Technical Note PR-TN 2007/00318
Issued: 05/2007
Multiple Primary LED Lamp Colour
Controller with Inherent Brightness
Limitation
R. Barcena (Univ. Politecnica de Catalunya); B. Ackermann
Philips Research Europe
Unclassified
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Authors’ address
Unclassified
R. Barcena (Univ.
Politecnica de
Catalunya)
tsade_rbs@hotmail.com
B. Ackermann
bernd.ackermann@philips.com
© KONINKLIJKE PHILIPS ELECTRONICS NV 2007
All rights reserved. Reproduction or dissemination in whole or in part is prohibited without the
prior written consent of the copyright holder .
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©
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Unclassified
Title:
PR-TN 2007/00318
Multiple Primary LED Lamp Colour Controller
with Inherent Brightness Limitation
Author(s):
R. Barcena (Univ. Politecnica de Catalunya); B. Ackermann
Reviewer(s):
Detlef Raasch, Meiling Schmelzer, Ulrich Schiebel
Technical Note:
PR-TN 2007/00318
Additional
Numbers:
Subcategory:
Project:
IntelliLED - Intelligent LED lamp solutions (2006-132)
Customer:
IP&S, BGLE, BU SSL
Keywords:
LED lamps, white LED, color control
Abstract:
There is a strong interest in using LEDs for general illumination due to the
potential they offer for energy saving, environmental friendliness, new
opportunities in lighting design, and control of the intensity, colour, and
spatial distribution of light. General illumination requires primarily white light
that can be obtained by mixing e.g. the light of red, green, and blue LEDs.
This enables also colour adjustability, which is considered to be a most
attractive feature of future LED lamps.
This master thesis takes as a starting point previous work that focused on
developing a setup which permits rapid control prototyping of a red, green and
blue LED-based white light source. Using this setup, some improvements and
new possibilities have been developed and tested.
A brightness control has been developed that limits the maximum brightness
of the light source if the LEDs are unable to reach the requested brightness.
This problem can appear if the user has set an unreachable brightness. It is
aggravated by the aging of the LEDs.
The RGB colour control has been modified in order to add more than three
primary colours to the light generation process. An RGBA (Red, Green, Blue,
Amber) colour control has been set up adding an amber LED.
Conclusions:
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Contents
1.
Introduction ...........................................................................................7
2.
RGB colour control .............................................................................10
2.1. RGB colour control theory..................................................................10
2.2. RGB colour control implementation ...................................................17
2.2.1. PWM implementation .........................................................................19
2.2.2. AM implementation ............................................................................21
2.2.3. Sensing ................................................................................................24
2.2.4. Calibration...........................................................................................26
2.3. System performance............................................................................31
3.
RGB colour control improvements .....................................................37
3.1. Brightness control ...............................................................................38
3.1.1. Theory of control.................................................................................39
3.1.2. System model ......................................................................................43
3.1.3. System performance............................................................................47
3.2. RGBA control .....................................................................................54
3.2.1. Theory of control.................................................................................56
3.2.2. System model ......................................................................................64
3.2.3. System performance............................................................................70
3.3. Systems integration .............................................................................75
Acknowledgements .........................................................................................77
References.......................................................................................................78
List of figures ..................................................................................................80
List of tables....................................................................................................83
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1.
PR-TN 2007/00318
Introduction
The use of LEDs for general illumination has become strongly interesting due to the
potential they offer for energy saving, environmental friendliness, new opportunities in
lighting design and control of the intensity, colour and spatial distribution of light.
A lot of applications can take advantage of the unique features that LEDs offer. Other
than illumination applications can benefit from the possibility of changing light colours
almost instantaneously without changing lamps. In medical applications, their cold light
and small size enables new ways of illumination. Used as traffic lights they reduce
dramatically maintenance compared with previous solutions. The automobile industry
can redefine the size and shape of headlights.
Figure 1- LEDs applications
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LEDs have been available commercially since the early 1960s when General Electric
introduced red GaAsP devices based on the pioneering work of Nick Holonyak Jr. The
early LEDs were priced at $260 and were available only in low volumes. Since then, the
semiconductor industry has dedicated huge efforts on improving features of these
devices. The first high volume vendor of light emitting diodes, Montsanto, was so
optimistic about the future of LEDs that in 1973 an advertisement was placed in the Wall
Street Journal showing an automobile with LED headlights. Nowadays, 30 years later,
this target is close to be achieved [6].
Contemporary LEDs have evolved over the past four decades, with remarkable progress
in the past decade. They have moved from being indicators to light sources and have
begun to replace conventional light sources in a variety of niche applications. LEDs will
replace conventional lighting technology for general illumination if researchers are able
to improve cost, production and performance limitations.
Next to improving the LEDs’ efficiency and reducing their cost, improved thermal
management and colour control are considered to be the key challenges lying ahead.
LEDs are light sources with narrow spectra that are typically a few ten nanometres wide.
As a consequence of this, they emit light with saturated colours and their colour points in
CIE 1931 chromaticity diagram are located close to the perimeter. White light is situated
in the centre of the chromaticity diagram (Fig. 2).
Figure 2. CIE 1931 Chromaticity Diagram. RGB white light generation.
There are two basic ways to obtain white light using LEDs, either colour mixing or using
phosphors for down converting the light of ultraviolet or blue LEDs. Down converting
can be implemented in a more straightforward way. However, colour mixing enables
colour adjustability, which is considered to be a most attractive feature for future LED
lamps. Mixing e.g. the light of red, green and blue LEDs, any colour can be created
inside the triangle defined by their chromaticity coordinates (Fig. 2).
Feedback colour control is needed when using colour mixing according to the poor
colour maintenance achieved because of LED characteristics variation. Optical properties
of LEDs vary with manufacturing spread, aging, temperature variations and drive current
amplitude variations.
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This master thesis project is fruit of the interest of the Research Group SSL at Philips
Research Laboratories, Aachen, Germany, in the achievement of a deep knowledge in
the semiconductor-based solid-state lighting field and its effort to implement new
illumination solutions.
Figure 3 - Philips Pedestrian LED Luminary Gold iF product design award, Philips LED
architectural Floodlight IF design award 2006 & The Inner Ring Road Bridge in
Bangkok, Thailand, lit up with Philips LED lighting systems.
This master thesis project takes as starting point a previous project done by M.Saura [1].
New topologies and control solutions for RGB white light generation had been developed
and tested at Philips Research Laboratories, supervised by Dr. Bernd Ackermann.
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RGB colour control
The recent improvements in high-power light-emitting diodes (LED) technology with
100+ lumens per LED chip and efficacy exceeding that of incandescent lamps brings
solid-state lighting close to reality. An LED light source made of Red, Green and Blue
(RGB) LEDs can provide a compact light source with unique features such as instant
colour variability.
RGB light sources have the following issues: uniform spatial light mixing and
distribution, white colour point maintenance and thermal management. Specifically, the
white colour point maintenance is a stringent requirement in many applications. Meeting
this requirement is a severe challenge due to the variation in the optical characteristics of
the RGB-LEDs with temperature, time, forward current and manufacturing spread of the
LED performance. This results in 1) an unacceptable high variability in white light
colour point and 2) difficulties in manufacturing reproducible LED lamps.
Controlling the colour of a LED lamp using a colour sensor has been investigated at
Philips Research Briarcliff, [Muthu 2002, Muthu 2003]. The LED lamp comprises 3
primary colours, usually red, green, and blue (RGB). The colour sensor comprises three
light sensors with peak sensitivity in different parts of the visible spectrum, usually also
red, green, and blue (RGB).
2.1.
RGB colour control theory
The control procedure described in the following emphasizes two considerations:
Firstly, the human eye acts as a low pass filter. Actually, it is required that there is no
visible flicker. This means that the transfer function of any part of the system that
impacts light emission must have a break frequency substantially higher than the break
frequency of the low pass filter of the human eye. In order to reproduce the light as
perceived by the human eye, a low pass filter is inserted into the feedback path of the
colour control system. This can be implemented either in the digital or in the analogue
part of the system. The break frequency of this low pass filter has to be substantially
lower than the break frequency of the transfer function of any part of the system. As a
consequence of this, apart from this low pass filter in the feedback path, all transfer
functions can be replaced by their low-frequency approximation for the design of the
controller.
Secondly, it will usually not be practical to determine individually the transfer functions
of the different components of the colour control system. Instead of that, they will be
grouped into larger modules, the transfer functions of which are determined in a
calibration procedure. It will be sufficient to determine the low-frequency approximation
of these transfer functions due to the first consideration.
The light to be emitted by a LED lamp is specified by its chromaticity coordinates x and
y and its luminous flux Φlum. From these the tristimulus values X, Y, and Z are
calculated.
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Y=
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Φ lum
lm
683
W
Y
y
(2.2)
Y
Y
= (1 − x − y )
y
y
(2.3)
X =x
Z=z
(2.1)
The tristimulus values are grouped into a vector TV (Tristimulus Values). It has to be
distinguished between the tristimulus values TVO of the light perceived by the observer,
i.e. a person looking at the LED lamp, and the tristimulus values TVS determined in the
feedback path of the colour control system.
⎛X⎞
⎜ ⎟
TV = ⎜ Y ⎟
⎜Z⎟
⎝ ⎠
(2.4)
Ideally, the colour sensor should sense the tristimulus values directly. However, this will
not be achieved in practice. The values R, G, and B sensed actually by the colour sensor
are grouped into a vector SR (Sensor Readings).
⎛ R⎞
⎜ ⎟
SR = ⎜ G ⎟
⎜ B⎟
⎝ ⎠
(2.5)
In a similar way, the control signals for the drivers for the red, green, and blue LEDs will
also be grouped into a vector CS (Control Signals). These may be duty cycles for a pulse
width modulation control or current amplitudes for an amplitude modulation control.
⎛r⎞
⎜ ⎟
CS = ⎜ g ⎟
⎜b⎟
⎝ ⎠
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Fig. 4 shows the general setup of a LED colour control system using a colour sensor. It is
indicated where the signals discussed above occur in the system. As to the tristimulus
values, the input signal TVset and the error signal TVerr are indicated in addition to the
output signals TVO and TVS.
TVset + TVerr
TVS
-
GCAL
GC
SR
CS
GLPS(s)
GD
GLED
GS
GOSO
GLPO(s)
TVO
GOSS
Figure 4 - Block diagram of a LED colour control system using a colour sensor.
The transfer functions depicted in the block diagram of the LED colour control system
using a colour sensor (Fig. 4) represent the following parts of the system:
- controller
GC
GD
- driver
- LEDs
GLED
GOSO
- optical system, from LEDs to observer
GLPO(s) - low pass filter observer (human eye)
GOSS
- optical system, from LEDs to sensor
GS
- colour sensor
GLPS(s) - low pass filter sensor
GCAL
- calibration matrix
Apart from the low pass filters all transfer functions have been replaced by their low
frequency limit. The amplitude of the low pass filters at their low frequency limit is
assumed to be part of the sensor or the human eye, respectively. Therefore, the low
frequency limit of the low pass filter of the sensor is just a unit matrix. Furthermore,
there will be a separate low pass filter for the red, green, and blue sensor.
