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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 9, SEPTEMBER 2014 4921

Illumination and Color Control in Red-Green-BlueLight-Emitting Diode

Chun-Wen Tang, Bin-Juine Huang, and Shang-Ping Ying

Abstract—The concept of red-green-blue (RGB) light-emitting-diode (LED) lighting has gained wide attention during recent yearsand is now one of the targets for future lighting solutions. However,the self-heating of LEDs and environmental temperature variationlead to luminous intensity droop and lighting color drift. The mainpurpose of this research is to investigate a novel flux feedbackand temperature feed-forward (FFB&TFF) control structure forRGB LED lighting control system, in order to provide a wide colorrange of input commands and regulation of both luminous andcolor outputs. The work in this paper was carried out in threemain steps. First, a thermal–electrical–luminous–chromatic modelwas derived and identified for RGB LED luminaire. Second, aconverter and a compensator were derived and applied to inputcommand conversion and temperature compensation, respectively.Finally, a diagonal proportional–integral controller designed by thedecentralized control approach was implemented to regulate thelighting outputs of luminous intensity and chromaticity coordinatesin CIE 1976 Uniform Chromaticity Space (UCS) diagram. Theresults of transient and steady-state experiments showed that theproposed control system was effective.

Index Terms—Decentralized control approach, flux feedbackand temperature feed-forward (FFB&TFF), red-green-blue (RGB)light-emitting-diodes (LEDs), system identification, thermal–electrical–luminous–chromatic model.

I. INTRODUCTION

L IGHT-EMITTING diodes (LEDs) are a highly effectivelighting technology. Energy saving and long lifetimes are

the main advantages in lighting applications. Red-green-blue(RGB) LED lighting is one of the most popular techniquesfor white light in the application of LCD backlighting, videoprojection and general lighting. Its chromatic changeability andwide color range can provide unique lighting experiences [1].However, the luminous and color outputs are easily affectedby self-heating of LEDs as well as environmental temperaturevariations [2], [3]. Thus, a control system for RGB LEDs iscalled for to regulate both luminous and color outputs. The keyissue of effective regulation is a proper control structure design.

Manuscript received November 15, 2012; revised January 15, 2013; acceptedFebruary 20, 2013. Date of current version April 30, 2014. Recommended forpublication by Associate Editor J. M. Alonso.

C.-W. Tang is with the Industrial Technology Research Institute, Hsinchu31040, Taiwan (e-mail: [email protected]).

B.-J. Huang is with the Mechanical Engineering Department, NationalTaiwan University, Taipei 106, Taiwan (e-mail: [email protected]).

S.-P. Ying is with the Opto-Electronic System Engineering Department,Minghsin University of Science and Technology, Hsinchu 30401, Taiwan(e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2013.2251428

Several studies in the literature have proposed and comparedto four control structures [4]–[10], that is, flux feedback (FFB),temperature feed-forward (TFF), FFB and temperature feed-forward (FFB&TFF), and color coordinates feedback (CCFB).Both FFB&TFF and CCFB algorithms have shown better colorstability. Because of easy implementation, CCFB methods havebeen studied by several authors [4]–[15] and shown effectivecolor accuracy. However, the accuracy of color output would berestricted by temperature effect [7], inverted sensor matrix [6],[7], and spectra responses mismatch of the filtered color sen-sor [6], [8]. The FFB&TFF method can avoid those drawbacksbut require complex flux measuring technique [7]. Moreover, analgorithm of temperatures to color control commands instead ofCCFB must be derived. Wang et al. [15] adopted a static lookuptable as feed-forward compensator for FFB&TFF method toimplement the algorithm and input command conversion. How-ever, the lookup table designed at 25 fixed operating conditionswould confine the color range of the input commands. There-fore, the aim of this research is further to investigate a novelFFB&TFF control structure that can apply a wide color rangeof input commands and achieve transient and steady-state re-quirements of both luminous and color outputs. The effect isexperimentally verified.

The paper is organized as follows. In Section II, a novelFFB&TFF control system with a thermal–electrical–luminous–chromatic model of RGB LED luminaire, a converter, and acompensator is proposed. In Section III, the system identifica-tion of the RGB LED luminaire, the converter, and the compen-sator are presented. In Section IV, the controller design is furtherintroduced. In Section V, the designed control system is imple-mented for performance analysis. Finally, some conclusions aredrawn in Section VI.

II. SYSTEM DESCRIPTION AND MODELING

A. System Description

In this study, a novel FFB&TFF control structure of RGBLED lighting is proposed as shown in Fig. 1, in which TCCrand Φr represent the correlated color temperature (CCT) com-mand and total luminous intensity command, respectively, andTCC ,OUT and ΦOUT represent CCT output and total luminousintensity output for lighting, respectively. A converter N is ap-plied to transform from TCCr and Φr to three dependent sig-nals: converted radiant power LA , converted electrical powerPA , and converted junction temperature TA . A compensator Mis applied to obtain the radiant compensation LM to compensatethe LA , by using the junction temperature of RGB LEDs TLED ,the electrical power of RGB LEDs PLED , converted electrical

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4922 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 9, SEPTEMBER 2014

Fig. 1. Control structure of the RGB LED lighting control system (Solid lines:scalar signals; mesh lines: vector signals).

power PA , and converted junction temperature TA . The radiantcommand LC = LA + LM is a reference which leads TCC ,OUTand ΦOUT following TCCr and Φr , respectively. The controllerK is adopted to calculate a relevant PLED according to the errorsignal e. The dynamics of RGB LED luminaire are modeled asGLED with two outputs: ΦOUT as luminous output; and chro-maticity coordinate in CIE1976 Uniform Chromaticity Space(UCS) diagram [u′

OUT , v′OUT]T as color outputs. The TCC ,OUT

is transformed from [u′OUT , v′

OUT]T by using a chromatic trans-former F . The FFB loop carries out the radiant power of RGBLEDs LS , acquired from the luminous intensity of RGB LEDsΦLED , tracking LC to regulate ΦOUT ; moreover, the TFF loopperforms TCC ,OUT following TCCr since the M provides ac-curate LM . Furthermore, a proper controller of FFB loop canguarantee transient and steady-state performance of ΦOUT andTCC ,OUT .

B. Modeling of RGB LED Luminaire GLED

RGB LED luminaire is a lighting fixture assembling mul-tiple RGB LED lamps on a common heatsink. The RGB LEDlamp is an electrical device, packaging red, green, and blue LEDchips, driven by electrical powers for diverse color LEDs indi-vidually. According to the law of energy conservation, LEDsemit photons and simultaneously generate heat when electricalpowers are applied. Photon emission will generate a spectrum,i.e., spectral power distribution (SPD), to produce luminous andcolor perception [16]. The heat will raise the junction tempera-ture, which leads to low quantum efficiency [17], spectral shiftof SPD [17], and current droop [18], [19], to cause color driftand luminous intensity droop.

