Indirect Control of Luminous Flux and Chromatic Shift Methodology Applied to RGB LEDs

Indirect Control of Luminous Flux and Chromatic Shift Methodology Applied to RGB LEDs Rodrigo G. Cordeiro, Alexandre S. Cardoso, Renan R. Duarte, Dieter G. Soares, Guilherme G. Pereira, William D. Vizzotto,Vitor C. Bender, Tiago B. Marchesan. Federal University of Santa Maria GEDRE Group of Intelligence in Lighting Santa Maria, Brazil rodrigo@gedre.ufsm.br Abstract This paper presents a method of control for RGB LED systems, modelling and equating of a system of LEDs are shown in details in order to obtain constant output luminous flux information for each color, reducing the color shift with the temperature variation. Also the paper discusses the control strategy employed and the methodology employed to eliminate the temperature influence on the color shift. Some simulation results are shown in order to prove the methodology, followed by some practical results. Keywords compensator; constant luminous flux; control; modelling; RGB LEDs; I. INTRODUCTION There are many applications with RGB LEDs at the decorative illumination and environments; also the use in Street Lighting is studied. The reason is its good performance on obtaining a high CRI (color rendering index) white, compared to blue LEDs with a layer of phosphor [1], [2], [3], [4]. The main issue in RGB systems is maintaining the desired color when the LED junction temperature varies. In order to do this, a constant luminous flux for each color is needed. However, usually an external measurement with photodiodes is used, which might increase the cost of the system [5]. To achieve a good performance synthesizing colors with an RGB system, PWM (Pulse Width Modulation) is commonly used as the dimming method. This method brings a lower chromatic shift at the desired color [6], [7]. The heatsink temperature variation represents an extremely slow dynamics compared to the frequency of dimming. This frequency is contemplated only with the measurement of the estimated flux and compensates a disorder with the current [2]. This paper proposes an indirect control of the output luminous flux for each color in RGB LEDs, through the measurement of the current on each LED and from the temperature on the heatsink in which they are attached. The main advantage of this system is going to be the replacement of an external optical sensor by a thermal sensor, which may reduce cost. II. RGB METHODOLOGY AND REFERENCE GENERATION A. Colorimetry Colorimetry is the study of the combinations from three colors, red, green and blue, in order to synthesize any color of the visible spectrum (from 400 nm to 700 nm) [8], [9], [10]. For LEDs, some studies show a solution in the synthesis of white, using the combination of these three primary colors, resulting in a white light source with a higher CRI [11], [12], [13], [14]. The CIE 1931 diagram (Figure 1) is mostly used in works on this subject as the standard to validate the coordinate from the desired color, [8]. Fig.1. CIE1931 Diagram [8] This color space represents mathematically the perception of color by the human eye. In this diagram, any color can be represented by two coordinates (Xc, Yc), where pure and saturated colors are located in the edges and the white light is at the center. However, CIE 1931 diagram does not present a perfectly uniform space and thus is not recommended to this type of analysis. Some studies were made to overcome this problem and resulted in two other color spaces that present better uniformity. These other diagrams are CIE1960 (Figure 2) and 978-1-4799-5551-0/14/$31.00 2014 IEEE

CIE 1976 (Figure 3). The equations for the conversion between the diagrams are shown in (1), (2), (3) and (4) [4]. 4x u 2x 12y 3 (1) 6y v 2x 12y 3 (2) B. Mac Adams Ellipses u' u (3) 3 v' v (4) 2 Fig. 4. Mac Adams elipses for CIE 1931 diagram [13] Mac Adams Ellipses rule is usually applied when analyzing chromaticity [8]. Due to the fact that the CIE 1931 diagram is a non-uniform color space, as shows Figure 4, it is necessary to convert x-y coordinates into u -v coordinates. Figure 5 shows the CIE 1976 diagram, where a better distribution of the ellipses is presented. Fig. 5. Mac Adams elipses for CIE 1976 diagram [8] Fig.2. CIE 1960 Diagram [8] The CIE 1976 diagram presents almost uniform ellipses, regarding to the human eye perception on color variation, as show both Figures 4 and 5. Equation (5) is used to analyze the chromatic shift. Smaller values for Δu v correspond to a small perception by the human eye. u ' v' ( u' u' ) ( v' v' ) 2 2 ref test ref test (5) C. Color flux reference Each color to be synthesized has a determined chromatic coordinate, calculated by the tri-stimulus represented in (6) array, as seen in [4]. Fig. 3. CIE 1976 Diagram [8] xr xg xb xc YR yr yg y B y C Y G 1 1 1. 