue of 40 % of the maximum speed. When the ther-mal transponder system was in a stable condition (i. e.no longer variation of the controlled temperature) thespeed was increased erratically to the maximum valueand the temperature was measured. The result is shownin Figure 9.

Figure 9: Measured step response of the transponders’thermal system.

It can be seen that the temperature shows a nonlinear be-havior. Due to the fact that the transfer of the internal heat

loss is increased with a higher fan speed the internal tem-perature decreases after the erratic speed change. Takinginto account this fact the result confirms that the thermalenvironment can be modeled with a nonlinear system offirst order with time delay, like described in Section 4.2.The corresponding system parameters can be derived asshown in Figure 8. The results are K = 0.05◦C per %fan speed, T = 28.5 minutes, and τ = 0.75 minutes.According to Ziegler-Nichols tuning method, describedin Section 4.3, the PID controller parameters were deter-mined with Equation 3, yielding to KP = 91% fan speedper ◦C, TI = 90 seconds, and TD = 22.5 seconds.

5 Measurements with PID Con-troller

The PID controller with the derived parameters from Sec-tion 4.3 was realized and implemented into the transpon-der temperature management system. The controllersfunctionality and performance was verified with a tem-perature measurement. For this purpose the transpon-der was placed inside a climatic chamber with a stabletemperature of 17◦ C. During this measurement all sub-components were switched on in order to achieve thesame internal thermal conditions as in normal operationmode. When the transponder temperature reached a sta-ble value the set-point temperature was reduced by onedegree C. Consequently the management system reactswith an increased fan speed and controls the internal tem-perature to the desired value. Figure 10 shows the mea-sured temperature behavior of the transponder.

Figure 10: Performance of the transponder temperaturemanagement system after changing the goal temperature.

the desired temperature was reached without any signif-icant overshoot. After 30 minutes the transponder hasa nearly stable behavior. Consider the fact that duringregular transponder operation the goal temperature is setseveral hours before an upcoming satellite overpass themeasured response time of the thermal system can beseen as efficient enough. Furthermore the implementedtransponder insulation delays the effect of external ther-mal disturbances. The designed controller should be ableto compensate these changes in a appropriate time so that

together with a implemented gain drift compensation theaccuracy of the transponders RCS is not be influenced.

6 ConclusionThis paper describes the temperature management sys-tem for SAR system calibration transponders. Next tothe control design a gain compensation concept is intro-duced in order to improve the temperature-depenendetaccuracy of the transponder RCS. For the design of a PIDcontroller two eligible methods are introduced shortlyand their applicability for the transponder temperaturemanagement system is compared. Due to effort consid-erations the controller tuning method is finally recom-mended as the most suitable strategy. According to thisconcept the thermal behavior of the transponder systemis identified from climatic chamber measurements. Thetemperature management concept for the transponder isimplemented with the derived control parameters. Finallythe functionality of the designed management system isverified with thermal measurements. The results showthat the chosen tuning method is a proper strategy for thedesign of a suitable temperature management system forSAR system calibration transponders.

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