In this study, the total luminous intensity output ΦOUT andchromaticity coordinates outputs in CIE 1976 UCS diagram[u′

OUT , v′OUT]T were both chosen as outputs of RGB LED lu-

minaire as follows:⎡⎢⎣

ΦOUT(s)

u′OUT(s)

v′OUT(s)

⎤⎥⎦ = GLED(s) · PLED(s) (1)

where GLED is the RGB LED luminaire model, PLED = [PR

PG PB ]T is the electrical power of RGB LEDs, in whichthe subscripts “R ,” “G ,” and “B ,” respectively, represent the“red,” “green,” and “blue” components of signal; and “∼” rep-resents perturbation. GLED is a thermal–electrical–luminous–

Fig. 2. Block diagram of thermal–electrical–luminous–chromatic model ofRGB LED luminaire.

chromatic model, as shown in Fig. 2, as follows:

GLED(s) =[

UE · (EP + ET · H(s))

UY · (YP + YT · H(s))

](2)

and can be divided into five perturbed submodels: electrical–thermal (E-T) model H represents thermal dynamics of lu-minaire; thermal–luminous (T-L) model ET and thermal–chromatic (T-C) model YT represent the opto-thermal effect;and electrical–luminous (E-L) model EP and electrical–chromatic (E-C) model YP represent the opto-electrical effect.UE = [1 1 1] is the luminous summation unit, and UY =

[ 1 1 1 0 0 00 0 0 1 1 1 ] is the chromatic summation unit. Refer-

ring to the derivation of [15] and [20]–[22], the total luminousintensity output is derived as follows:

ΦOUT(s) = UE · ΦLED(s) = UE · (ΦP (s) + ΦT (s))

= UE · (EP · PLED(s) + ET · TLED(s))

= UE · (EP + ET · H(s)) · PLED(s)

= UE · GE (s) · PLED(s) (3)

where GE is the luminous model, ΦLED = [ΦR ΦG ΦB ]T isthe luminous intensity of RGB LEDs, TLED = [TR TG TB ]T isthe junction temperature of RGB LEDs. All H,EP , and ET arederived by the input–output relation as follows, respectively:

H(s) =

⎡⎢⎣

HRR (s) HGR (s) HBR (s)HRG (s) HGG (s) HBG (s)HRB (s) HGB (s) HBB (s)

⎤⎥⎦

=

⎡⎢⎣

TR (s)/PR (s) TR (s)/PG (s) TR (s)/PB (s)TG (s)/PR (s) TG (s)/PG (s) TG (s)/PB (s)TB (s)/PR (s) TB (s)/PG (s) TB (s)/PB (s)

⎤⎥⎦

at Ta∼= 0 (4)

ET (s) =

⎡⎢⎣

ET R 0 00 ET G 00 0 ET B

⎤⎥⎦

=

⎡⎢⎣

ΦR (s)/TR (s) 0 00 ΦG (s)/TG (s) 00 0 ΦB (s)/TB (s)

⎤⎥⎦

(5)

TANG et al.: ILLUMINATION AND COLOR CONTROL IN RED-GREEN-BLUE LIGHT-EMITTING DIODE 4923

EP (s) =

⎡⎢⎣

EP R 0 0

0 EP G 0

0 0 EP B

⎤⎥⎦

=

⎡⎢⎣

ΦR (s)/PR (s) 0 0

0 ΦG (s)/PG (s) 0

0 0 ΦB (s)/PB (s)

⎤⎥⎦ .

(6)

Due to the same phenomenon of opto-electrical and opto-thermal effects, the dynamics of luminous responses can beextended to chromatic responses. The chromaticity coordinatesoutputs are similarly derived as follows:

[u′

OUT(s)

v′OUT(s)

]=

[u′

P (s)

v′P (s)

]+

[u′

T (s)

v′T (s)

]

= (UY · YP · PLED(s) + UY · YT · TLED(s))

= UY · (YP + YT · H(s)) · PLED(s)

= UY · GY (s) · PLED(s) (7)

where GY is the chromatic model and the subscripts “P ” and“T ” represent the effects of “electrical power” and “junctiontemperature,” respectively.

Both YP and YT , are derived by the input–output relationas well. First, the T-C model YT represents the influence onchromaticity coordinates of junction temperature as follows:

[u′

T (s)

v′T (s)

]= UY · YT (s) · TLED(s). (8)

Similar to the deviation of ET , YT is of zeroth order with aconstant gain, defined in terms of linear perturbation concept asa 6×3 transfer function:

YT =[

YT u

YT v

]=

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

YT uR 0 0

0 YT uG 0

0 0 YT uB

YT vR 0 0

0 YT vG 0

0 0 YT vB

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

u′R (s)/TR (s) 0 0

0 u′G (s)/TG (s) 0

0 0 u′B (s)/TB (s)

v′R (s)/TR (s) 0 0

0 v′G (s)/TG (s) 0

0 0 v′B (s)/TB (s)

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(9)

where the YT further divides into two diagonal 3 × 3 submod-els YT u and YT v to represent the responses of the u′-coordinateand v′-coordinate, respectively. Second, the E-C model YP rep-resents the influence on chromaticity coordinates of electrical

power as follows:[

u′P (s)

v′P (s)

]= UY · YP (s) · PLED(s). (10)

Similarly, YP is of zeroth order with a constant gain, defined interms of linear perturbation concept as a 6 × 3 transfer function:

YP =[

YP u

YP v

]=

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

YP uR 0 0

0 YP uG 0

0 0 YP uB

YP vR 0 0

0 YP vG 0

0 0 YP vB

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

u′R (s)/PR (s) 0 0

0 u′G (s)/PG (s) 0

0 0 u′B (s)/PB (s)

v′R (s)/PR (s) 0 0

0 v′G (s)/PG (s) 0

0 0 v′B (s)/PB (s)

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(11)

where the E-C model YP divides into two 3 × 3 submodels YP u

and YP v , the same as in the YT .In addition, the chromatic transformer F represents a map-

ping from the chromaticity coordinate outputs [u′OUT , v′

OUT]T

onto CCT output TCC ,OUT . According to [23] and [24], CCT isobtained from a nonlinear approach as follows:

F :

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

TCC ,OUT = 449n3 + 3525n2 + 6823.3n + 5520.3

n =x − 0.3320.1858 − y

x =9u′

OUT

6u′OUT − 16v′

OUT + 12

y =4v′

OUT

6u′OUT − 16v′

OUT + 12(12)

where n is the converting operator, and x and y are the chro-maticity coordinates in CIE 1931 diagram.

C. Modeling of Converter N

Converter N carries out a conversion to transform from theinput commands of TCC ,r and Φr , to three corresponding con-trol signals: converted radiant power LA , converted electricalpower PA , and converted junction temperature TA ; these fiveparameters were interdependent. The N is described as follows:

(LA, TA , PA ) = N (TCC ,r ,Φr ) . (13)

The N must be consistent with the dynamics of RGB LEDluminaire; therefore, N is obtained from a set of experimentaldata of RGB LED luminaire, i.e., TCC ,OUT ,ΦOUT , LS , PLED ,and TLED , to construct the (13). Furthermore, N could divideinto three identical submodels when the set of experimental data


Fig. 3. Block diagram of converter N .

Fig. 4. Block diagram of compensator M .

is interdependent, described as follows:

N :

⎛⎜⎝

LA = NL (TCC ,r ,Φr )

TA = NT (TCC ,r ,Φr )

PA = NP (TCC ,r ,Φr )

(14)

where NL is the radiant converter, NT is the temperature con-verter, and NP is the electrical converter. Its detailed blockdiagram is shown in Fig. 3.

D. Modeling of Compensator M

M is a feed-forward compensator, producing radiant compen-sation LM , compensating the color drift and luminous intensitydroop during the entire operating period due to junction tem-perature rise, and adjusting the signal mismatch between theconverter N outputs and initial responses of RGB LEDs forjunction temperature and electrical power. M consists of threesubmodels: temperature-compensator MT , initial-temperature-compensator WT , and initial-electrical-compensator WP , asshown in Fig. 4. The output of compensator LM is described asfollows:

LM (s) = LT (s) + ΔLIT + ΔLIP

= MT (s) · TLED(s) + WT · ΔTI + WP · ΔPI . (15)

where LT is the feed-forward compensation, ΔLIT the ra-diant difference of temperature, ΔLIP the radiant differenceof electrical power, ΔTI the initial temperature difference de-fined the difference between converted junction temperatureTA , and initial junction temperature of RGB LEDs TLED ,0 , i.e.,ΔTI = TA − TLED ,0 . Similarly, the initial power difference isdefined as ΔPI = PA − PLED ,0 .