0
0 ⎞
⎛ LPR (s )
⎛1 0 0⎞
⎜
⎟
⎜
⎟
0 ⎟ G LPS (s → 0) = ⎜ 0 1 0 ⎟
G LPS (s ) = ⎜ 0
LPG (s )
⎜ 0
⎜0 0 1⎟
0
LPB (s )⎟⎠
⎝
⎝
⎠
(2.7)
The control system parts are grouped into modules for which the transfer function can be
easily determined in a calibration procedure.
The first one is the transfer function GC2T from the control signals CS to the tristimulus
values TVO perceived by the human eye, neglecting the dynamics of the low pass filter of
the human eye.
G C 2T = G OSO ⋅ G LED ⋅ G D
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(2.8)
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TV O = G C 2T ⋅ CS
(2.9)
The second one is the transfer function GC2S from the control signals CS to the sensor
readings SR, neglecting the dynamics of the low pass filter acting on the sensor signals.
G C 2 S = G S ⋅ G OSS ⋅ G LED ⋅ G D
(2.10)
SR = G C 2 S ⋅ CS
(2.11)
The calibration matrix GCAL can be determined from the requirement that the tristimulus
values TVS in the feedback path have to be equal to the tristimulus values TVO perceived
by the observer.
TV O = TV S
(2.12)
Inserting (2.11) and (2.12) into (2.9) results in
−1
TV S = G C 2T ⋅ G C 2 S ⋅ SR
(2.13)
The block diagram Fig. 4 of the colour control system indicates that the tristimulus
values determined in the feedback path of the system are linked to the sensor readings by
the calibration matrix, which results in
−1
−1
−1
G CAL = G C 2T ⋅ G C 2 S = G OSO ⋅ G OSS ⋅ G S
(2.14)
Obviously, no calibration is needed if GCAL=1. This requires the optical path from the
LEDs to the sensor to be identical to the optical path from the LEDs to the observer,
apart from an attenuation k of the total amount of light received.
G OSS = k ⋅ G OSO
(2.15)
Furthermore, the sensor has to be ideal, i.e. to measure the tristimulus values X, Y, Z
directly, apart from compensating for the attenuation k of the total amount of light
received.
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⎛1 0 0⎞
⎟
1⎜
GS = ⎜ 0 1 0⎟
k⎜
⎟
⎝0 0 1⎠
(2.16)
The transfer functions GC2T and GC2S from the control signals to the tristimulus values
and sensor readings, respectively, can be determined in a calibration procedure. Three
measurements are taken. They are denoted in the following by indices I, II and III. For
each measurement the control signal for each LED colour is set to a specific value.
Sensor readings are taken and the tristimulus values of the light observed are determined
using a spectrometer. The results obtained are stored as outlined in (2.17) to (2.20).
⎛ rI ⎞
⎜ ⎟
CS = ⎜ g I ⎟
⎜b ⎟
⎝ I⎠
⎛ rII ⎞
⎜ ⎟
CS = ⎜ g II ⎟
⎜b ⎟
⎝ II ⎠
⎛ rIII ⎞
⎜
⎟
CS = ⎜ g III ⎟
⎜b ⎟
⎝ III ⎠
⎛ rI
⎜
CS = ⎜ g I
⎜b
⎝ I
rII
g II
bII
Ö
⎛ XI ⎞
⎜ ⎟
TV O = ⎜ YI ⎟ ,
⎜Z ⎟
⎝ I⎠
⎛ RI ⎞
⎜ ⎟
SR = ⎜ GI ⎟
⎜B ⎟
⎝ I⎠
(2.17)
Ö
⎛ X II ⎞
⎜
⎟
TV O = ⎜ YII ⎟ ,
⎜Z ⎟
⎝ II ⎠
⎛ RII ⎞
⎜ ⎟
SR = ⎜ GII ⎟
⎜B ⎟
⎝ II ⎠
(2.18)
Ö
⎛ X III ⎞
⎜
⎟
TV O = ⎜ YIII ⎟ ,
⎜Z ⎟
⎝ III ⎠
⎛ RIII ⎞
⎜
⎟
SR = ⎜ GIII ⎟
⎜B ⎟
⎝ III ⎠
(2.19)
rIII ⎞
⎛ XI
⎜
⎟
g III ⎟ ; TV O = ⎜ YI
⎜Z
bIII ⎟⎠
⎝ I
X II
YII
Z II
X III ⎞
⎛ RI
⎜
⎟
YIII ⎟ ; SR = ⎜ GI
⎜B
Z III ⎟⎠
⎝ I
RII
GII
BII
RIII ⎞
⎟
GIII ⎟
BIII ⎟⎠
(2.20)
(2.9) and (2.20) result in
G C 2T = TV O ⋅ CS
−1
(2.21)
(2.11) and (2.20) result in
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G C 2 S = SR ⋅ CS
−1
(2.22)
If for each measurement the control signal for one LED colour is set equal to one and the
control signals for the other two LED colours are set equal to zero, then
⎛1 0 0⎞
⎜
⎟
CS = ⎜ 0 1 0 ⎟
⎜0 0 1⎟
⎝
⎠
(2.23)
and the transfer functions GC2T and GC2S are
G C 2T = TV O
(2.24)
G C 2 S = SR
(2.25)
Using (2.10), the block diagram of the LED colour control system (Fig. 4) can be
simplified as depicted in Fig. 5.
TVset + TVerr
TVS
-
GC
CS
GC2S
GLPS(s)
SR
GCAL
Figure 5 - Simplified block diagram of the LED colour control system.
Furthermore, the LED colour control system can be described using the sensor readings
as the control variable by dragging GCAL across the summation point.
TVset
GCAL-1
SRset + SRerr
SR -
GCAL
GC
CS
GC2S
GLPS(s)
Figure 6 - Block diagram of the LED colour control system with the sensor readings as
control variable.
The MIMO (Multiple Input Multiple Output) control is implemented by decoupling the
control signals and sensor readings for the different colours. This is achieved by choosing
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G C ⋅ G CAL = G C 2 S ⋅ G dyn (s )
−1
(2.26)
The block diagram representation of (2.26) is given in Fig.7.
GCAL
=
GC
GC2S-1
Gdyn(s)
Figure 7 - Block diagram representation of (2.26).
As to GC2S it is important to take into account, that in Fig. 6 it represents the real plant
that may exhibit nonlinear behaviour, whereas in (2.26) and Fig.7 the inverse of a linear
approximation to it is used. For the purpose of control design this difference may be
neglected. Then the structure of the system simplifies as depicted in Fig. 8.
TVset
GCAL-1
SRset + SRerr
-
SR
Gdyn(s)
GLPS(s)
Figure 8 - Block diagram of the decoupled LED colour control system.
As a consequence of (2.7) the part of the controller described by the transfer function
Gdyn(s) is a diagonal matrix the elements of which can be designed independent from
each other, using e.g. PI controllers as described in [1].
⎛ Gdyn , R (s )
0
0 ⎞
⎜
⎟
G dyn (s ) = ⎜ 0
Gdyn ,G (s )
0 ⎟
⎜ 0
Gdyn , B (s )⎟⎠
0
⎝
(2.27)
Fig. 9 then gives the overall block diagram of the decoupled colour control system.
TVset
GCAL-1
SRset + SRerr
-
SR
Gdyn(s)
GC2S-1
GLPS(s)
GS
CS
GD
GLED
GOSS
Figure 9 - Overall block diagram of the decoupled LED colour control system.
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2.2.
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RGB colour control implementation
The RGB LED-based light source consists of four different modules. There is one LEDdriving module which provides the currents to the LEDs, one sensor module which
measures the amount of light from the LEDs, a control module which adjusts the current
of every single LED depending on what is measured on the sensor and a LED lamp
comprising red, green and blue LEDs.
Figure 10 – Colour mixing and control [2].
The setup in the laboratory used to develop the RGB LED lamp comprises the four
modules cited before plus an integration sphere where the lamp and sensor are placed, a
dSPACE [13] system, an spectrometer to measure the power spectral flux of the light
inside the sphere and to calculate their chromaticity coordinates, two PCs which support
the rapid control prototyping software of the dSPACE system and the spectrometer
applications [15], an oscilloscope and power supplies.
Figure 11 – Research Group SSL at Philips Research Laboratories, Aachen, Germany.
Laboratory setup.
The role of the control system and the sensor module were outlined at the beginning of
this report in chapter 2. RGB colour control. The role of the LED-driving module and
what this implies is outlined in the following.
The intensity of the light emitted by one LED is virtually directly proportional to the
current through it. The Luxeon Star LEDs [11] used in the setup have a maximum DC
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current of 350mA. It is then necessary to include a subsystem that drives the current
through the LEDs and permits to change its value to control the luminous flux of each
LED.
There are two basic schemes to drive the LEDs, pulse width modulation (PWM) and
amplitude modulation (AM).
The first one, PWM, is the most common solution adopted nowadays in many electronic
devices and almost all microcontrollers include a PWM generator. The second one, AM,
is less popular but there have no studies been done which advise against its application.
Initially, the PWM solution was implemented by the Research Group SSL at Philips
Research Laboratories, Aachen, Germany. The setup is described in Marc Saura’s master
thesis [1] and it was the starting point for the next improvements of the RGB control.
A dSPACE rapid control prototyping system [13] is used to control the signals for the
PWM driver. These signals are passed through a digital to analog converter (DAC) in
their last step before being injected into the driver instead of being delivered by a
dedicated PWM generator. This means that these signals include all the typical errors in a
DAC and they affect the proper response of the system. This was the main reason why
the AM solution was adopted for the next setups used in the investigation described in
this report.
LED Lamp
dSPACE
(control)
Driver
LEDs
Sensor
electronics
Sensors
Figure 12 – RGB colour control. System overview.
The dSPACE rapid control prototyping is a flexible development system to optimize
control designs. It allows controlling the RGB colour control system and changing the
specifications easily.
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M a tla b / S i m u lin k
M odel
dSPACE
I m p le m e n ta tio n
S o ft w a r e
R e a l- T im e in t e r fa c e
P ro c e s s o r / B o a r d s
R e a l- T im e H a r d w a r e
C o n tro l D e s k
E x p e r im e n t S o f t w a r e
REAL
W O RLD
Figure 13 - dSPACE rapid control prototyping system.
RBG colour control models implemented in MATLAB/Simulink [14] are transferred to
dSPACE and implemented into the dSPACE prototyping hardware using the dSPACE
Real Time Interface (RTI) software. Internally, the system reconfigures itself according
to the downloaded model and creates the I/O interface with the outside world. The
dSPACE software also allows developing GUI applications (Control Desk) used to
control the experiments.