1 Y B 1 xr yr 1 xg yg 1 xb y B 1 xc y C yr yg yb yc 1 (6) The solution of this matrix results in flux percentages of each color in relation to its predetermined nominal flux, thus generating a reference for the control system. This color system is processed by an identification algorithm, which will be set through a user command. All colors used in the color

palette have a chromaticity coordinate on a table for the user access. The calculation of each color contribution depends on an initial data from a chromatic coordinate and on the total flux to be achieved. In order to maintain the luminous flux without a color variation, it is necessary that each LED presents a constant flux. The luminous flux emitted by an LED relies on two variables: direct current and junction temperature. The higher the current is, the greater is the flux, but also higher is the junction temperature. Furthermore, the LED presents a decrease in its instantaneous flux. For the red LED the impact of the junction temperature variation is greater than the blue and green ones, due to their thermal parameters and thermal constants. Even though they are from the same family of LEDs, they present distinct both electrical and thermal characteristics. III. CONTROL SYSTEM A. Control strategy As the block diagram of Figure 6 shows, the program starts and so does the determination of the operating point of color and total flux, either by a user command or by standards established values. This operating point is sent to the control system as values of luminous flux, resulting in the first output values of the RGB system. The first values result in a luminous flux overshoot due to the initial system current saturation. The heatsink temperature and the average direct current are measured, and in possession of this, it is possible to calculate the estimated junction-case temperature of each RGB LED. With the values of current and junction temperature, the approximate flux output is estimated, without the need to measure it directly. Then, the luminous flux is compared with the selected color and flux reference block. If it differs from the reference chosen by the user, the compensation occurs through the control system before it is measured again. If it does not differ, a new measurement is made. Fig.6. Flowchart of the algorithm for each color B. Proposed System The system consists of a static converter working as a direct current source supplying a LED system, consisting of three LEDs, being one red, one green and one blue. The dimming is made by the switches S R, S G and S B through the PWM method, as shown in Figure 7. This current is controlled by switches in parallel with the LEDs, through the control that considers the current required to reach a predefined value of luminous flux and also the junction temperature effect of each LED. The major gain of this system is the luminous flux control of each color separately, reducing the chromatic shift. The system is supplied by a controlled current source. The current source s design is independent of the luminous flux control, which is not the focus of this work. Fig. 7. RGB system with current source

C. Proposed Control The control system diagram is presented in Figure 8. Direct Current (A) Low-Pass Filter (PWM to AvG Value) Heatsink Temperature ( C) Direct Voltage Calculation (V) Junction Temperature Calculation ( C) Fig. 8. Flowchart of the proposed control The calculation of the junction temperature is performed by measuring the heatsink temperature (H THS(s)), considering a thermal equilibrium. With the junction temperature value and the measurement of the average current in each LED (H id(s)), it is possible to estimate the output luminous flux (GΦ idths(s)). This value is compared to a predetermined reference value (Φ ref), either by the user or by a program synthesizer. The error (e Φ) is compensated by a flux compensator (C Φ(s)), generating a control action (u), which, through the luminous flux model (GΦD(s)) generates the control law (d) for the modulator (M(s)). The modulator synthesizes