The three submodels are derived by the input–output relation.First, temperature compensator MT represents the influence onfeed-forward compensation LT of junction temperature TLED

as follows:

LT (s) = MT (s) · TLED(s) (16)

and is defined as a perturbed model as

MT (s) =

⎡⎢⎣

NRR (s) NGR (s) NBR (s)

NRG (s) NGG (s) NBG (s)

NRB (s) NGB (s) NBB (s)

⎤⎥⎦

=

⎡⎢⎣

LT R (s)/TR (s) LT R (s)/TG (s) LT R (s)/TB (s)

LT G (s)/TR (s) LT G (s)/TG (s) LT G (s)/TB (s)

LT B (s)/TR (s) LT B (s)/TG (s) LT B (s)/TB (s)

⎤⎥⎦.

(17)

Second, initial-temperature-compensator WT and initial-electrical-compensator WP represent the radiant difference byinitial temperature difference ΔTI and initial electrical powerdifference ΔPI , respectively, as follows, respectively:

ΔLIT = WT · ΔTI (18)

ΔLIP = WP · ΔPI . (19)

The WT and WP are defined as follows, respectively:

WT =

⎡⎢⎣

WT RR WT GR WT BR

WT RG WT GG WT BG

WT RB WT GB WT BB

⎤⎥⎦

=

⎡⎢⎣

ΔLIT R/ΔTIR ΔLIT R/ΔTIG ΔLIT R/ΔTIB

ΔLIT G/ΔTIR ΔLIT G/ΔTIG ΔLIT G/ΔTIB

ΔLIT B /ΔTIR ΔLIT B /ΔTIG ΔLIT B /ΔTIB

⎤⎥⎦

(20)

WP =

⎡⎢⎣

WP RR WP GR WP BR

WP RG WP GG WP BG

WP RB WP GB WP BB

⎤⎥⎦

=

⎡⎢⎣

ΔLIP R/ΔPIR ΔLIP R/ΔPIG ΔLIP R/ΔPIB

ΔLIP G/ΔPIR ΔLIP G/ΔPIG ΔLIP G/ΔPIB

ΔLIP B /ΔPIR ΔLIP B /ΔPIG ΔLIP B /ΔPIB

⎤⎥⎦.

(21)

The model of M must be consistent with the dynamics ofRGB LED luminaire; for the functions of M is including themodification for ΦLED and [u′

OUT , v′OUT]T due to junction tem-

perature rise, and adjustment of signal mismatch between theoutputs of converter N and initial responses of RGB LEDs.Therefore, the M can be derived from RGB LED luminairemodels as mentioned previously, that is, EP ,ET , YP , and YT .The detailed derivation is discussed in next section.

III. SYSTEM IDENTIFICATION

A. Experimental Setup

In this study, an RGB LED luminaire [21] was set up forsystem identification and lighting control; it is assembled by fiveRGB LED lamps [25] with a joint 900 g aluminum heatsink.


Fig. 5. Illustration of driver design for red LEDs.

TABLE IELECTRICAL POWER CONDITIONS OF RGB LED LUMINAIRE FOR WHITE

LIGHT GENERATION

Four lamps were installed in front of the luminaire for lightingand the fifth lamp with an Si photodiode [26] as the LED sensorwas set inside the luminaire to measure junction temperatureTLED and radiant power LS of RGB LEDs.

Three color LEDs were independently driven by three drivers,as shown in Fig. 5, which were connected to identical colorLEDs of five lamps in series connection. The three driversindependently produced direct current pulsewidth modulation(DCPWM) outputs. The ON/OFF current levels were suppliedat 350 mA/1 mA, and the switching frequencies were fixed120 Hz to avoid flicking perception [27]. The maximum elec-trical power in a single RGB LED lamp is PLED ,max = [1212.56 1.27]T W ≡ [100 100 100]T %, described in watt orpercentage (%), where the power levels are proportionally ma-nipulated by duty cycle. The unit of electrical power is thusdefined as “%.” The electrical power conditions of three CCTs,i.e., 3500, 6000, and 8000 K, are listed in Table I for the follow-ing experiments. A thermal pad was attached to the luminaireto introduce extra thermal disturbance. By using the forwardvoltage method [28]–[30], the TLED were estimated by measur-ing the average forward voltage of the LED sensor, VLOW =[VT R VT G VT B ]T , while 1 mA constant current were appliedduring the OFF period of DCPWM, as follows:

TLED = ST · VLOW (22)

where ST is the temperature sensitive parameter obtained fromthe calibration experiment by 1 mA constant current pulse with

Fig. 6. Voltage responses of RGB LEDs and Si photodiode within one period.

50 μs pulsewidth, as follows [15]:

ST =

⎡⎢⎣

ST R 0 0

0 ST G 0

0 0 ST B

⎤⎥⎦=

⎡⎢⎣

1.82 0 0

0 5.90 0

0 0 2.20

⎤⎥⎦× 10−3 .

(23)The luminous intensity of RGB LEDs ΦLED can be obtained

by measuring the radiant powers LS = [LR LG LB ]T asfollows:

LS = SD · ΦLED . (24)

The luminous detector model SD was then obtained by ex-perimental calibration [15] as

SD =

⎡⎢⎣

SDR 0 0

0 SDG 0

0 0 SDB

⎤⎥⎦=

⎡⎢⎣

0.0287 0 0

0 0.0212 0

0 0 0.1077

⎤⎥⎦.

(25)Hence, the luminous intensity ΦLED can be measured directlyand individually.

The radiant powers LS was measured by the LED sensor, i.e.,the fifth lamp with an Si photodiode. The procedures were ar-ranged as follows [4]. First, it is designed that the three DCPWMoutputs were synchronous and their negative slope edge wereoccurred sequentially. The order was set red, green, and blueLEDs in turn, and the each time intervals of signals were set 2%duty cycle, i.e., 166.66 μs. The voltage responses of DCPWMsand Si photodiode are shown in Fig. 6. Second, the voltagefalling edge of red LEDs was set as reference point to trig-ger the voltage measurement of Si photodiode at three specifictime points, i.e., 1%, 3%, and 99% duty cycle delayed to refer-ence point. Its corresponding voltage values are equal to VS,1 =VSG + VSB , VS,3 = VSB , and VS,99 = VSR + VSG + VSB , re-spectively, where VSR , VSG , and VSB are Si photodiode sensedvoltage of red, green, and blue LEDs. Third, the sensed voltages


of RGB LEDs are decoupled as follows:⎡⎢⎣

VS,1

VS,3

VS,99

⎤⎥⎦ =

⎡⎢⎣

o 1 1

0 0 1

1 1 1

⎤⎥⎦ ·

⎡⎢⎣

VSR

VSG

VSB

⎤⎥⎦

⇒

⎡⎢⎣

VSR

VSG

VSB

⎤⎥⎦ =

⎡⎢⎣

o 1 1

0 0 1

1 1 1

⎤⎥⎦−1

·

⎡⎢⎣

VS,1

VS,3

VS,99

⎤⎥⎦

=

⎡⎢⎣

VS,99 − VS,1

VS,1 − VS,3

VS,3

⎤⎥⎦ . (26)

Finally, the radiant powers LS is obtained as follows:

LS =

⎡⎢⎣

LR

LG

LB

⎤⎥⎦ =

⎡⎢⎣

DC R · VSR

DC G · VSG

DC B · VSB

⎤⎥⎦ (27)

where DC R,DC G , and DC B are the duty cycles of red, green,and blue LEDs, respectively.