2.2.1. PWM driving
PWM is thoroughly explained in Marc Saura’s thesis report [1].The main characteristics
of the system he developed are highlighted below.
A PWM signal with variable duty cycle is given from the dSPACE rapid control
prototyping system to the LED drivers. These PWM signals are outputs from the
dSPACE to the lamp. Three duty cycles, red, green and blue are calculated in the
dSPACE system following the ideas explained in the RGB colour control theory
paragraph.
Figure - 14 Block diagram of the LED colour control system.
In Fig. 15 some components of the Simulink model for the PMW colour control system
are grouped and related to the RGB colour control theory.
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Figure 15 – Simulink model. PWM control scheme.
An extra subsystem block that does not appear in the RGB colour control block diagram
converts the chromaticity coordinates (x,y) and luminous flux (Y) into tristimulus values.
A MAZeT true colour sensor [12] is used for the feedback control of the colour
coordinates. The sensor gives a three channel current output signal, one for red, one for
green and one for blue, which is conditioned to obtain a voltage signal at good working
levels. In absence of light, the sensor, after conditioning, gives a high voltage level
around 0.5 volts that drops, when the light increases, close to 0 volts. For the colour
control these sensor readings have to be directly proportional to the duty cycle and
without offset. In order to accomplish this requirement all the sensor readings are
subtracted to the maximum value.
Figure 16 – MAZeT true colour sensor: MTCSiCS.
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A block working as a current limitator is placed before the PWM generator. It limits the
maximum levels of the control signal between 0 and 1. The drivers used have been
designed to adapt these levels to a current range of 0 to 350mA.
The D/A converter board DS2102 is used to give the PWM signals to the LED drivers
and the A/D converter board DS2001 is used to read the values from the sensor.
As it was said before, a thorough study of the design and performance of the PWM
colour control system is described in [1]. [3] can be used as a reference.
2.2.2. AM driving
The main difference between PWM and AM colour control is the way in which the LEDs
are driven. In the PWM system, the amplitudes of the signals never change and what is
controlled is the time they are on and off. Now, the signals are always on and what is
changed is their voltage level in order to control the amplitude of the currents through the
LEDs.
The first things that have to be changed for the new setup are the drivers. Fig. 17 and Fig.
18 show the scheme of the drivers used.
Figure 17 – AM driver. Power circuit.
Figure 18 – AM driver. Signal conditioning.
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The drivers are designed to work with inputs up to 50V @1A. The power circuit has two
low dropout voltage regulators, LM317HVT and LM7808CT. The first one is adjusted to
18 volts with two resistors while the second one has a fixed output voltage of 8 volts.
Some capacitors are used to stabilize the signal.
The main structure of the driver is a voltage follower. The signal injected from the
control system is passed through a voltage divider that adjusts its level. Then it is passed
through the voltage follower and transformed into a current signal by R4 and R6 resistors
in order to drive the transistor present in the output of the circuit. R9 fixes the maximum
current that the driver can give.
In the circuit of Fig.18, R4||R6 and C4 also serve to counteract the loss of phase margin
by feeding the high frequency component of the output signal back to the amplifier’s
inverting input, thereby preserving phase margin in the overall feedback loop.
Capacitive load driving capability is enhanced by using a pull up resistor R2 to V+.
Typically a pull up resistor conducting 500 µA or more will significantly improve
capacitive load responses. The value of the pull up resistor must be determined based on
the current sinking capability of the amplifier with respect to the desired output swing.
The open loop gain of the amplifier can also be affected by the pull up resistor.
Figure 19 – AM driver board.
To simplify the appearance of the Simulink model, the system has been divided into the
subsystems shown in Fig. 20. There are no differences in the main principles of control
between the PWM and the AM scheme. The new Simulink model now includes a
feedback loop with a subsystem that reproduces the behaviour of the plant. This permits
an easy way to simulate the behaviour of the whole system before implementing it in the
dSPACE rapid control prototyping system.
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Figure 20 – AM colour control subsystems.
As for the PWM system, Simulink model and colour control theory are related in Fig. 21.
Figure 21 – Simulink model. AM control scheme.
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2.2.3. Sensing
The sensing circuitry uses a MAZeT sensor [12]. It has three photodiodes with sensitivity
curves close to the CIE colour-matching functions and gives a current dependant on the
amount of light that it receives. The higher the intensity of the light received the more
current is provided by the photodiodes.
As the signal provided by the sensor is a very low current and the dSPACE environment
works with voltage signals, it is firstly necessary to amplify the signal and secondly to
transform it into a voltage. The MTI04 IC is a programmable gain transimpedance
amplifier used to accomplish these requirements.
Fig.22 shows the circuit used as a conditioning for each channel.
Figure 22 – Sensing. Conditioning circuit.
The circuit is an inverting amplifier plus a low-pass filter. It provides an output of 2.5
volts at darkness conditions. This value drops with increasing light input. The signal to
be filtered is around 100Hz and the cut-off frequency of the low-pass filter is set at 1Hz.
Figure 23 – Sensing. Old sensor & conditioning circuit used in [1].
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The initial implementation of this circuit made by M.Saura [1] was modified to improve
its behaviour in terms of interference rejection, easy modification of the gain, size (Fig.
24 and Fig. 25).
Figure 24 – Sensing. New sensor & conditioning circuit.
Figure 25 – Sensing. New sensor & conditioning circuit.
The gain of the transimpedance amplifier MTI04 can be programmed. Table 1 shows the
different levels of gain. This gain is the same for the four channels of the amplifier.
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Table 1 – MTI04 gain.
The contribution of each primary colour to the sensor readings is quite different. Green
LEDs have the biggest luminous flux of the three primaries used now. On the contrary,
blue LEDs have the lowest. The relation between them is around 1/10. If the maximum
sensor reading with all LEDs fully on uses the full band of work, then the levels for each
primary working individually are acceptable. If this condition is not fulfilled, then the
blue channel has a very low variation and a very low signal level and a little variation on
it caused by any source of interference can completely change its value.
As a consequence of that, selection of the gain is critical. Changing the gain of the
MTI04 transimpedance amplifier can result in dividing the sensitivity even by five
between two steps of gain. Then it is may not be possible to use the full band of work.
It is recommendable to modify the implemented conditioning circuit in order to avoid
this problem. It could be solved adding an external potentiometer to adjust the gain. It
could be even better if the gain could be adjusted for every channel individually. Price
and size restrictions must also be considered that can apply to new implementations.
Such investigations of the analog circuitry were not in the scope of this project and were
not pursued further.
2.2.4. Calibration
As it was explained in the control theory chapter, the system needs to be calibrated in
order to calculate the matrices
GCal −1 = GC 2S GC 2T −1
and
GC 2 S −1
where GC2S is the matrix of sensor readings and GC2T the matrix of tristimulus values,
both calculated when calibrating.
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GC 2 S
⎛R
⎜ r
= ⎜ Gr
⎜
⎜ Br
⎝
Rg
Gg
Bg
Rb ⎞⎟
Gb ⎟
⎟
Bb ⎟
⎠
GC 2T
⎛ Xr
⎜
= ⎜ Yr
⎜
⎜ Zr
⎝
Xg
Yg
Zg
X b ⎞⎟
Yb ⎟
⎟
Zb ⎟
⎠
For the nine possible combinations of red, green and blue LEDs and red, green and blue
channels of the sensor, each element of the matrix of the sensor readings GC2S is
calculated as the value in volts of the difference between the signal delivered, after being
conditioned, by the sensor module when the sensor is in dark conditions and when it is
illuminated by a LED.
For example, the Rr value is the difference between the signals for the red channel of the
sensor when all the LEDs are off and when the red LED is on. Following the same rule,
the Gb value is the difference between the signals for the green channel of the sensor
when the LEDs are off and when the blue LED is on.
The elements of GC2T are the tristimulus values of each LED. Their measurement can not
be done directly. The spectrometer gives the chromaticity coordinates of the light and its
luminous flux, from which it is possible to obtain the required tristimulus values using
these formulas
Y=
Φ lum
lm
683
W
X =x
Y
y
Z=z
Y
Y
= (1 − x − y )
y
y
The calibration procedure consists of switching fully on one LED each time and
measuring the value of the sensor readings, chromaticity coordinates and luminous flux.
These calibration measurements are needed to determine which sensor readings
correspond to a desired light output and what are its characteristics.
The aim of the calibration is to know how each channel of the sensor is affected by a
known kind of light. It means to know what the relation is between the control signal and
the sensor readings and between the control signal and the tristimulus values. What is
what we are measuring (sensor readings) and what we are really seeing (tristimulus
values). The values we obtain and the matrices we implement will allow the control to
correct the error of perception introduced by the sensor.
In an ideal sphere no losses would occur because the light from the LEDs would be
perfectly reflected at the walls, but in a real sphere some light is lost. Another calibration
process is needed to account for changes in the conditions inside the sphere, like placing
the LEDs board, cables, etc. This is achieved with a calibration lamp and software
provided with the spectrometer.
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Figure 26 – Sphere plus LEDs and sensor board.
The next figures show two different Simulink models used for calibration. They differ as
to how the signals that will drive the LEDs are generated. The first diagram was created
for an AM modulation while the second one was for a PWM modulation. These two
Simulink models permit to switch on each LED individually.
Figure 27 – AM calibration Simulink model.
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Figure 28 – PWM calibration Simulink model.
The next two figures show the applications from where the measurements are taken.
The first one is a capture of a Control Desk window of the dSPACE system for the PWM
modulation. In this case, the duty cycle of the signals that drive the LEDs are controlled.
The system automatically presents the sensor readings of each one of the three channels
of the sensor, red, green and blue. The window for the AM modulation permits to control
the amplitude of the signals in a similar way and also shows the sensor readings.
Figure 29 – dSPACE PWM control desk.
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The next capture shows how the spectrometer software application presents the spectral
power density of the light, the chromaticity coordinates and the luminous flux.
Figure 30 – Spectral lamp measurement system ver.5.1.5.0.
The calibration process is a critical procedure that has a huge effect in the results of the
colour control system. A wrong calibration will result in a wrong colour point of work.
This procedure is the subject of separate investigations.
As the LEDs are affected by its temperature of work, it is also necessary to wait a little
time allowing them being warmed up before taking the measurements. Waiting five
minutes gives enough good results.
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Figure 31 – Effect of temperature variation on the spectral emission of a red 1W Luxeon
LED [11].
2.3.
System performance
The system to be characterized uses the AM colour control solution and it is the starting
point for the next studies and improvements of the system performance.
To test the system performance, a test point in the chromaticity diagram is set.
Figure 32 – CIE 1931 Chromaticity Diagram. Selected point of work.
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In a first approximation, the system is simulated in a non real time setup, using the
Simulink model with the new block that implements the behaviour of the plant.