the PWM (D) to drive the switches, resulting in an average current for each LED. This current heats the heatsink, through the effect of non-radiative recombination of electrons and gaps on the semiconductor structure. The main prerequisites of the control system are: to maintain a constant luminous flux for each color, with minimal chromatic shift; to allow a great variability of colors to be synthesized by the system; to prevent LED overcurrent. D. Lumen Output Estimation This estimation requires the measurement of the current in each LED, or each branch of LEDs, and the temperature from the heatsink. The temperature is related to the luminous flux and is the junction-case temperature of the LEDs, and must be determined to be included in the calculation of luminous flux, as shown in figure 9. The junction temperature and forward voltage of the LEDs are defined by (7) and (8) respectively: E. Compensator Estimated Flux Calculation (lm) Control System (as controllable variable) Fig. 9. Flux estimation block diagram Considering the prerequisites of the RGB system, it requires a response that follows the reference and presents zero steady-state luminous flux error, guaranteeing the color and the total luminous flux desired. In order to obtain this response, a PI compensator is used. This compensator ensures zero error in steady state and a high gain at low frequency. The PI characteristic equation is represented by (9). Ki C( S) Kp S IV. SYSTEM MODELING For the modeling of the system, first, some information is needed from the datasheet of the selected LED, such as junction-case thermal resistance (R JC), nominal luminous flux and nominal current. Along with these values, usually, the datasheet presents the luminous flux related to the direct current and related to junction-case temperature (Figure 10). (9) T T R. V. I. k (7) jc HS JC F F h V V R. I (8) F fnom s F Fig. 10. Flux characteristic related to the junction temperature [15]

Thus, approximating the relative luminous flux by first order functions, it results in linear coefficients, which are used in the equations for the luminous flux modeling as shown in (10)..( c c. I ).( d d. T ) ( If, Tjc) NOM 0 1 f 0 1 jc (10) The current of the system depends on the duty cycle of the switches, as shown in (11). I (11) Due to the slow dynamics compared to the current and the operating range, the thermal parameters were shortly disregarded in the calculation of the reference flux. Thus, isolating the luminous flux and D(t), the transfer function is obtained. C 0 is equal to zero because the flux tends to zero when the current is zero, thus resulting in (12). ( t). C. I. C. D( t). I (12) NOM 1 NOM NOM 1 NOM Applying Laplace transform, it is possible to obtain the luminous flux model related to the duty cycle, as shown in (13). ( S) Ds () NOM CI 1. NOM (13) V. SIMULATION A. Calculation through parameters f (1 D). I NOM The parameters are shown in Table 1, referring to Cree LEDs, from Cree XLamp XR-C and XR-E families, as shown in Figure 11. Fig. 11. LED XR star from Cree [13] For this system, the following model equations were obtained from (13): G DRe d( S) 74.726 (14) G DGreen( S) 118.945 (15) G DBlue( S) 51.849 (16) The coefficient c 0 is usually equal to zero. The temperature of the system will act only as a disturbance to be compensated. Table 1. Absolute Values [15] Parameters Value Unit Nominal Current 0.7 A Linearization coefficient c 1 (Red) 2.6822 - Linearization coefficient c 1 (Green) 2.5286 - Linearization coefficient c 1 (Blue) 2.4206 - Linearization coefficient d 0 (Red) 1.0715 - Linearization coefficient d 0 (Green) 1.0474 - Linearization coefficient d 0 (Blue) 1.0119 - Linearization coefficient d 1 (Red) 0.0051 - Linearization coefficient d 1 (Green) 0.0019 - Linearization coefficient d 1 (Blue) 0.00051 - Junction resistance (Red) 15 C/W Junction resistance (Green and Blue) 8 C/W Direct resistance (Red) 0.7691 Ω Direct resistance (Green and Blue) 1.103 Ω Forward voltage (Red) 1.892 V Forward voltage (Green and Blue) 2.76 V Kh (transformation constant of energyluminosity) 0.85 - Nominal flux (Red) 39.8 lm Nominal flux (Green) 67.2 lm Nominal flux (Blue) 30.6 lm Thus, the compensator was calculated so that in steady state, at low frequency, presents a high gain, eliminating the luminous flux error. In steady state, the zero of the PI was added to one-tenth of the dimerization frequency (300 Hz). This frequency is commonly chosen to