For identification, a set of testing apparatuses, the sameas [15] (see Fig. 6), was installed to acquire total lumi-nous intensity output ΦOUT , chromaticity coordinate outputs[u′

OUT , v′OUT]T , and CCT output TCC ,OUT . Moreover, the cal-

culation of [u′OUT , v′

OUT]T was obtained as follows [23]:[

u′OUT

v′OUT

]=

[4X/(X + 15Y + 3Z)

9Y /(X + 15Y + 3Z)

]= CT (D) ,

where

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎩

X =∫ 780

380D · x · dλ

Y =∫ 780

380D · y · dλ

Z =∫ 780

380D · z · dλ

(28)

where D is the SPD of RGB LEDs; x, y and z are the colormatching function; and X,Y and Z are the tristimulus values.

B. Identification of RGB LED Luminaire GLED

The five submodels of GLED carried out system identificationindividually. First, the E-T model H was obtained from (4) and isshown in [15], [20], and [21]. Second, the T-L model ET and theT-E model EP were obtained from (5) and (6), respectively, andthe both models were identified as constant gain in [15] and [21].Furthermore, the model of ET is observed as linearly electrical-dependent (see Fig. 7); in other words, the ET is different fromand linear to diverse electrical power conditions. In order tosimplify the model description among operating range, ET canbe characterized as follows:

ET = ET (PLED)

=

⎡⎢⎣−0.139 0 0

0 −0.151 0

0 0 −0.012

⎤⎥⎦ ·

⎡⎢⎣

PR

PG

PB

⎤⎥⎦

Fig. 7. Relations of thermal–luminous model ET and electrical power ofRGB LEDs PLED .

Fig. 8. Relations of electrical–luminous model EP and junction temperatureof RGB LEDs TLED .

+

⎡⎢⎣−0.369 0 0

0 −0.661 0

0 0 −0.251

⎤⎥⎦ . (29)

Similarly, the model of EP was observed as linearlytemperature-dependent (see Fig. 8) as well.

EP = EP (TLED)

=

⎡⎢⎣−0.139 0 0

0 −0.125 0

0 0 −0.012

⎤⎥⎦ ·

⎡⎢⎣

TR

TG

TB

⎤⎥⎦

+

⎡⎢⎣

25.26 0 0

0 76.72 0

0 0 11.00

⎤⎥⎦ . (30)

Third, the T-C model YT was obtained from (9) and identifiedas a constant gain by linear regression. The PLED were setconstant, in turn, of the operating conditions given in Table Iin the experiment. Accordingly, the TLED was determined byself-heating and thermal interaction among three color LEDs.The TLED rise would cause SPD variation of three color LEDs,respectively. In order to decouple the chromatic responses of thethree color LEDs, the SPDs of RGB LEDs were thus defined as


Fig. 9. u′-coordinate experimental responses of thermal–chromatic modelYT u at CCT 6000 K. (a) u′-coordinate responses of red LEDs. (b) Relations ofYT u and PLED .

follows:

⎧⎪⎨⎪⎩

SPD of red LEDs: DR = D|780 nmλ1

SPD of green LEDs: DG = D|λ1λ2

SPD of blue LEDs: DB = D|λ2380 nm

(31)

where λ1 is the wavelength of the spectrum trough betweenblue and green LEDs and λ2 is the wavelength of the spectrumtrough between green and red LEDs. Referring to (28), theperturbations of [u′

T , v′T ]T influenced by junction temperature

of single-color LEDs were calculated from

[u′

T

v′T

]= CT (D + Di) − CT (D), for Ti , where i = R,G,B.

(32)

The modeling of u′-coordinate T-C model for the red LEDsYT uR at CCT 6000 K are shown in Fig. 9(a). Furthermore, YT

is observed as linearly electrical-dependent. In the example ofCCT 6000 K, the u′-coordinate T-C model YT u was depicted as

a linear function of PLED [see Fig. 9(b)] as follows:

YT = YT (PLED) =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

1.485 0 0

0 0.730 0

0 0 0.188

0.495 0 0

0 −0.377 0

0 0 −1.009

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

×10−6 ·PLED

+

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

−8.046 0 0

0 1.821 0

0 0 −0.110

−1.947 0 0

0 −1.171 0

0 0 2.981

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

× 10−4 . (33)

Fourth, the E-C model YP was obtained from (11) and iden-tified as a constant gain by linear regression. The PLED werefirst set constant, in turn, of the operating conditions given inTable I in the experiment. Additionally, PLED were applied, inturn, extra perturbations of PR = ±2.0%, PG = ±1.5%, andPB = ±1.0% with five divisions, individually. The extra pertur-bations are small enough to hold the chromaticity coordinatesapproximately remained at designing CCT. The perturbationsof electrical powers were calculated from (28) as follows:

[u′

P

v′P

]=

[u′

OUT

v′OUT

]−

[u′

T

v′T

]

= (CT (D + Di) − CT (D)) − UY · YT · TLED ,

for Pi , where i = R,G,B. (34)

The modeling of u′-coordinate E-C model for the red LEDsYP uR at CCT 6000 K are shown in Fig. 10(a). Furthermore, YP

is observed as linearly electrical-dependent. In the example ofCCT 6000 K, the u′-coordinate E-C model YP u was depictedas a linear function of PLED [see Fig. 10(b)] as follows:

YP = YP (PLED) =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

−0.259 0 0

0 1.927 0

0 0 0.326

−0.054 0 0

0 −1.307 0

0 0 2.245

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

×10−4 ·PLED

+

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

3.271 0 0

0 −8.871 0

0 0 1.235

0.659 0 0

0 5.962 0

0 0 −8.791

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

× 10−3 . (35)


Fig. 10. u′-coordinate experimental responses of electrical–chromatic modelYP u at CCT 6000 K. (a) u′-coordinate responses of red LEDs. (b) Relations ofYP u and PLED .

C. Identification of Converter N

The converter N represents the transmission path from CCTcommand TCCr and total luminous intensity command Φr toconverted junction temperature TA , converted electrical powerPA , and converted radiant power LA . The three submodelsNL,NP , and NT were carried out with curve-fitting tech-nique, individually, by using the interdependent responses of theT-C model identification, i.e., TCC ,OUT ,ΦOUT , TLED , PLED ,and LS . In the example of NL,LA can be obtained from the re-lations among TCC ,OUT ,ΦOUT , and LS according to (37). Theidentification consists of three steps: First, the ΦOUT of threeCCTs are overlapping and can be fitted as a single linear functionof the radiant power of green LED LG , as shown in Fig. 11(a).Second, normalized radiant power LN is defined as follows:

LN =

⎡⎢⎣

LN R

LN G

LN B

⎤⎥⎦ =

⎡⎢⎣

LR/(LR + LG + LB )

LG/(LR + LG + LB )

LB /(LR + LG + LB )

⎤⎥⎦ . (36)

The ratio of three elements of LN is constant to ΦOUT , asdepicted in Fig. 11(b). Third, the TCC ,OUT are linear to LN ,as shown in Fig. 11(c). Combining these three relations, NL isobtained as follows:

NL : LA ≡ LS = LN · LAG

LN G=

⎡⎢⎣

LN R

LN G

LN B

⎤⎥⎦ · LAG

LN G,

Fig. 11. Experimental responses for identification of radiant-converter NL .(a) ΦOUT versus LG . (b) ΦOUT versus LN at CCT 3500 K. (c) TCC ,OUTversus LN .

where

⎧⎪⎪⎪⎨⎪⎪⎪⎩

LAG = 0.01197Φr − 0.4440

LN R = −2.963e−5 · TCC ,r + 0.585

LN G = −2.164e−6 · TCC ,r + 0.387

LN B = 3.180e−5 · TCC ,r + 0.0028

. (37)

Similarly, the same analytical technique was applied foridentification of NP and NT . NP and the NT are given by,


respectively,

NP : PA ≡ PLED = PN · PAG

PN G=

⎡⎢⎣

PN R

PN G

PN B

⎤⎥⎦ · PAG

PN G,

where

⎧⎪⎪⎪⎨⎪⎪⎪⎩

PAG = 7.678 e−3Φr − 0.386

PRN = −3.174 e−5 · TCC ,r + 0.801

PGN = 3.459 e−6 · TCC ,r + 0.195

PBN = 2.828 e−5 · TCC ,r + 0.0004

(38)

NT : TA ≡ TLED = TN · TAG

TN G=

⎡⎢⎣

TN R

TN G

TN B

⎤⎥⎦ · TAG

TN G,

where

⎧⎪⎪⎪⎨⎪⎪⎪⎩

TAG = 2.580 e−3Φr + 36.38

TN R = −1.346 e−6 · TCC ,r + 0.350

TN G = −7.156 e−7 · TCC ,r + 0.333

TN B = 2.062 e−6 · TCC ,r + 0.317

(39)

where PN is the normalized electrical power and TN is thenormalized junction temperature.