The transient response of the system for the requested colour point and brightness of 0.08
is shown in Fig. 33.
Figure 33 – AM colour control. Simulated transient response.
Fig.34 shows the transient response of the system when the brightness is changed from
0.08 to 0.03.
Figure 34 – AM colour control. Simulated transient response II.
As it can be seen from these two figures, the system is able to find a constant relation
between the signals for the red, green and blue LEDs when they reach the steady state. It
is also possible to see in both pictures a period where the signals achieve their maximum
permitted levels, 0 and 1. If a signal limitator would not have been included in the setup,
in a real situation, the LEDs would be damaged. With this limitator, this problem is
avoided but then the relation between signals is not constant since the limit is reached.
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This causes a variation in the colour point every time the brightness is changed and the
limits are reached. As it is seen in Fig. 33, in this particular case, this change in the
chromaticity coordinates can last even more than two seconds.
When the requested brightness is too high, the control tries to satisfy this requirement
increasing the signal for the LEDs and again the maximum value is reached. This means
that the colour point obtained is not the one desired. This situation must be avoided in
order to preserve the desired colour point. Fig. 35 shows this situation for a requested
brightness of 0.12.
Figure 35 – AM colour control. Simulated transient response III.
The next figure shows the response of the system for some set brightness values. It is
interesting to see how these responses have a high over shoot that brings the Am signal to
saturation.
Figure 36 – AM colour control. Simulated transient response IV.
Once the simulated colour control model works satisfactorily, it is transferred to the rapid
control prototyping system. In the Simulink model used, the plant description block is
replaced by the AD and DA converters (Fig. 37).
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Figure 37 – AM colour control. RTI1103 dSPACE model.
The signals captured with an oscilloscope are shown in Fig. 38 and Fig. 39.
Figure 38 – AM colour control. Transient response I.
Figure 39 – AM colour control. Transient response II.
The main differences with the expected results are two:
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The first one is the different final level of the signals. This is caused because the model
of the plant used in the simulation does not match perfectly its real behaviour. Some
characteristics have been assumed linear but they are not in their whole range of work.
The second one is the ripple that appears in these signals. This is caused because of the
interferences the sensor receives, as for example external light, changes in temperature or
electromagnetic fields. Also the signal from the sensor injected into the control is too
low, as it was explained in the sensing chapter, and a little contribution of these
interferences force a non-negligible change in the control. LEDs are also affected by
these external disturbances and also change their response contributing to this ripple.
A detail of the ripple is shown in Fig.40. The cause of this waveform is that the control
signal is generated in a D/A converter.
Figure 40 – AM colour control. Detail of D/A characteristics of the response.
As a result of all these differences, the system does not match the exact point in the
chromaticity diagram and the difference in xyY coordinates seems to be considerable. At
this point a variable transformation from xyY to uv(Y) coordinates is necessary. It is
considered that a difference less than 0.005 in these uv coordinates is not detected by the
human eye. This means that the human eye cannot distinguish the difference of the
colour characteristics of two colours that differ no more than 0.005 in uv coordinates.
This is going to be explained in a following chapter of this report.
Fig. 41 shows the spectral power density distribution of the RGB colour point achieved.
Figure 41 – AM colour control. Spectral power density.
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The difference between the desired and the obtained colour point in uv coordinates is,
x set = 0.33
Desired:
y set = 0.33
xm = 0.3313
Obtained:
Yset = 0.05
Error:
y m = 0.3312
Ym = 0.0501
(Δu , Δv) = (0.0004,0.0006)
The conclusion after the analysis of the system performance, in spite of the differences
that appeared between what is desired and what is obtained, is that it is possible to reach
a good RGB colour control. However, it would be good to improve the transient state
behaviour in order to avoid the saturation of the channels and also the saturation in the
steady state when the requested brightness is not reachable.
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RGB colour control improvements
Once satisfactory RGB colour control has been achieved, the next step is to add more
functionality to the system in order to accomplish some of the requirements that a
commercial lamp could have.
For example, it is interesting to limit the maximum brightness that can be requested to
the system to avoid the change of the colour of the light emitted when the relation among
the amplitudes of the signals that control the LEDs are changed. It is also important to
prevent the system against the consequences of aging, that can reduce the maximum
brightness by even 50% of its nominal value, provoking also the loss of the selected
colour of the light.
The colour rendering index (CRI) is a metric used to evaluate light sources. The LED
industry is working hard to improve the CRI of the LED based lamps so that the
technology will be widely accepted for general illumination applications.
Because the CRI score is directly related to the spectral power distribution of the light
source, it is possible to manipulate the spectrum to produce a higher CRI value. The use
of more than three primary colours allows modifying this spectrum and increasing the
CRI.
Figure 42 - Eye sensitivity function.
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In the following two different ways to add functionality and to improve the RGB colour
control characteristics are going to be studied.
The first one tries to control the maximum brightness that can be requested to the system
in order to avoid the clamping of the signals that drive the LEDs and the loss of the
colour point. It also tries to minimize the effect of aging, another factor that can cause the
same effect. In this second case the problem is not the brightness requested but the
reduction of it that the LEDs suffer in time.
The second one tries to improve the Colour Rendering Index (CRI) reachable by adding a
fourth primary colour, i.e. amber.
The starting point for these improvements is the system implemented for the RGB colour
control in its amplitude modulation solution.
At the end of this study both solutions are implemented together.
3.1.
Brightness control
Aging is one of the most important sources of variation of the maximum brightness.
There is no mathematical model for the impact of aging on the lumen output of an LED.
Aging can cause the loss of even 50% of brightness in a LED. Aging changes only the
amplitude of the power spectral density but not its shape. To maintain the power spectral
density, the current through the LEDs must be increased.
The maximum current for the LEDs used in this setup is 350mA. If the current exceeds
this level, the LEDs can be damaged. To solve the problem of the maximum current, a
block in the Simulink model limitates the control signal (voltage) for the drivers. At its
maximum level, it allows a current of 350mA. The signals to the LEDs are clamped
when their value is out of the work margin of 0 to 1.
Brightness control is an important target to accomplish. At present, there are three
parameters that have to be fixed to obtain a certain light in terms of colour gamut and
intensity. Two of them are xy coordinates and the third one is the brightness. Each of
these parameters has a possible region of work. For xy coordinates this space is inside the
triangle that the red, green and blue LEDs coordinates describe in the chromaticity
diagram. Brightness is the third dimension of this region. Fig.43 shows a possible region
of work. It should be noted that this figure is only qualitative, it is just used to illustrate
how the work region could be.
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Figure 43 – Brightness control. xyY region of work.
Any set value, i.e. combination of xyY, outside this area is not reachable and causes a
control error. This wrong control provokes the saturation of the signals that drive the
LEDs. In the particular situation in which the requested xy coordinates are inside the
region of work and the brightness is out of it, the control tries to increase the current
through the LEDs. Almost one but probably most of the signals to the LEDs will be
bigger than the maximum value permitted. This will provoke the clamping of the signals,
the change of the needed relation between them and the loss of the desired xy
coordinates. It is then necessary to control the requested brightness to the system to
avoid this situation, that can appear when aging decreases the maximum brightness
reachable for an LED at the beginning of its life or when the set brightness is directly too
high.
3.1.1. Theory of control
There are two problems related to the brightness that should be solved, aging and the
maximum brightness that can be requested.
In a first attempt, a model was tested which tried to solve the effects of aging. It worked
properly. However, it was not able to solve the problem of the maximum brightness. It is
interesting to explain this solution although it was not useful in the end because it will
help us to better understanding the aging problematic.
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The way to avoid the problems related to the brightness is to know which is its maximum
value reachable and to not permit a request larger than it. Unfortunately, this is not
possible to accomplish during the manufacturing process because brightness depends on
many external factors as for example manufacturing spread, temperature or aging. It is
also not possible to fix a working range for the brightness due to the wide range of
variation it has. Aging can cause a variation of even 50% of the LEDs initial brightness
value and no mathematical model is known for it. It is then necessary to know the
maximum brightness at every single moment during the LEDs’ operation.
Sensor readings are the measurement of the light emitted by LEDs. When the light
emitted decreases, sensor readings also decrease their value and the RGB colour control
system tries to compensate this by increasing the current through the LEDs. This
reduction of the light intensity is by definition a reduction of the brightness. When the
brightness of the LEDs decreases too much, the control tries to increase the current
through the LEDs over the maximum level allowed trying to maintain the set brightness.
For fixed xy coordinates, the brightness is maximum when one of the control signals
almost reaches its maximum level without going over it.
As the first step to obtain a desired kind of light, xy coordinates and brightness (Y) are
set. These three parameters are then transformed into tristimulus values and passed
through Gcal-1 to obtain the set sensor readings (SRset). This transformation from xyY to
SRset is bidirectional and it could be done in the inverse direction. This means that it is
possible to calculate the brightness of the light using the sensor readings.
If we know when we have the maximum brightness and how to obtain its value from the
sensor readings, then the problem of controlling the brightness is solved. When the
maximum signal for one LED is achieved, the brightness will be calculated from the
sensor readings and it will be set as the maximum value for the brightness. In the future,
aging will decrease the maximum brightness that the LEDs can achieve, so it will be
mandatory to reduce the new Yset allowing the system to detect a new future saturation of
the control signals. The control procedure will detect the achievement of the maximum
value for the control signals, will calculate the brightness value and will set as the
maximum Y we can request, for example, 90% of it.
The solution adopted can solve perfectly the effects of the aging in the RGB colour
control sytem. However, this solution does not work properly when the problem is not
the aging but the brightness set manually. To modify manually the set brightness means
to introduce a step in the control system. The variation of the control signals is faster than
the dynamics of the measuring system. It is necessary that the variation of the control
signals is slower than the measuring system allowing it to take the measurements of the
sensor readings before the signals saturate. The problem is not if the first signal saturates.
The problem is that the other signals are still increasing their value and the brightness and
they are also modifying the xy coordinates.
To solve the problem of the step caused by the manual set of the desired brightness, the
main idea of the brightness control must be changed completely. The control signals for
the LEDs (Am signals) have the information of when the system reaches its maximum
level of brightness. It is not mandatory to know at which level of brightness this occurs, it
is only necessary to not allow them to go over it. Hence it is possible to base the control
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of the maximum brightness on the information that the Am signals provide. They are
then used as a feedback to control the set brightness (Yset).
As it was shown in a previous chapter, the RGB colour control system presents an
overshoot that can bring the transient response of the system to saturation despite it can
work properly in the steady state. This is caused because any change of Yset means to
inject a step in the control. To avoid this behaviour, the control of the Yset is necessary.