avoid the flicker frequency, from (7): ( s 188) C 0.009607 s ( s 188) CGreen 0.0059279 s ( s 188) CBlue 0.013614 s Red (17) (18) (19) This system has a converter operating as a controlled current source, working as a DC supply to the LEDs, as shown in Figure 7. The dimming is made by MOSFETs in parallel with the LEDs. Each luminous flux control loop corresponds to a color of the LED with its predefined parameters. Using the LED parameters from Table 1 and the equations (7), (8) and (10), it is possible to obtain the equations for the junction temperature, voltage and luminous flux for each color: TjcR THS 12.75 VFR I FR (20) TjcG THS 6.8V FGI FG (21) TjcB THS 6.8V FBI FB (22) VFR 1.892 0.7691 IFR (23) VFG 2.76 1.103 IFG (24) VFB 2.76 1.103 IFB (25) R ( IfR, TjcR ) 39.8(2.682 IfR)(1.0715 0.0051 TjcR ) (26) G ( IfG, TjcG ) 67.2(2.5286 IfG)(1.0474 0.0019. TjcG ) (27) B ( IfBTjcB, ) 30.6 (2.4206 IfB)(1.0119 0.00051 TjcB ) (28) The compensator also needs to be discretized to be used on a practical implementation. Therefore, the function is discretized using the ZOH (Zero-Order-Hold) method,

resulting in (29), (30) and (31) on z-domain and then after converted into differential equations in (32), (33) and (34). Gr () z 0.009607z 0.008454 Er ( z) z 1 (29) Gg () z 0.005928z 0.005217 Eg ( z) z 1 (30) Gg () z 0.01361z 0.01198 Eg ( z) z 1 (31) ur ( k 1) ur ( k) 0.009607 Er ( k) 0.008454 Er ( k 1) (32) ug ( k 1) ug ( k) 0.005928 Eg ( k) 0.005217 Eg ( k 1) (33) u ( k 1) u ( k) 0.01361 E ( k) 0.01198 E ( k 1) (34) B. Results b b b b The heatsink temperature should be equal for all the LEDs. The assumption is that all the LEDs are on the same heatsink and for this simulation the heatsink temperature is 25 ºC. In order to validate the method, distortions were included in the heatsink temperature. The first was an increase of 100 C after 400ms, and the second was a decrease of -40 C after 500ms, as shown in Figures 12, 13 and 14. Fig. 14. Estimated flux (lumens), Green LED current (I(Green)) and Green LED average current (AVG(I(Green))) with heatsink temperature disturbance The rise in the temperature causes a very significant reduction on the luminous flux for the red LED, saturating the current of the system. It can be concluded that the control responds to the temperature variation of the heatsink and the luminous flux is regulated by the average current using the PWM method. The impact of heatsink temperature variation on the red LED is greater than on the blue and green ones, due to their thermal parameters. Regardless of being from the same family, the three LEDs present distinct electrical and thermal characteristics. The disturbance has been applied to be visible for the three cases, with the blue and green LEDs under lower influence on the disturbances of heatsink temperature. On the red LED, the control signal reached its saturation until the next disturbance. The maximum current reached by the LED was not enough to maintain a steady luminous flux, saturating the system and keeping the maximum possible value. VI. IMPLEMENTATION AND VERIFIED COLORS Fig. 12. Estimated luminous flux (lumens), Red LED current (I(Red)) and Red LED average current (AVG(I(Red))) with heatsink temperature disturbance Fig. 13. Estimated luminous flux (lumens), Blue LED current (I(Blue)) and Blue LED average current (AVG(I(Blue))) with heatsink temperature disturbance The system has been implemented with the following components: RGB LEDs Xlamp XR-C e XR-E from Cree [15]. Kit LM4F120XL launchpad from Texas Instruments. Current sensors (ACS712). Drivers for isolated command. IRFZ24N MOSFETS for dimming. DC current source for LEDs (Inventfine CHL-8B). Temperature measurement device (LM35). Heater and cooler device. Integrating Sphere for Chromatic test (Inventfine). Some results were obtained with the system running, where 3 different colors were verified. Testing with the heatsink on approximately 50 C, it is possible to observe the position of the initial chromatic coordinate at approximately 30 C, in open loop and in closed loop. The procedure was, first, to use a closed-loop system, noting the approximate duty cycles for the synthesized color and making the first chromatic test. Then, raising the temperature in closed-loop, the second chromatic test was made. Lastly, the system was cooled and the procedure was repeated in open loop, starting at 30 C. So far, for all tests, the maximum luminous flux chosen is 150 lm.