D. Derivation of Compensator M

The compensator M produced radiant compensation LM

by using initial temperature difference ΔTI and initial elec-trical power difference ΔPI ; in addition, M must be consistentwith the dynamics of RGB LED luminaire to compensate thecolor drift and luminous intensity droop. Therefore, we con-structed a combined relation of TLED , PLED , LS ,ΦOUT , u′

OUT ,and v′

OUT in advance. The combined relation sets the differenceof ΦOUT , u′

OUT , and v′OUT equal to zero and then transforms

into M . M can produce radiant compensation LM to modifyradiant command LC according to the dynamics of RGB LEDluminaire. Eventually, a proper LC set as reference can guar-

antee luminous and chromatic stability by using the FFB loopcontrol, as shown in Fig. 1.

The combined relation is solved by using the identified mod-els as mentioned previously, i.e., EP ,ET , YP , and YT . First,combining (3) and (24), ΦLED is given by

ΦLED(s) = S−1D · LS (s) = EP · PLED(s) + ET · TLED(s)

then

PLED(s) = (E−1P · S−1

D ) · LS (s) − (E−1P · ET ) · TLED(s).

(40)We capture the u′-coordinate and v′-coordinate models of (9)and (11), i.e., YP u , YP v , YT u , and YT v . Their relations are re-constructed by (40) as follows:

⎡⎢⎣

u′R (s)

u′G (s)

u′B (s)

⎤⎥⎦ = YP u · PLED(s) + YT u · TLED(s)

= (YP u · E−1P · S−1

D ) · LS (s)

+ (YT u − YP u · (E−1P · ET )) · TLED(s). (41)

⎡⎢⎣

v′R (s)

v′G (s)

v′B (s)

⎤⎥⎦ = (YP v · E−1

P · S−1D ) · LS (s)

+ (YT v − YP v · (E−1P · ET )) · TLED(s). (42)

Referring to the definition of (3) and (24), the total luminousintensity output ΦOUT is described in

ΦOUT = UE · ΦLED(s) = UE · S−1D · LS (s). (43)

Combining (41)–(43) and the definition of TLED , u′OUT , and

v′OUT into a 12× 12 simultaneous equation yields the following,

as shown (*), at the bottom of this page.

(*)


The solution is, as shown (44), at the bottom of the page.Referring to (1), (3), and (7), the perturbation “∼” is redefined

as difference “Δ” for the RGB LED luminaire outputs at theinitial moment as follows:

⎡⎢⎣

ΦOUT

u′OUT

v′OUT

⎤⎥⎦Δ≡

⎡⎢⎣

ΔΦI

Δu′I

Δv′I

⎤⎥⎦=

[UE · ET

UY · YT

]· ΔTI +

[UE · EP

UY · YP

]· ΔPI .

(45)Substituting (45) into the upper three rows of (44), we get

LS =

⎡⎢⎣

F7,1 F8,1 F9,1

F7,2 F8,2 F9,2

F7,3 F8,3 F9,3

⎤⎥⎦ · TLED +

⎡⎢⎣

F10,1 F11,1 F12,1

F10,2 F11,2 F12,2

F10,3 F11,3 F12,3

⎤⎥⎦

·

⎡⎢⎣

ΦOUT

u′OUT

v′OUT

⎤⎥⎦

≡

⎡⎢⎣

F7,1 F8,1 F9,1

F7,2 F8,2 F9,2

F7,3 F8,3 F9,3

⎤⎥⎦ · TLED +

⎡⎢⎣

F10,1 F11,1 F12,1

F10,2 F11,2 F12,2

F10,3 F11,3 F12,3

⎤⎥⎦

·([

UE · ET

UY · YT

]· ΔTI +

[UE · EP

UY · YP

]· ΔPI

). (46)

Referring to (15), the three sub-models of compensator,i.e., MT ,WT , WP , are modeled in comparison to (46) asfollows:

MT =

⎡⎢⎣

F7,1 F8,1 F9,1

F7,2 F8,2 F9,2

F7,3 F8,3 F9,3

⎤⎥⎦ (47)

WT =

⎡⎢⎣

F10,1 F11,1 F12,1

F10,2 F11,2 F12,2

F10,3 F11,3 F12,3

⎤⎥⎦ ·

[UE · ET

UY · YT

](48)

Fig. 12. Block diagram of FFB loops for controller design. (a) FFB loop.(b) Decoupled red LED loop (Solid lines: scalar signals; mesh lines: vectorsignals).

WP =

⎡⎢⎣

F10,1 F11,1 F12,1

F10,2 F11,2 F12,2

F10,3 F11,3 F12,3

⎤⎥⎦ ·

[UE · EP

UY · YP

]. (49)

Since M is derived by EP ,ET , YP , and YT , which are electrical-or temperature-dependent, M will constantly vary during theentire operating period. Therefore, the three submodels of M ,i.e., MT ,WT , and WP , must be remodeled in each controlperiod.

IV. CONTROLLER DESIGN

Regarding the FFB&TFF structure shown in Fig. 1, it is notedthat the performance of the RGB LED lighting control systemis dominated mainly by the FFB loop if the converter N andcompensator M provide exact radiant command LC . Therefore,we segmented the FFB loop for the controller design, as depictedin Fig. 12(a). The plant of FFB loop GES is defined as theaverage luminous model GE 0 with luminous detector modelSD , i.e., GES = SD · GE 0 , where the GE 0 is obtained by the

(44)


identification of H,EP , and ET .

GE 0(s) =

⎡⎢⎣

GE 0,RR (s) GE 0,GR (s) GE 0,BR (s)

GE 0,RG (s) GE 0,GG (s) GE 0,BG (s)

GE 0,RB (s) GE 0,GB (s) GE 0,BB (s)

⎤⎥⎦

=

⎡⎢⎢⎢⎢⎢⎢⎢⎣

14.907 · (s + 0.00799)s + 0.00083

−0.582 · (s + 0.00368)s + 0.00087

−0.083 · (s + 0.00229)s + 0.00083

66.937 · (s + 0.00864)s + 0.00087

−0.014 · (s + 0.00212)s + 0.00082

−0.065 · (s + 0.00167)s + 0.00083

−0.321 · (s + 0.00346)s + 0.00085

−0.125 · (s + 0.00245)s + 0.00084

10.138 · (s + 0.00847)s + 0.00085

⎤⎥⎥⎥⎥⎥⎥⎥⎦

(50)

In this study, the decentralized control approach was appliedto simplification, that is, relative gain array (RGA) method [31],[32] was introduced to measure of the interactions and diagonaldominance. The RGA of the plant GES is equal to identitymatrix in the typical operating range ω = 10−4 to 103 rad/s asfollows:

Λ(GES )

= GES · ∗(GTES )−1

=

⎡⎢⎣

1.00+0.00i 0.00+0.00i 0.00+0.00i

0.00+0.00i 1.00+0.00i 0.00+0.00i

0.00+0.00i 0.00+0.00i 1.00+0.00i

⎤⎥⎦≡ I ∀ω (51)

where the operator “·∗” denotes Schur (element by element)matrix multiplication. According to the rule of pairing selection,the plant GES is close to diagonal and essentially a collection ofthree independent subsystems. Therefore, the FFB loop is properto treat as three single-input–single-output (SISO) loops, andthe controller K is designed in diagonal form in proportional–integral (PI) strategy as follows:

K(s) =

⎡⎢⎣

KR (s) 0 0

0 KG (s) 0

0 0 KB (s)

⎤⎥⎦

=

⎡⎢⎣

KP R + KIR/s 0 0

0 KP G + KIG/s 0

0 0 KP B + KIB /s

⎤⎥⎦.