To prevent going over the maximum and under the minimum values of the Am signals,
these minimum and maximum values will be used as asymptotes for the limits of the
working region of these Am signals. Yset will be controlled to eliminate the step to the
control system. Yset will be increased or decreased using these formulas,
(
)
(
)
Y = Ycalc + e (Yset −Ycalc )ninc − e − (Yset −Ycalc )ninc ( Ammax − Am )minc
Y = Ycalc + e (Ycalc −Yset )ndec − e − (Ycalc −Yset )ndec ( Ammin − Am )mdec
where Ycalc is the previous value of Y, Ammax and Ammin are the maximum and minimum
values of the Am signals and the asymptotes for the curves, Am is the actual value of
these signals and ninc, minc, ndec and mdec are parameters that allow to control the speed
and the overshoot of the Am response.
The difference (Yset-Ycalc) controls the increment of Y. When this difference is close to
zero, the increment applied to Y is also close to zero. If the difference is negative, the
increment is then also negative. This allows the system to reach the Yset controlling how
it is reached with the n parameters.
Fig. 44 shows the curve for the increment that is added to Ycalc to which the next formula
corresponds,
(e(
Yset −Ycalc )ninc
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Figure 44 – Factor of increment.
Fig. 45 shows how Yset is theoretically reached depending on the selection of n.
Figure 45 - Yset.
The m parameter present on the second half of the formula will have a similar effect on
the set brightness.
Both parameters will be selected in order to obtain a certain transient response in terms of
speed and maximum allowed overshoot.
The decrement of Y, when Yset is smaller than the actual Y, follows the same rules seen
before but in the opposite direction of correction.
The value of Yset affects directly the value of the increment. The bigger Yset, the bigger
the increment will be. Two different values of the reachable Y will present a different
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behaviour in spite of that the final Am value will be the same. In the worst case the
system will be even unstable and will oscillate. To improve and try to avoid this
behaviour, the maximum value for Yset allowed will be the result of the sum of the
brightness of every single LED working at its maximum current.
When the Am signal is close to its maximum or minimum permitted value, the difference
(Ammax-Am) or (Ammin-Am) also reduces the increment or decrement to add to Ycalc. It
will be close to zero when the Am signals are close to the limits of the working region
pre-established allowing describing the asymptotic behaviour for them. Am is the highest
value among the Am signals when Y is increased and it is the lowest one when it is
decreased.
Aging can cause the reduction of even 50% of the maximum brightness reachable. To
compensate this loss of brightness, the system will try to maintain Yset increasing the
current through the LEDs. This will be done increasing the Am signals. If these signals
go over the limit of the working region, then the colour of the light will change. To avoid
this behaviour, Yset must be reduced accordingly. In this situation, (Ammax-Am) will be
negative, helping the increment for Y to be also negative and as a consequence the new Y
for the control system will be reduced.
The time constant for the aging is high enough to allow the control to reduce Yset before
the colour of the light varies. This permits to work with the entire available brightness
unlike it occurs with the solution of control explained at the beginning of this chapter. In
spite of this, a 10% of security margin is adopted to avoid other sources of interferences
that can affect the brightness.
3.1.2. System model
The starting point for the implementation of the brightness control solution is the RGB
colour control diagram in its amplitude modulation version.
Figure 46 –AM RGB colour control. Simulink diagram.
In the Fig. 47 the modifications introduced in the Simulink model are shown. The set
brightness (Yset) is now passed through the Brightness control block where it is modified
as it was explained in the theory chapter. The Am signals are the feedback for the control
procedure. These signals are measured before passing through the Signals level adapter
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block. It is important to know their real value before being clamped when they are out of
the working area in order to select among them the biggest or smallest one.
Figure 47 – AM RGB colour control with brightness limitation. Simulink diagram
modifications.
The brightness control block is shown in Fig.48.
Figure 48– Brightness control block.
All the functional subsystems have been highlighted for the easy understanding of the
control system.
In the maximum brightness detector, Yset is compared with the maximum brightness that
can be set. If it is bigger than this maximum value, Ymax is passed as the set brightness.
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The maximum brightness detector includes the maximum brightness calculator (Fig. 49),
where the maximum brightness (Ymax) that can be set is calculated as the sum of the
brightness of every single LED when the maximum current allowed flows through them.
In the calibration procedure of the RGB colour control system, the LEDs work at 50% of
their maximum current. The brightness achieved in this procedure is then half of the
theoretical maximum value. The brightness is supposed to be directly proportional to the
current through the LEDs. Then, it is necessary to multiply these measured values of
brightness by a factor of two to obtain the brightness at full current. This is not fully
correct because in the operation limits of the LEDs the brightness does not follow this
rule and does not increase its value in the same way. However, this difference will
provide us a little margin to guarantee the possibility to fix Yset at the maximum level that
the system can achieve.
The limitation of Yset is needed because the factor of correction that has to be applied in
the Y calculation depends directly on the difference between the Yset and the actual Y
delivered to the RGB colour control. If Yset is too high, the system can be unstable, as it
was explained in the control theory chapter.
Figure 49 – Maximum brightness calculator.
The brightness memory block provides the feedback for the calculation of the correction
factor (increment or decrement).
The output of the brightness control block is the value of Y that must be injected to the
RGB colour control. It is obtained as the sum of the previous value of brightness, Ycalc,
and the correction factor, Yinc. The result, Y, is passed through a memory block and
becomes Ycalc for the next calculus. Yinc is calculated in the correction factor block. In
this block the two possible corrections, increment and decrement, are calculated
according to the inputs Yset, Ycalc and Am in its two versions, Ambig and Amsmall.
The correction factor block (Fig.50) implements the formulas for the increment and
decrement values. The parameters ninc, minc, ndec and mdec can be adjusted internally to
modify the control law.
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Figure 50 – Correction factor block.
As outputs, the correction factor block delivers two values, one for the increment and
another for the decrement of Y. The set brightness change detector will decide which of
them will be used. This subsystem memorizes the last value of brightness set when the
Yset is changed. This change is detected by the detect change block. This block detects
any event in its input and delivers a short pulse in its output. This pulse changes the
position on the selector block and the last Y sent to the control system is then passed
through it. This selector has also a closed loop between its output and one of its inputs
with a memory block which memorizes the previous value passed. This new memorized
value is then compared with the new Yset requested. Depending on the result of the
comparison, the subsystem will decide if the value for the correction has to be an
increment or a decrement.
Am selector (Fig.51) chooses among the Am signals the biggest and the smallest one.
These two signals are used later to calculate the increment and decrement values as
outlined before.
Am signals are passed through a memory block before the Am selector block. Simulink
forces to do it in this way to permit the use of the feedback loops.
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Figure 51 - Am selector block.
3.1.3. System performance
As for the RGB colour control implementation, the first step to analyze the system
performance will be to work in a simulated environment and later the model of the
system will be transferred to the rapid control prototyping system.
The set point selected for the RGB colour control implementation is maintained to
compare both solutions and highlight the improvements of the new brightness control.
The response of the system for the set point
shown in Fig.52,
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x = 0.33 y = 0.33 Y = 0.08
is
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Figure 52 – AM RGB colour control. Brightness control. Simulated transient response.
and the response for the RGB colour control before controlling the brightness is depicted
in Fig. 33 as it was shown in a previous chapter.
Figure 33 – AM colour control. Simulated transient response.
As it can be seen (Fig. 52), the overshoot has disappeared and the relation between the
Am signals is never lost. This means that the colour of the light does not change during
the transient response unlike it did before.
Without controlling the brightness, the system reaches its final value 1.5 seconds after
being turned on. Now, a longer time is needed to reach the same value. However, 0.5
seconds after being turned on, the value reached differs by approximately 15% from its
final value, after 1.5 seconds it is close to 5% and in 4 seconds around 1.5%. This
difference can be accepted as a good response of the system because of the
characteristics of the human eye. The human eye is not too sensitive to brightness
changes. However, it can detect little changes in colour. Therefore, it is appropriate to
say that the response of the system has been improved.
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The next two figures are used to show how the response of the system for some set
brightness was before limiting its set value and how it has changed after limiting it.
Fig. 53 is also interesting to show how the new system implementation has a different
response in terms of speed and over shoot depending on the set brightness in spite of the
work point (x,y) not having been changed.
Figure 53 – AM RGB colour control. Brightness control. Simulated transient response II.
Figure 36 – AM colour control. Simulated transient response IV.
Fig. 54 shows the response of the system with brightness control and Fig. 34 without it
when the brightness is changed from 0.08 to 0.03. The same behaviour as for increasing
Yset can be observed.
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Figure 54 – AM RGB colour control. Brightness control. Simulated transient response
III.
Figure 34 – AM colour control. Simulated transient response II.
Fig. 55 shows the curve described by the brightness delivered to the colour control
system. It should be noted that this curve is obtained for a specific value of the
parameters n and m, brightness and working point.
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Figure 55 – AM RGB colour control. Set brightness.
The response of the system can be modified by changing the values of the parameters m
and n that are present in the formula that control the brightness. With these two
parameters it is possible to control the transient response of the Am signals.
The next figures show different system responses for some values of m and n and the set
point x=0.33 , y=0.33 , Y=0.05.
Figure 56 – AM RGB colour control. AM and brightness transient responses. ‘n’
modification.
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Figure 57 – AM RGB colour control. AM and brightness transient responses. ‘m’
modification.
As it can be seen, both m and n control the speed of the system response and the
magnitude of the overshoot. This response is also influenced by its proximity to the
maximum Am value.
In the future, it could be interesting to control these two parameters allowing them to
vary according to the value of the set brightness, what can make the response of the
system more uniform independent of this set brightness.
Once the desired results have been obtained in the simulation environment, the model of
the system is transferred to the rapid control prototyping system. Figures 58 and 59 show
the shape of the transient response of the system at different brightness values. This
shape depends basically on two values:
The first one is the difference between the requested brightness and the brightness
requested previously, where we are and where we want to arrive. In this case, Fig. 58
shows the rise up of the Am signals starting with the system off, brightness equal to zero,
and Fig. 59 shows the inverse situation, starting from Ysetmax.
The second one is the distance between which is going to be the final value of the Am
signals and the maximum permitted value for them. How far we are from the Ammax.
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Figure 58 – AM RGB colour control. AM transient response I.
Figure 59 – AM RGB colour control. AM transient response II.
In both figures it is possible to see a little overshoot for the lower difference of brightness
requested that disappears when it is increased. This effect is a consequence of the second
value explained previously. This value brings the system to an over damped response
when it decreases.
To this point, the behaviour of the system is as what we obtained as a result when we
used the Simulink model of the plant before.
The next figures show how the system response changes with the m and n parameters.
Here only the situation in which the system starts from a set brightness of zero is shown.
All the other possible scenarios, as for example the decrement of Yset, will show a similar
behaviour.
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Figure 60 – AM RGB colour control. Transient response. Variation of n.
Figure 61 – AM colour control. Transient response. Variation of m.
3.2.