A. White (R=50 lm, G=50 lm e B=50 lm) Table 2 shows the results for the white color. Table 2. Absolute values for White (R = 50 lm, G = 50 Lm, B = 50 Lm) Temperature Open-loop 30 C 0.3041 0.2483 149.6 lm 52 C 0.276 0.2492 130.4 lm Variation 0.0228-0.0009 19.2 lm Temperature Closed loop 30 C 0.2873 0.2463 142.3 lm 52 C 0.2867 0.2452 134.9 lm Variation 0.0006 0.0011 7.4 lm In closed loop, the white color (R = 50 lm, G = 50 lm, B = 50 lm) presented a reduction of 97.36% in variation for Xc coordinate, but an increase of 18% for Yc coordinate, using the CIE1931 diagram coordinates. The luminous flux variation was about 38.54% compared to open loop. B. Cyan (R=19.597 lm, G=116.644 lm and B=13.738 lm) For the cyan color, results are show in Table 3. Table 3.Absolute Values for Cyan (R = 19.597 Lm, G = 116.644 Lm, B = 13.738 Lm) Temperature Open-loop 30 C 0.2631 0.439 153.1 lm 52 C 0.243 0.445 141.5 lm Variation -0.020 0.0060 11.6 lm Temperature Closed loop 30 C 0.2563 0.446 146.4 lm 52 C 0.2525 0.4521 141.6 lm Variation -0.0038 0.0061 4.8 lm In closed loop, the cyan color (R=19.597 lm, G=116.644 lm, B=13.738 lm) presented a reduction of 81% in variation for Xc coordinate, but an increase of 1% for Yc coordinate, using the CIE1931 diagram coordinates. The luminous flux variation was about 58.62% compared to open loop. C. Orange (R=61.623 lm, G=88.022 lm and B=0.355 lm) Table 4 shows the results for the orange color. Table 4. Absolute Values for Orange (R=61.623 Lm, G=88.022 Lm, B=0.355 Lm) Temperature Open-loop 30 C 0,5034 0,4315 155.4 lm 52 C 0,4743 0,4532 132.4 lm Variation -0,0291 0,0217 23 lm Temperature Closed loop 30 C 0.5021 0.4363 159.5 lm 52 C 0.4998 0.4394 149.1 lm Variation -0,0023 0,0031 10.4 lm In closed loop, the orange color (R = 61.623 lm, G = 88.022 lm and B = 0.355 lm) presented a reduction of 92.09% in variation for Xc coordinate, but an increase of 85.71% for Yc coordinate, using the CIE1931 diagram coordinates. The Luminous flux variation was about 54.78% compared to open loop. Through the conversion equations (1), (2), (3), (4) and the chromatic varation (5), it is possible to analyze the variation in terms of CIE 1976. After the conversion, it can be concluded that the Δu v variation is significantly greater in open loop, as seen on table 5. Table 5. Chromatic variation Δu v for open-loop and closed-loop Color Δu v Open Loop Δu v closed Loop White 0,02373790 0,00092400 Cyan 0,01218590 0,00344700 Orange 0,02765290 0.00294914 D. Chromatic test views The chromatic shift is not usually mathematical analized throught the CIE 1931 space because it is a non-uniform diagram for color shifting, however, the chromatic shift can be viewed through the CIE 1931 space coordinates, only for illustration. The figures 15, 16 and 17 shows the color shift on CIE 1931 diagram for the white color (R=50lm, G=50lm, B=50 l, the cyan color (R = 19.597lm, G = 116.644lm, B = 13.738lm) ant the orange color (R=61.23lm, G=88.022lm and B=0.355). To the 3 cases, the chromatic shift presented a relevant reduction for the closed loop test. Fig. 15. Color shift for white Fig. 16. Color shift for cyan