(52)

According to the stability theorem [31], suppose that the plantG is stable, if RGA Λ(G) = I ∀ω, the stability of each ofindividual loops implies stability of the entire system. Therefore,the stability of the FFB loop is determined by the stability of thediagonal loops of three color LEDs independently. By using theRouth–Hurwitz stability test, the stabilities of three loops wereevaluated, respectively. The stability conditions were KP R >

Fig. 13. Simulation results of decoupled red LED loop. (a) Time responses ofproportional control test. (b) Frequency responses of sensitivity function SE R

for PI control test.

−1.75 and KIR > 0 for red, KP G > −0.66 and KIG > 0 forgreen, and KP B > −0.89 and KIB > 0 for blue LED loops.

The performance of PI controller is tuned by usingSIMULINK in MATLAB. In this study, the control system re-quirements are defined as follows:

1) rise time (time for step response from 10% to 90%) < 1 s;2) settling time (time to reach 98% of reference) < 4 s.Using the time-domain simulation, optimal tuning may be

carried out by finding the minimum of the integral of the absolutevalue of the error (IAE), which also satisfies the aforementionedsystem requirements, as follows:

IAEi =∫ ∞

0|ei(t)| dt, where i = R,G,B (53)

where the error is e = [ eR eG eB ]T = Lc − LS .The tuning procedures are simulated by step test. In the exam-

ple of the decouple red LED loop [see Fig. 12(b)], the integralgain KIR is first set at zero in order to find the effective range ofproportional gain KP R . The simulated responses of P controlare not significant since the KP R > 11.0, as shown in Fig. 13(a). Second, the KP R = 7.0–11.0 chosen for finding the min-imum integral gain KIR satisfied the requirements of risingtime and settling time. Its simulated results of IAE are listed in


TABLE IISIMULATION RESULTS OF PI CONTROL TEST OF DECOUPLED FEEDBACK LOOPS

Fig. 14. Implementation of RGB LED lighting control system.

Table II. Third, the controller should be robust with respect to theplant uncertainty. A sensitivity function SER is defined for theclosed-loop transfer function HER with respect to the variationof open-loop transfer function GESR as

SER (s) =∂HER (s)∂GESR (s)

· GESR (s)HER (s)

=1

1 + KR (s) · GESR (s).

(54)The frequency responses of the SER are plotted in the con-

troller parameters of Table II, as shown in Fig. 13(b). Con-sequently, the acceptable PI controller, satisfying the systemrequirements, the stability condition, the criterion of minimumIAER , and low sensitivity of the uncertainty of the plant GESR ,is designed as KP R = 11.0, KIR = 5.6. Repeating the sameprocedures, the controller K is finally designed as follows:

K(s) =

⎡⎢⎣

11 + 5.6/s 0 0

0 9 + 3.0/s 0

0 0 7 + 3.0/s

⎤⎥⎦ . (55)

V. EXPERIMENTAL RESULT AND DISCUSSION

A control system and a verification system, same as given in[15, Fig. 14 (b) and (c)], were set up for verification. For thecontrol system, the designed converter N , compensator M , andcontroller K were implemented by using a PC with LabVIEWand a data acquisition card (DAQ), as shown in Fig. 14. Becauseof the limitation of the DAQ, the sampling time of discretecontrol was set T = 0.1 s. The discrete PI controller K ′ designed

with zero-order hold was obtained as follows:

K ′(z) =1

z − 1

⎡⎢⎣

11z + 10.44 0 0

0 9z + 8.7 0

0 0 7z + 6.7

⎤⎥⎦ .

(56)

For the verification system, the sampling time of data loggingfor total luminous intensity was T = 1.0 s due to the limitationof the General Purpose Interface Bus (GPIB) card.

Two experiments were designed to verify the systemperformances in total luminous intensity output ΦOUTand color difference of chromatic coordinate Δu′v′ =√

(u′OUT − u′

0)2 + (v′

OUT − v′0)

2 , where u′0 and v′

0 are the ini-tial desired chromaticity coordinates. In the transient experi-ments, the CCTs were set at constant 3800, 5000, and 6000 K,respectively; and the total luminous intensity commands Φr

were applied sequentially from 2000 to 3500 cd in intervals of500 cd with 120 s for each step. The CCT conditions of 3800 and5000 K differ from identification conditions 3500 and 6000 Kin order to verify the control capability for various input com-mands. The experimental results are listed in Table III. Both risetime and settling time of ΦOUT are all within the requirements;the root-mean-square error (RMSE) of ΦOUT and their signal-to-noise (SN) ratios show low steady-state error; and averageΔu′v′ are shown low color drift as well. In the example of CCT3800 K, the experimental responses are revealed in Fig. 15. First,the ΦOUT follow the Φr and the TCC ,OUT follow the TCC ,r , asshown in Fig. 15(a) and (b), respectively. Second, the color dif-ferences show effective regulation, as depicted in Fig. 15(b). Itsresponses at several step perturbation moments reveal large fluc-tuations; in that, the external electromagnetic disturbances, e.g.,the power supply of driver, might interfere with the spectrome-ter; it is evident that there are no corresponding fluctuations tothe ΦOUT , TLED , and LS . Third, the junction temperature TLEDand heatsink temperature Tb revealed self-heating of LEDs, asshown in Fig. 15(c). Finally, measured radiant power LS andelectrical power PLED of RGB LEDs are depicted in Fig. 15(d)and (e), respectively.

In the steady-state experiments, the input commands were setΦr at constant 3000 cd and CCT at 3800, 6000, and 8000 K, inturn, for the proposed control system. Moreover, the open-loopsystem driving constant electrical powers that are of the corre-sponding input commands at the initial time were tested as well.In addition, an extra 15 W thermal disturbance almost twicethat of the power consumption of the RGB LED luminaire wasapplied during 4000–10 000 s for both the systems. It causedan approximate 30 ◦C junction temperature rise for each LEDs.The experimental results obtained during t = 9000–10 000 sare listed in Table IV. For the proposed control system, theRMSE of ΦOUT and average color difference Δu′v′ are bothshown low steady-state error and low color drift, respectively.In the example of CCT 6000 K, the experimental responses areshown in Fig. 16. All the ΦOUT , TCC ,OUT , and Δu′v′ of theproposed control system are indicated well regulation, as shownin Fig. 16(a)–(c). Fig. 16(d) illustrates the temperature rise dur-ing the experiment. TLED and Tb dramatically rose at 4000 s.


Fig. 15. Experimental responses to a serial total luminous intensity command and constant CCT 3800 K for proposed control system. (a) Total luminous intensityoutput. (b) Chromatic output. (c) Temperature. (d) Radiant power. (e) Electrical power.

Correspondingly, the PLED showed noticeable compensation inFig. 16(e).