RGBA control
A high lumens-per-watt value does not necessarily mean that the quality of the light is
also good. The notion of colour quality can be a subjective measure. The colour
rendering index is a unit of measure that defines how well colours are rendered by
different illumination conditions in comparison to a standard. The CRI has been widely
adopted and used by the lighting industry to characterize the quality of a light source [4].
Light sources are compared to a reference with the same colour temperature and scored
based on the colour shift from a palette of base colours.
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Figure 62 – RGBA control. CRI improvement. Colour rendering for different light
sources.
LED lamps comprising more than three primary colours exhibit an increased colour
gamut and improved CRI. This is the reason why it is interesting to modify the system to
allow it to control more than three primary colours.
Figure 63 – RGBA board prototype.
Because the CRI score is directly related to the spectral power distribution of the light
source, it is possible to manipulate the spectrum to produce a higher CRI value. In our
implementation a fourth amber LED is used to improve the CRI.
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3.2.1. Theory of control
If more than 3 primary colours are mixed then the control procedure outlined in chapter 2
has to be modified. This will be discussed in the following for mixing 4 primary colours,
i.e. red, green, blue, and amber (RGBA). Whilst there are still 3 sensor readings as
specified by (2.5), there have to be now 4 control signals instead of the 3 control signals
specified in (2.6).
⎛r⎞
⎜ ⎟
⎜g⎟
CS = ⎜ ⎟
b
⎜ ⎟
⎜a⎟
⎝ ⎠
(3.1)
As a consequence of this, the matrices GC2T as defined in (2.9) and GC2S as defined in
(2.11) will no longer be quadratic but matrices with 3 rows and 4 columns. Therefore, it
is no longer possible to determine their inverse which would be needed in (2.13), (2.14),
and (2.26).
The control of this LED lamp with 4 primary colours will be implemented by reducing it
to the control of a LED lamp with 3 primary colours dealt with in chapter 2. This is
achieved by introducing a fixed relation between the control signals of 2 of the 4 primary
colours. In the following, the control signals ‘r’ and ‘a’ for the drivers for the red and
amber LED will be derived from a common control signal ‘ra’ and a parameter k
defining their ratio.
⎛ ra ⎞
⎜ ⎟
CS = ⎜ g ⎟
⎜b⎟
⎝ ⎠
(3.2)
0 ≤ k ≤1
k < 1 / 2 : r = ra
a = 2 ⋅ k ⋅ ra
(3.3)
k > 1 / 2 : a = ra r = 2 ⋅ (1 − k ) ⋅ ra
Using this fixed relation between 2 control signals, the control procedure outlined in
chapter 2 can be applied for each value of k. Making k a variable parameter of the control
procedure that can be adjusted in a feed forward scheme allows to exploit fully the colour
gamut of the LED lamp and may be used to optimize its colour rendering. In order to do
so, the transfer functions GCAL-1 and GC2S-1 (cf. Fig. 2.6) have to be known for each k.
Interestingly, Gdyn(s) does not depend on k since the control is designed such that the
sensor signals are decoupled.
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The transfer functions GCAL-1 and GC2S-1 can be determined as a function of k by
executing the calibration procedure outlined in chapter 2 for several values of k and
interpolating in between. k is defined piecewise on the intervals 0 ≤ k ≤ 1 / 2 and
1 / 2 ≤ k ≤ 1 . Therefore, when considered as functions of k, the elements of the transfer
functions GCAL-1 and GC2S-1 are expected to exhibit discontinuities at k = 1 / 2 and these
two intervals will be dealt with separately.
Then the most simple procedure would be to determine the transfer functions GCAL-1 and
GC2S-1 for k=0, k=1/2, and k=1 and interpolate linearly in between in the intervals
0 ≤ k ≤ 1 / 2 and 1 / 2 ≤ k ≤ 1 , respectively.
When the light of two LEDs is mixed, the resultant light has its chromaticity coordinates
placed in the line that joins their chromaticity coordinates. The final point in this line
depends on the luminous flux of the LEDs and also depends on their chromaticity
coordinates. It will vary according to the LEDs used.
The exact characteristics of the mixed light can only be obtained measuring them with an
oscilloscope. However, this can not be done in a real environment. It is not practical to
measure these characteristics every time the mixing relation between the LEDs is
changed. Because of this, it is necessary to use a procedure which will estimate these
values automatically according to a previous calibration.
The solution adopted at this moment only takes care of the changes because of the
modification of the k parameter presented before. This parameter will change the signal
that drives the LEDs. This will affect the luminous flux of the LEDs. Other influences as
for example temperature variation or aging are not taken into account.
Measurements of the mixed light are taken at some k values with the spectrometer.
Results are shown below and in Fig. 64. These values will be used later to check how
accurate the procedure is.
AMBER-RED LEDS
(measured)
Am
0,5
k
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
x 0,6960 0,6756 0,6603 0,6507 0,6450 0,6417 0,6359 0,6275 0,6154 0,5964 0,5672
y 0,3034 0,3238 0,339 0,3484 0,3542 0,3574 0,3632 0,3715 0,3837 0,4024 0,4314
Y 0,0134 0,0166 0,0199 0,0226 0,0248 0,0264 0,0247 0,0226 0,0201 0,0174 0,0146
Table 2 – Spectrometer measurements of the mixed light of amber-red LEDs.
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Figure 64 – Chromaticity coordinates of amber-red light.
Also the light characteristics of each LED are individually measured at some Am values.
Results are shown below. Later, some of these values will be used as the values for the
calibration procedure.
RED LED
Am
0,5
0,4
0,3
0,2
0,1
k
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
x 0,6961 0,6961 0,6961 0,6961 0,6961 0,6961 0,6958 0,6956 0,6954 0,6947
y 0,3034 0,3034 0,3034 0,3034 0,3034 0,3034 0,3035 0,3036 0,3038 0,3037
Y 0,0134 0,0134 0,0134 0,0134 0,0134 0,0134 0,0112 0,0085 0,006 0,003
0
1
0
0
0
AMBER LED
Am
0
0,1
0,2
0,3
0,4
0,5
k
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
x
0
0,5545 0,5567 0,5601 0,5636 0,5672 0,5672 0,5672 0,5672 0,5672 0,5672
y
0
0,4433 0'4414 0,4382 0,4348 0,4314 0,4314 0,4314 0,4314 0,4314 0,4314
Y
0
0,0036 0,0075 0,0105 0,0129 0,0146 0,0146 0,0146 0,0146 0,0146 0,0146
Table 3 – Individual spectrometer measurements of amber LED and red LED lights.
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Once defined the real behaviour of the LEDs we are going to work with in terms of
chromaticity coordinates and luminous flux for any of the fixed k values, the mixed light
will be then calculated according to next formulas,
Yi
yi
x= i
Yi
∑y
i
i
∑ xi
y=
∑ Yi
i
Yi
∑y
i
i
z = 1− x − y
where xi, yi and Yi are the chromaticity coordinates and the luminous flux of each of the
LEDs involved in the light generation. The chromaticity coordinates and luminous flux
of one light can be calculated as the addition of some individual lights, in this case the
light of some LEDs.
The next table shows the supposed characteristics of the light using the previous formulas
for the same k values used before when they were measured with the spectrometer.
AMBER-RED LEDS
(calculated)
Am
0,5
k
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
x 0,6961 0,6741 0,6575 0,6481 0,6428 0,6401 0,6341 0,6252 0,6147 0,5962 0,5672
y 0,3034 0,3252 0,3416 0,3509 0,3562 0,359 0,3648 0,3736 0,3842 0,4023 0,4314
Y 0,0134 0,017 0,0209 0,024 0,0263 0,028 0,0258 0,0231 0,0207 0,0177 0,0146
Table 4 – Calculated brightness and chromaticity coordinates of amber-red mixed light
using individual spectrometer measurements of each LED.
The results obtained do not match exactly with what was measured using the
spectrometer. This difference can be assumed not important if there is not a big
difference between light characteristics. It is assumed that a change in light
characteristics can not be observed by the human eye if this variation is smaller than
∆uv<0.0035 when using uv coordinates, however, according to a “4-step” MacAdam
ellipse, a difference of 0.005 can be accepted.
A methodology was created by MacAdam in 1943 for mathematically constructing
ellipses about target points (somewhat useful to lamp industry and now part of ANSI
standards). The goal of the original research was to determine a series of boundaries
around several colour targets (x, y coordinate) on the CIE chromaticity diagram,
illustrating how much one can “stray” from the target (along various colour axes) before
perceiving a difference from the target colour [10].
MacAdam ellipses are described as having “steps,” which really means “standard
deviations.” If a large sample of the population were used (which it was not) and if a
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trained observer could reliably repeat his observations (which he can not), then the steps
would translate to probabilities for the general population as follows:
1 sd = 68.26 % of the general, colour-normal population
2 sd = 95.44 % “
3 sd = 99.44 % “
Any point on the boundary of a “1-step” ellipse, drawn around a target, represents 1
standard deviation from the target. Note that this also means that drawing a line through
the target from that point, thereby creating a point on the opposite boundary, the 2
boundary points will be 2 standard deviations from one another. Any point on the
boundary of a “2-step” ellipse represents 2 standard deviations from the target. For a “3step” ellipse, the boundary represents 3 standard deviations from the target, and so on.
ANSI recommends that lamp manufacturers stay within a “4-step” MacAdam ellipse.
This means that, given a certain target point on the CIE diagram, lamp manufacturers are
given a fairly wide range of perceptible differences. Consider that a point on the
boundary of a 4-step ellipse is 8 standard deviations from a point on the opposite side of
that same boundary.
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Figure 65 – MacAdam ellipses.
As it was said before, uv coordinates are going to be used to check the accuracy of the
calculated characteristics. A difference smaller of 0.005 between measured and
calculated light will indicate that the approximation is good enough (4-step ellipse). Light
characteristics can be calculated as the combination of two LEDs with the previous
formulas.
The following formulas carry out the coordinate’s transformation and the calculation of
the deviation ∆uv in colour point (u,v) from the reference (ur,vr).
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u=
Unclassified
4X
( X + 15Y + 3Z )
v=
6Y
( X + 15Y + 3Z )
Δuv = (u − ur ) 2 + (v − vr ) 2
In the next three tables can be seen the deviations between the measured light by the
spectrometer, the reference, and the expected light using formulas.
AMBER-RED LEDS
(measured)
Am
0,5
k
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
x 0,6960 0,6756 0,6603 0,6507 0,6450 0,6417 0,6359 0,6275 0,6154 0,5964 0,5672
y 0,3034 0,3238 0,339 0,3484 0,3542 0,3574 0,3632 0,3715 0,3837 0,4024 0,4314
Y 0,0134 0,0166 0,0199 0,0226 0,0248 0,0264 0,0247 0,0226 0,0201 0,0174 0,0146
Table 2 – Spectrometer measurements of the mixed light of amber-red LEDs.