Fig. 17. Color shift for orange VII. CONCLUSION This work has proven to be satisfactory to the view of proposing a solution to an RGB control system concerning chromatic shift originated from the junction temperature. A methodology assuming the thermal and electrical behavior of the red, green and blue LEDs, taking into consideration its key features was presented. The system was solved and a mathematical routine was created in order to maintain constant luminous flux for each color, thus ensuring reduced chromatic shift to the desired color. The methodology has proven to be effective through simulation, making the luminous flux invariant in time, even with sudden heatsink temperature disturbances. It should be noticed that this system can be extended to a larger number and different kinds of LEDs of each color, making only the luminous flux of each pattern in the arrangement relevant. The practical results present a good reduction of the absolute values of variation, both chromatic and flux for each color and with mixed colors. [5] S. Muthu, J. Gaines, Red, green and blue LED-based white light source: implementation challenges and control design, Industry Applications Conf. - IAS, vol. 1, pp. 515-522, 2003. [6] Buso, S., Spiazzi, g., & Meneghini, m. Performance Degradation of High-Brightness Light Emitting Diodes Under DC and Pulsed Bias. IEEE TRANSACTIONS ON DEVICE AND MATERIALS RELIABILITY, pp. 312-322, 2008. [7] Tan, S. C. General n-level Driving Approach for Improving. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, pp. 1342-1353, 2010. [8] Schubert, E. F. Light-emitting diodes (2ª ed.). Cambridge University Press, 2007. [9] Ying, S. P., Tang, C. W., Huang, B. J, Charaterizing LEDs for Mixture of Colored LED light sources, IEEE, 2006. [10] Yang,Y.R. A High-Brightness RGB-LED Lamp Using Palette and PNM Current Driver, IEEE Industry Electronics, 2009. [11] Xiaohui Qu, Siu Chung Wong and Chi K. Tse, Color Control System for RGB LED Light Sources Using Junction Temperature Measurement, IECON 2007. [12] Pinto, R. A; Cosetin, M.R. ; Marchesan, T.B. ; da Silva, M.F. ; Denardin, G.W. ; Fraytag, J. ; Campos, A. ; do Prado, R.N. Design procedure for a compact lamp using high-intensity LEDs, IECON 2009.. [13] Cree, LED Color Mixing: Basics and Background, Applicaton note, Cree 2010. [14] Hui, S.Y.R, Qin, Y.X, A General Photo-Electro- Thermal Theory for Light Emitting Diode (LED) Systems, IEEE, 2009. [15] Cree, Cree XLamp XR-C and XR-E LEDs, Datasheet, Cree, 2010 Taking into consideration the rule of Mac Adam ellipses, of the CIE 1976 diagram, it follows that in the final analysis of the results, the data in closed loop corresponds to a smaller variation considering the perception of the human eye compared to the data in open loop, validating the proposed methodology. ACKNOWLEDGMENT The authors are grateful to CAPES for the financial support given during the research. REFERENCES [1] B. Ackermann, V. Schulz, C. Martiny, A. Hilgers, X. Zhu, Control of LEDs,IAS 2006. [2] Bender, V. C; Cardoso, A. S; Flores, G. C;Rech, C; Marchesan, T. B. Electrothermal Feedback of a LED Lighting System:Modeling and Control,IECON 2012. [3] D. Gacio, J. M. Alonso, J. Garcia, M. S. Perdigao2,3, E. Saraiva, F. E. Bisogno, Effects of the Junction Temperature on the Dynamic Resistance of White LEDs, IEEE 2012. [4] Vizzotto, W. D., Pereira, G. G., Cordeiro, R. G., Bender, V. C., Dalla Costa, M. A., Marchesan, T. B., Electrothermal Characterization Applied To The Study Of Chromaticity Coordinates In Rgb Leds, COBEP 2013.