These results show that the proposed control system, includ-ing the converter N , the compensator M , and the controller K,is effective; that is, our results indicate that both luminous andcolor outputs can achieve the requirements despite temperaturerise and the system can operate at wide range color command.Regarding the results of Tables III and IV, the SN ratios ofRMSE of ΦOUT could be treated as a steady-state error and all

less than 2%, where typically within 1%–0.1% for the transientexperiment and 1.6%–0.16% for the steady-state experiment.Meanwhile, all of the Δu′v′ were typically within 0.0035. Thesefindings also support the hypothesis that the proposed controlsystem can provide a wide color range of input command. Itis evident that the system can operate at CCTs different fromthe identification conditions in the transient and steady-state ex-periments. Moreover, the RMSE of ΦOUT , as well as Δu′v′,showed slight variation and inconsistency among the CCT or


Fig. 16. Experimental responses to constant input command of Φr = 3000 cd and TCC ,r = 6000 K for open-loop and the proposed control system. (a) Totalluminous intensity output. (b) CCT output. (c) Color difference output. (d) Temperature of proposed control system. (e) Electrical power of proposed controlsystem.

electrical power conditions. For the transient experiment, thediscordant results should be mainly caused by lack of perfor-mance of K and accuracy of N ; besides, it further introduces thelack of accuracy of M for steady-state experiment due to largejunction temperature rise. Therefore, the system performancecould be further improved by obtaining precise N and M and

more accurate controller design, e.g., Robust Control [15]. Theaccuracy of N and M can be improved by providing more ex-perimental data of system identification for the four submodels,i.e., EP ,ET , YP , and YT .

For the steady-state experiment, the Δu′v′ results showed0.00297 (maximum) and 0.00171 (minimum) by approximate


TABLE IIIEXPERIMENTAL RESULTS OF THE TRANSIENT EXPERIMENTS

40 ◦C junction temperature variation. Earlier publicationsshowed several comparable results for RGB LEDs as follows.Muthu et al. [4], [8] and Muthu and Gaines [9] reported that the

TABLE IVEXPERIMENTAL RESULTS OF THE STEADY-STATE EXPERIMENTS

color point changes in CIE 1960 are Δuv = 0.004 (FFB&TFF),0.006 (CCFB), and 0.008 (CCFB) for a heatsink temperaturechange of 50 ◦C. Hoelen et al. [5], [7] demonstrated a max-imum color point error Δu′v′ in white of 0.007 (FFB&TFF)with 35 ◦C and 0.0092 (FFB&TFF) and 0.0084 (CCFB) with75 ◦C heatsink temperature change, respectively. Deurenberget al. [6] pointed out that the temperature induced color accu-racy errors of average Δu′v′ = 0.0035 and 0.0048, respectively,for the FFB&TFF and CCFB systems for a heatsink temperaturevariation of 50 ◦C. Wang et al. [15] showed a typical Δu′v′ =0.001 under 25 ◦C junction temperature rise.

The proposed control system was discussed in-depth as fol-lows. It appears that both N and M of the TFF loop provideaccurate radiant command LC to the following FFB loop. TheFFB loop implemented in three SISO loops regulates the lumi-nous intensity of RGB LEDs ΦLED as well as the total lumi-nous intensity output ΦOUT . Moreover, the TFF loop compen-sates temperature variation further to regulate the color differ-ence Δu′v′ and CCT output TCC ,OUT . A thermal–electrical–luminous–chromatic model, including five submodels, is de-rived from RGB LED luminaire, where the four submodels, i.e.,EP ,ET , YP , and YT , were modeled as temperature-dependentor electrical-dependent due to low quantum efficiency, spectralshift, and current droop by the junction temperature rise. Com-pared to [15], a converter and a compensator, which are designedas compact linear models and instead of a lookup table, are in-troduced in the TFF&FFB structure. The advantage is that thelighting system can operate at wide color range and would notrestrict at specific CCT conditions. In contrast, the disadvantageis that the compensator must be remodeled by the four compactlinear models in each control period due to the temperature-dependent and electrical-dependent properties. A diagonal PI


controller designed by decentralized control approach is shownconcise and effective. The diagonal effect is because the photonemission is dominated by the electrical power of the correspond-ing color LEDs, and the thermal interaction is minor in contrastto the optical effect.

VI. CONCLUSION

This paper has proposed a novel FFB&TFF structure for anRGB LED lighting control system, in which a converter wasapplied for command conversion and a compensator was usedto compensate the temperature variation and to adjust the signalmismatch between the converter outputs and initial responses ofRGB LEDs. The RGB LED luminaire was modeled and experi-mentally identified as a thermal–electrical–luminous–chromaticmodel, including five submodels, where T-L, T-C, and E-C mod-els were treated as functions of electrical power and E-L modelas a function of junction temperature in order to simplify themodeling calculation of the compensator. The converter was ob-tained from the experimental results of T-C model identification.From the point of view of decentralized control approach, thecontrol system designed in the three SISO loops with PI diagonalcontroller could guarantee system stability and performance. Fi-nally, the designed controller was implemented for experimen-tal verification. The experimental results of both transient andsteady-state experiments showed low color drift and low totalluminous intensity droop. Compared to previous work [15], thenovel FFB&TFF control structure can operate at a wide colorrange and would not restrict at specific CCT conditions. Theproposed control system were shown to be effective.

REFERENCES

[1] E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,”Science, vol. 308, no. 5726, pp. 1274–1278, May 2005.

[2] Y. Gu, N. Narendran, T. Dong, and H. Wu, “Spectral and luminous ef-ficacy change of high-power LEDs under different dimming methods,”in Proc. SPIE, 2003, vol. 6337, p. 63370J. Available: http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=1291526

[3] M. Dyble, N. Narendran, A. Bierman, and T. Klein, “Impact of dimmingwhite LEDs: Chromaticity shifts due to different dimming methods,” inProc. SPIE, 2005, vol. 5941, pp. 291–299.

[4] S. Muthu, F. J. Schuurmans, and M. D. Pashley, “Red, green, and blueLEDs for white light illumination,” IEEE Trans. J. Sel. Top. QuantumElectron., vol. 8, no. 2, pp. 333–338, Mar./Apr. 2002.

[5] C. Hoelen, J. Ansems, P. Deurenberg, T. Treurniet, E. van Lier, O. Chao,V. Mercier, G. Calon, K. van Os, G. Lijten, and J. Sondag-Huethorst,“Multi-chip color variable LED spot modules,” in Proc. SPIE, 2005,vol. 5941, p. 59410A. Available: http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=1330744.

[6] P. Deurenberg, C. Hoelen, J. van Meurs, and J. Ansems, “Achieving colorpoint stability in RGB multi-chip LED modules using various color controlloops,” in Proc. SPIE, 2005, vol. 5941, pp. 63–74.

[7] C. Hoelen, J. Ansems, P. Deurenberg, W. van Duijneveldt, M.Peeters, G. Steenbruggen, T. Treurniet, A. Valster, and J. W. terWeeme, “Color tunable LED spot lighting,” in Proc. SPIE, 2006,vol. 6337, p. 63370Q. Available: http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=1291531.

[8] S. Muthu, F. J. Schuurmans, and M. D. Pashley, “Red, green, and blueLED based white light generation: Issues and control,” in Proc. Ind. Appl.Conf., 2002, pp. 327–333.

[9] S. Muthu and J. Gaines, “Red, green, and blue LED-based white lightsource: Implementation challenges and control design,” in Proc. Ind. Appl.Conf., 2003, pp. 515–522.

[10] B. Ackermann, V. Schulz, C. Martiny, A. Hilgers, and X. Zhu, “Controlof LEDs,” in Proc. IEEE IAS’06, Oct., pp. 2608–2615.

[11] K.-C. Lee, S.-H. Moon, B. Berkeley, and S.-S. Kim, “Optical feedbacksystem with integrated color sensor on LCD,” Sens. Actuator A, Phys.,vol. 130–131, pp. 214–219, 2006.