AMBER-RED LEDS
(calculated)
Am
k
0,5
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
x
0,6961 0,6741 0,6575 0,6481 0,6428
0,6401
0,6341
0,6252
0,6147
0,5962
0,5672
y
0,3034 0,3252 0,3416 0,3509 0,3562
0,359
0,3648
0,3736
0,3842
0,4023
0,4314
Y
0,0134
0,028
0,0258
0,0231
0,0207
0,0177
0,0146
0,017
0,0209
0,024
0,0263
Table 4 – Calculated brightness and chromaticity coordinates of amber-red mixed light
using individual spectrometer measurements of each LED.
∆uv
0
0,0028 0,0049 0,0044 0,0036 0,0027 0,0028 0,0034 0,0009
6E-05
0
Table 5 – Deviation between measured and calculated characteristics of amber-red mixed
light.
At this point, the obtained error is the difference between how we think the mixed light
is, starting from the characteristics of two single LEDs, and how the spectrometer says it
is. This error is smaller than ANSI recommends in the whole range measured. However,
despite we have been working with the real characteristics of the LEDs, previously
measured with the spectrometer, the error is not null. This means that the method
employed introduces some kind of errors. This was also seen when the calibration
procedure was explained in a previous chapter. Here appears again the same problematic
when dealing with LEDs. Their characteristics have many sources of interferences that
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can vary the measurements. It is then necessary to be critical with these results and even
more with the ones we are going to obtain when interpolating.
Considering good results the ones obtained before, it is possible to assert that we can
know how the mixed light is going to be if the lights it comes from are known. The next
step will be to be able to know how these lights are, which the characteristics of the
LEDs are, and using the previous procedure to calculate the mixed light characteristics.
It is neither possible nor practical to measure every combination of LEDs. It is then
necessary to interpolate between pre-established values. The selected values for
interpolation are those for Am=0.1 and Am=0.5 of each LED. The variations of LED
characteristics are considered linear when varying Am. However, this is not true at all
and it is mandatory to use only the linear section to avoid later errors. That is why not the
whole Am range of work is used. The upper 0.5 limit is imposed by that used when
calibrating, while 0.1 is used because measurements at lower Am values cause wrong
spectrometer results related to the little light generated by the LED. This means that the
effective range of work of k is from 0.1 to 0.9, which corresponds to full red LED
(Amr=0.5) and 20% amber LED (Ama=0.1) and 20% red LED (Amr=0.1) and full amber
LED (Ama=0.5). Just to point, this limited range of Am to 0.5 is later extended to Am=1
so the maximum brightness of the LEDs is accessible. Talking here about Am is always
related to the calibration procedure and not to the normal working stage.
To check how the interpolation works, the mixed light is calculated for the same k values
used before. Results are shown in next table.
RED
LED
interpolated
Am
0,5
0,4
0,3
0,2
0,1
k
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
x 0,6961 0,6961 0,6961 0,6961 0,6961 0,6961 0,6957 0,6954 0,6950 0,6947
y 0,3034 0,3034 0,3034 0,3034 0,3034 0,3034 0,3035 0,3035 0,3036 0,3037
Y 0,0134 0,0134 0,0134 0,0134 0,0134 0,0134 0,0108 0,0082 0,0056 0,003
AMBER
0
1
0
0
0
LED
interpolated
Am
k
x
y
Y
0
0
0,1
0,1
0,2
0,2
0,3
0,3
0,4
0,4
0,6
0,5
0,7
0,5
0
0,5545
0,5577
0,5608
0,5640
0,5672
0,8
0,9
1
0,5672
0,5672
0,5672
0,5672
0,5672
0
0,4433
0'4403
0,4374
0,4344
0,4314
0,4314
0,4314
0,4314
0,4314
0,4314
0
0,0036
0,0064
0,0091
0,0119
0,0146
0,0146
0,0146
0,0146
0,0146
0,0146
Table 6 – Amber-red LED characteristics as a result of interpolation (blue) and
spectrometer measurements (black).
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AMBER-RED LEDS
(measured)
Am
0,5
k
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
x 0,6960 0,6756 0,6603 0,6507 0,6450 0,6417 0,6359 0,6275 0,6154 0,5964 0,5672
y 0,3034 0,3238 0,339 0,3484 0,3542 0,3574 0,3632 0,3715 0,3837 0,4024 0,4314
Y 0,0134 0,0166 0,0199 0,0226 0,0248 0,0264 0,0247 0,0226 0,0201 0,0174 0,0146
Table 2 – Spectrometer measurements of the mixed light of amber-red LEDs.
AMBER-RED LEDS
(calculated)
Am
k
0,5
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
x
0,6961 0,6741 0,6620 0,6527 0,6456
0,6401
0,6330
0,6241
0,6124
0,5962
0,5672
y
0,3034 0,3252 0,3371 0,3464 0,3535
0,359
0,3659
0,3747
0,3862
0,4023
0,4314
Y
0,0134 0,0170 0,0198 0,0225 0,0253
0,028
0,0254
0,0229
0,0203
0,0177
0,0146
Table 7 – Calculated brightness and chromaticity coordinates of amber-red mixed light
using individual interpolated characteristics of each LED.
∆uv
0
0,0028 0,0032 0,0035 0,0011 0,0027 0,0045 0,0051 0,0041
6E-05
0
Table 8 – Deviation between measured and calculated by interpolation characteristics of
amber-red mixed light.
Using interpolation, ∆uv is still smaller than the maximum recommended. The method
used gives good results and is useful to predict how the light characteristics we are
dealing with are. In spite of that, the error is uncontrolled and very dependant on the
calibration procedure. Improving this procedure it is supposed to be possible to improve
the ∆uv.
It is possible to reduce the number of effective LEDs from four to three with the
procedure presented in this chapter in order to be able to use the formulas presented in
the RGB colour control theory chapter.
Summarizing, from now on the calibration procedure to follow when RGBA colour
control is used will consist of firstly measuring the characteristics of the four LEDs at
Am equal to 0.5 and secondly measuring the characteristics of the red and amber LEDs at
Am equal to 0.1 in order to be able to interpolate later. When the system will be running,
a calibration module will calculate the third LED characteristics from the stored data of
red and amber LEDs according to the value of k and then the calibration matrices GCAL-1
and GC2S-1.
3.2.2. System model
As for the brightness control solution, the starting point for the implementation of the
RGBA control is the RGB colour control diagram in its amplitude modulation version.
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Figure 46 –AM RGB colour control. Simulink diagram.
Fig. 66 shows the modifications introduced into the Simulink model.
Figure 66 – AM RGBA colour control. Simulink diagram.
The new model has four main elements, a slider gain named “RA” which controls the
relation between the red and amber LEDs as it was seen in the theory chapter, a block
named “RA Limits” which establishes the range of proportionality available for the mix
of the LEDs, another block named “RA to R-A” which splits one AM control signal into
two AM signals, one for the red LED and another one for the amber LED according to
the RA value selected, and finally, one block which recalculates the matrices GCAL-1 and
GC2S-1.
The proportion in which the red and amber LEDs are mixed is limited. The minimum
relation between them is 100%-20% in both combinations, red-amber or amber-red. This
limit is used to avoid the problems that appear working at lower relations when
calculating the calibration matrices.
In this Simulink model, the colour control system calculates the calibration matrices
depending on which the relation between red and amber LEDs is. Remember that both
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LEDs will be dealt as a unique LED. It is supposed that the characteristics of a LED in
terms of luminous flux and chromaticity coordinates are linear in its whole range of
work. However, that is not real at all. In the limits of the work region, when the signal
that drives the LED is too small or close to one, these characteristics are not linear and
this results in a wrong estimation of the resultant LED and, consequently, and in a wrong
calculation of the calibration matrices.
The “RA Limits” block is presented in next figure. RA is limited between 0 and 1 and the
block allows any value between 0.1 and 0.9. If RA is smaller than 0.1, the output is fixed
to 0 and if it is bigger than 0.9 it is fixed to 1.
Figure 67 – ‘RA Limits’ block.
The “RA to R-A” block applies the relation presented in the theory chapter (note that k is
renamed in the Simulink model by RA).
0 ≤ k ≤1
k < 1 / 2 : r = ra
a = 2 ⋅ k ⋅ ra
k > 1 / 2 : a = ra r = 2 ⋅ (1 − k ) ⋅ ra
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Figure 68 – ‘RA to R-A’ block.
The calculation of the calibration matrices is now partially automated. The calibration
process described at the beginning of this report has been somewhat modified. Following
the new calibration recommendations suggested by the investigations described before,
tristimulus values of the four LEDs are measured at 50% of the LED maximum driving
signal. This allows reducing the non-linearity of the LEDs at their maximum power.
Sensor readings are also measured and extended to the work region (multiplied by two).
It is still necessary to measure the tristimulus values of the red and amber LEDs at 20%
of the previous driving signal. It is 10% of their maximum power. With these last
measurements and the ones at 50% of the red and amber LEDs is calculated, depending
on the RA value, a new pattern of tristimulus values that correspond to a ‘new’ redamber LED. Remember that it was mandatory to reduce the number of LEDs in order to
be able to use the expressions presented in the RGB control theory.
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Figure 69 – CIE 1931 Chromaticity diagram. LEDs reduction.
The automation of the process refers to the automatic interpolation between the
tristimulus values of the red and amber LEDs at 50% and 10% according to RA value
and the procurement of the ‘new’ LED and subsequent calculation of the matrices.
Previously it was made by hand. The next figures show what is inside the block. Its
functionality has already been explained. Here the formulas are implemented that
calculate each element of the GCAL-1 and GC2S-1 matrices.
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Figure 70 - GCALinv & GC2Sinv matrices calculation block and subsystems.
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Adding a fourth LED also enforces other changes in the Simulink model. The modelled
plant used in simulation now accounts for the contribution of the new LED.
Figure 71 – Plant model of the system used in simulation development mode.
3.2.3. System performance
The same point of work used testing the RGB colour control is now used.
x = 0.33 y = 0.33 Y = 0.08
RA is set to 0.3, what means a relation 1/0.6 between red and amber LEDs. As it can be
seen in the next figures, the final amplitudes of the driving signals have changed from
those we obtained previously, however their shape is similar.
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Figure 72 – RGBA colour control. Transient response I.
Figure 73 – RGBA colour control. Transient response II.
Fig. 74 shows how the driving signals change when RA is changed from 0, RGB colour
control, to 1, GBA colour control in steps of 0.1. It is interesting to see that the GBA
control is not stable at these rates and how the amber signal saturates. This occurs
because the requested brightness is not reachable. The amber LED has less brightness
than the red LED. This problem would be solved using the brightness control presented
in the previous chapter.
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Figure 74 – RGBA colour control. Simulated transient and steady state response for some
RA values.
Once the model is tested by simulation obtaining good results, it is transferred to the
dSPACE rapid control prototyping. The next figure is a capture of the driving signals in
the dSPACE environment.