[12] S.-Y. Lee, J.-W. Kwon, H.-S. Kim, M.-S. Choi, and K.-S. Byun, “Newdesign and application of high efficiency LED driving system for RGB-LED backlight in LCD display,” in Proc. IEEE PESC’06, Jun., pp. 1–5.

[13] K. Lim, J. C. Lee, G. Panotopulos, and R. Helbing, “Illumination andcolor management in solid state lighting,” in Proc. IEEE IAS’06, Oct.,pp. 2616–2620.

[14] S. Robinson and I. Ashdown, “Polychromatic optical feedback control,stability, and dimming,” in Proc. SPIE, 2006, vol. 6337, p. 633714.

[15] F.-C. Wang, C.-W. Tang, and B.-J. Huang, “Multivariable robust controlfor a red-green-blue LED lighting system,” IEEE Trans. Power Electron.,vol. 25, no. 2, pp. 417–428, Feb. 2010.

[16] E. F. Schubert, Light Emitting Diodes. Cambridge,, U.K.: CambridgeUniversity Press, 2003.

[17] J. Senawiratne, A. Chatterjee, T. Detchprohm, W. Zhao, Y. Li, M. Zhu,Y. Xia, X. Li, J. Plawsky, and C. Wetzel, “Junction temperature, spectralshift, and efficiency in GaInN-based blue and green light emitting diodes,”Thin Solid Films, vol. 518, no. 6, pp. 1732–1736, Jan. 2010.

[18] M.-H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek,and Y. Park, “Origin of efficiency droop in GaN-based light-emittingdiodes,” Appl. Phys. Lett., vol. 91, no. 18, p. 183507, 2007. Available:http://apl.aip.org/resource/1/applab/v91/i18/p183507_s1.

[19] D. Saguatti, L. Bidinelli, G. Verzellesi, M. Meneghini, G. Meneghesso,E. Zanoni, R. Butendeich, and B. Hahn, “Investigation of efficiency-droop mechanisms in multi-quantum-well InGaN/GaN blue light-emittingdiodes,” IEEE Trans. Electron Devices, vol. 59, no. 5, pp. 1402–1409, May2012.

[20] B.-J. Huang, C.-W. Tang, and M.-S. Wu, “System dynamics model of high-power LED luminaire,” Appl. Therm. Eng., vol. 29, no. 4, pp. 609–616,2009.

[21] B.-J. Huang and C.-W. Tang, “Thermal-electrical–luminous model ofmulti-chip polychromatic LED luminaire,” Appl. Therm. Eng., vol. 29,no. 16, pp. 3366–3373, 2009.

[22] S. S. Hui and Y. X. Qin, “A general photo-electro-thermal theory for lightemitting diode (LED) systems,” IEEE Trans. Power Electron., vol. 24,no. 8, pp. 1967–1976, Aug. 2009.

[23] G. Wyszecki and W. S. Stiles, Color Science, Concepts and Methods,Quantitative Data and Formulae, 2nd ed. New York, NY, USA: Wiley,1982.

[24] A. R. Robertson, “Computation of correlated color temperature and dis-tribution temperature,” J. Opt. Soc. Amer., vol. 58, pp. 1528–1535, 1968.

[25] Everlight Electronic Co. RGGB high power LED—4W datasheet EHP-B02. (2008). [Online]. Available: http://www.everlight.com/

[26] Hamamatsu Photonics. Si photodiode S1133 datasheet. (2008). [Online].Available: http://hamamatsu.com/

[27] M. Doshi and R. Zane, “Control of solid state lamps using a multiphasepulse width modulation technique,” IEEE. Trans. Power Electron., vol. 25,no. 7, pp. 1894–1904, Jul. 2010.

[28] D. L. Blackburn, “Temperature measurements of semiconductordevices—A review,” Proc. 20th Ann. IEEE Semicond. Therm. Meas.Manag. Symp., pp. 70–80, Mar. 2004.

[29] T.-P. Sun and C.-H. Wang, “Specially designed driver circuits to stabilizeLED light output without a photodetector,”,” IEEE Trans. Power Electron.,vol. 27, no. 3, pp. 1598–1607, 2012.

[30] X. Tao, H. Chen, S. N. Li, and S. Y. Hui, “A new noncontact method for theprediction of both internal thermal resistance and junction temperature ofwhite light-emitting diodes,” IEEE Trans. Power Electron., vol. 27, no. 4,pp. 2184–2192, Apr. 2012.

[31] S. Skogestad and I. Postlethwaite, Multivariable Feedback Control, Anal-ysis and Design, 2nd ed. New York, NY, USA: Wiley, 2000.

[32] P. Albertos and S. Antonio, Multivariable Control Systems an EngineeringApproach. New York, NY, USA: Springer-Verlag, 2003.

Chun-Wen Tang was born in Taipei, Taiwan, in1976. He received the B.S. degree in mechanical engi-neering from the National Taiwan University of Sci-ence and Technology, Taipei, in 1990, and the M.Sc.and Ph.D. degrees from the Control Group, Mechan-ical Engineering Department, National Taiwan Uni-versity, Taipei, in 2000 and 2009, respectively.

He is currently a Project Manager at the IndustrialTechnology Research Institute, Hsinchu, Taiwan. Hiscurrent research interests include light-emitting diodelighting and control, independent solar photovoltaic

(PV) system, PV/T system, solar microgrid technology system, zero-energytechnology, greenhouse engineering, and emotional design.


Bin-Juine Huang received the Master’s degrees inmechanical and chemical engineering from CaseWestern Reserve University, USA and the doctoratedegree from Odessa State Academy of Refrigeration,Odessa, Ukraine.

He is currently a Professor in the Department ofMechanical Engineering, National Taiwan Univer-sity, Taipei, Taiwan, where he is the Director of theSolar Energy Research Center (SERC), which is sup-ported by the Global Research Partnership (GRP)Award of King Abdullah University of Science and

Technology (KAUST). He was involved in researching a broad array of fields,including energy systems (solar photovoltaic (PV), geothermal, ocean ther-mal, wind, boiler, and waste heat), cooling technology (absorption, ejector,desiccant, cryocoolers, and thermoelectric), solid-state lighting (light-emittingdiode), and control technology. His current research include bridging the gapbetween academia and industry. He has developed more than 30 products withindustry. He is the author or coauthor of more than 200 academic papers and150 technical reports. He holds more than 60 worldwide patents.

Prof. Huang was a recipient of the 1972 Outstanding Youth of the YearAward, the 1991 National Outstanding Engineering Professor Award, the 1995Academician of Academy of Sciences of Technological Cybernetics of UkraineAward, the 1996 Academician of International Academy of Refrigeration,Ukraine Branch Award, the 1996 Tong-Yuan Science and Technology Award,the 2000 Outstanding Researcher Award of the National Science Council, the2005 Science and Technology Award of China-Tech Foundation, and the 2005Solar and New Energy Contribution Award of the Solar and New Energy Societyof Taiwan.

Shang-Ping Ying was born in Taiwan in 1968. He re-ceived the Ph.D. degree in photonics (fabrication andcharacterization of II-VI semiconductor microstruc-ture doped glass) from the National Chiao Tung Uni-versity, Hsinchu, Taiwan, in 1999.

He was the Opto-Electronics and Systems Lab-oratories, Industrial Technology Research Instituteof Taiwan, Hsinchu, where he was involved in theepitaxy of GaN, illumination and color managementof red-green-blue light-emitting diodes (LEDs), lightsource technology in photodynamic therapy (PDT),

optical simulation, and optical system design in the fields of solid state light-ing. He is currently an Assistant Professor in the Department of Opto-ElectronicSystem Engineering, Minghsin University of Science and Technology, Hsinchu.His current research interests include high-power LED packaging technology,chip-on board LED modules, phosphor characteristic for white LED, and accu-rate and reliable optical–electrical measurements of high-power LEDs.

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