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Figure 75 – RGBA colour control. AM transient response.
With RGBA control, it is interesting to test the improvement of the CRI, the major aim of
the modifications introduced in the Simulink model. It was said previously that the CRI
could be improved controlling the spectral power density of the light generated.
The next figures show the spectral power density before and after the addition of the
fourth LED. It is easy to observe that the gap between the green and red peeks is now
filled by the amber LED. Therefore, it is possible to assert that the CRI can be changed
and improved.
Figure 76 – Spectral power density of resultant light using RGB and RGBA colour
control.
Next figure shows a series of captures of the spectral power density for different values
of RA, starting with RA=1 and finishing with RA=0.1.
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Figure 77 – Spectral power density for some RA values.
The next table shows the colour points and brightness values obtained with a
spectrometer for the previous combinations of LEDs.
Table 9 – Brightness and chromaticity coordinates of RBGA mixed light.
uv coordinates give us a reference to confirm whether the colour point obtained is good
enough. As it was explained in a previous chapter of this report, the ∆UV error must be
lower than 0.005 if it is desired that the human eye does not observe any difference in the
colour of the light.
The worst obtained case from the table has an error of
Δ (u , v) < (0.008,0.003)
This error is bigger than it is desirable; however, it is quite close to an acceptable value.
This increasing of the error is probably caused by the calibration process, where red and
amber LEDs are measured at power levels too close to zero. As it was explained in the
calibration process, at these rates the characteristics of the LEDs are not as linear as they
were supposed to be.
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3.3.
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Systems integration
At this point, both modifications of the original RGB colour control, brightness control
and RGBA colour control are implemented together. These modifications are
independent from each other and only a few extra modifications are needed.
Fig. 78 shows the resultant Simulink model.
Figure 78 – Multiple primary LED lamp colour controller with inherent brightness
limitation.
The system performance follows the behaviour found previously. As example, Fig.79
shows the response of the system when a lower brightness is requested from the
maximum brightness reachable by the system for a colour point (x,y)=(0.33,0.33) and
RA=0.3 (red fully on and amber at 60% of its maximum brightness).
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Figure 79 – RGBA colour control. AM transient response for some RA values.
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Acknowledgements
This master thesis project is the culmination of many years of study and the last step
before obtaining my degree as electronic engineer. All over these years, many people
related to my studies have formed part of my life and most of them have contributed to
the way I grew up as person. I would like to thank all these people, friends and enemies,
because I could not have been what I am without them.
It was an amazing experience to live in Aachen for six months and to have had the
opportunity to have known about some of the traditions of the German culture. I love the
Aachen-Köln Carnival and how people enjoy this celebration. It was also incredible how
people filled the streets during the Football World Cup and how they supported all the
teams (not Holland). I can not forget Berlin, the Love Parade and the million people
dancing in the Victory Square. I was even allowed to stay for a week in the house of the
“Studentenverbindung k.St.V.Wiking im KV zu Aachen”, a German student association,
and later I was invited to assist to the ‘Diplomfeier’ of a member. I would like to thank
all the people I met in Germany for welcoming and helping me there.
I especially would like to thank everybody of the Solid State Lighting group at Philips
Research Laboratories in Aachen (Germany) and particularly to my supervisor Dr. Bernd
Ackermann for all his support.
I cannot forget to mention the ‘Tomato Group’ and their members, the Polish team
(Matheus, Michael I, II & III, Greg and Kasia), the Italian connection (Elena), the shortstory writer from India (Sammy), the Canadian moose eater (Sabrina), the new Spanish
from Germany (Marco) and the Spanish team (Dani, Roger, Bertran & Helena). Without
all you, this experience could not have been what it was. Really, thanks.
Finally, I want to thank my parents for all their support and patience during all these
years. For sure, they are the main reason why I am writing this.
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References
[1]
B. Ackermann, M.Saura, “Rapid control protoyping of a red, green and blue
LED-based white light source”, Philips Research Manuscript PR-R 25.735, 2005.
Master Thesis of M. Saura, Univ. Politecnica de Catalunya.
[2]
B.Ackermann, V.Schulz, C.Martiny, A.Hilgers, X.Zhu, “Control of LEDs”,
Conference Record of the 41st IEEE IAS Annual Meeting, Volume 5, 2608–
2615, 2006.
[3]
M. Dyble, N. Narendran,A. Bierman,T. Klein, “Impact of dimming white LEDs:
Chromaticity shifts due to different dimming methods”, Fifth International
Conference on Solid State Lighting, Proceedings of SPIE, vol. 5941, 291-299,
2005. Bellingham, WA: International Society of Optical Engineers.
[4]
N. Narendran, L. Deng, “Color Rendering Properties of LED Light Sources”,
Proceedings of the SPIE - The International Society for Optical Engineering,
vol.4776, 61-7, 2002.
[5]
N. Narendran, N. Maliyagoda, A. Bierman, R. Pysar, M. Overington,
“Characterizing white LEDs for general illumination applications”, Proceedings
of the SPIE - The International Society for Optical Engineering vol.3938, 240-8,
2000.
[6]
M.G. Craford, “LEDs a challenge for lighting,” in Light Sources 2004,
Proceedings of the 10th International Symposium on the Science and Technology
of Light Sources, Toulouse, 18-22 July 2004, G. Zissis, Ed. Bristol: Institute of
Physics Publishing, 2004, pp. 3–13.
[7]
E.F. Schubert, Light-Emitting Diodes, Cambridge: Cambridge University Press,
2003.
[8]
S. Muthu, F.J.P. Schuurmans, M.D. Pashley, “Red, green, and blue LEDs for
white light illumination,” IEEE Journal on Selected Topics in Quantum
Electronics, vol. 8, no. 2, March/April 2002, pp. 333-338.
[9]
S. Muthu, F.J.P. Schuurmans, M.D. Pashley, “Red, green, and blue LED based
white light generation: Issues and control,” Conference Record of the 2002 IEEE
Industry Applications Conference, 37th IAS Annual Meeting, Pittsburgh, PA,
USA, 13-18 Oct. 2002, vol. 1, 2002, pp. 327-333.
[10]
S. Muthu, J. Gaines, “Red, green, and blue LED-based white light source:
Implementation challenges and control design,” Conference Record of the 2003
IEEE Industry Applications Conference, 38th IAS Annual Meeting, Salt Lake
City, UT, USA, 12-16 Oct. 2003, vol. 1, 2003, pp. 515-522.
[11]
Power light source Luxeon emitter, Lumileds technical datasheet DS25,
www.lumileds.com.
[12]
http://www.mazet.de/produkte/jencolour/sensor-ic/mtcs/en
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[13]
www.dspace.com
[14]
www.mathworks.com
[15]
www.labsphere.com
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A List of figures
Figure 1
LEDs applications.
Figure 2
CIE 1931 Chromaticity Diagram. RGB White light generation.
Figure 3
Philips Pedestrian LED Luminary Gold IF product design award, Philips
LED architectural Floodlight IF design award 2006 & The Inner Ring
Road Bridge in Bangkok, Thailand, lit up with Philips LED lighting
systems.
Figure 4
Block diagram of a LED colour control system using a colour sensor.
Figure 5
Simplified block diagram of the LED colour control system.
Figure 6
Block diagram of the LED colour control system with the sensor readings
as control variable.
Figure 7
Block diagram representation of (2.26).
Figure 8
Block diagram of the decoupled LED colour control system.
Figure 9
Overall block diagram of the decoupled LED colour control system.
Figure 10
Colour mixing and control.
Figure 11
Research Group SSL at Philips Research Laboratories, Aachen, Germany.
Laboratory setup.
Figure 12
RGB colour control. System overview.
Figure 13
dSPACE rapid control prototyping system.
Figure 14
Block diagram of the LED colour control system.
Figure 15
Simulink model. PWM control scheme.
Figure 16
MAZeT true colour sensor: MTCSiCS.
Figure 17
AM driver. Power circuit.
Figure 18
AM driver. Signal conditioning.
Figure 19
AM driver board.
Figure 20
AM colour control subsystems.
Figure 21
Simulink model. AM control scheme.
Figure 22
Sensing. Conditioning circuit.
Figure 23
Sensing. Old sensor & conditioning circuit.
Figure 24
Sensing. New sensor & conditioning circuit.
Figure 25
Sensing. New sensor & conditioning circuit
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Figure 26
Sphere plus LEDs and sensor board.
Figure 27
AM calibration Simulink model.
Figure 28
PWM calibration Simulink model.
Figure 29
dSPACE PWM control desk .
Figure 30
Spectral lamp measurement system ver.5.1.5.0.
Figure 31
Effect of temperature variation on the spectral emission of a red 1W
Luxeon LED [11].
Figure 32
CIE 1931 Chromaticity Diagram. Selected point of work.
Figure 33
AM colour control. Simulated transient response.
Figure 34
AM colour control. Simulated transient response II.
Figure 35
AM colour control. Simulated transient response III.
Figure 36
AM colour control. Simulated transient response IV.
Figure 37
AM colour control. RTI1103 dSPACE model.
Figure 38
AM colour control. Transient response I.
Figure 39
AM colour control. Transient response II.
Figure 40
AM colour control. Detail of D/A characteristics of the response.
Figure 41
AM colour control. Spectral power density.
Figure 42
Eye sensitivity function.
Figure 43
Brightness control. xyY region of work.
Figure 44
Factor of increment.
Figure 45
Yset.
Figure 46
AM RGB colour control. Simulink diagram .
Figure 47
AM RGB colour control with brightness limitation. Simulink diagram
modifications.
Figure 48
Brightness control block.
Figure 49
Maximum brightness calculator.
Figure 50
Correction factor block.
Figure 51
Am selector block.
Figure 52
AM RGB colour control. Brightness control. Simulated transient response.
Figure 53
AM RGB colour control. Brightness control. Simulated transient response
II.
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Figure 54
AM RGB colour control. Brightness control. Simulated transient response
III.
Figure 55
AM RGB colour control. Set brightness.
Figure 56
AM RGB colour control. AM and brightness transient responses. ‘n’
modification.
Figure 57
AM RGB colour control. AM and brightness transient responses. ‘m’
modification.
Figure 58
AM RGB colour control. AM transient response I.
Figure 59
AM RGB colour control. AM transient response II.
Figure 60
AM RGB colour control. Transient response. Variation of n.
Figure 61
AM colour control. Transient response. Variation of m.
Figure 62
RGBA control. CRI improvement. Colour rendering for different light
sources.
Figure 63
RGBA board prototype.
Figure 64
Chromaticity coordinates of amber-red light.
Figure 65
MacAdam ellipses.
Figure 66
AM RGBA colour control. Simulink diagram.
Figure 67
‘RA Limits’ block.
Figure 68
‘RA to R-A’ block
Figure 69
CIE 1931 Chromaticity diagram. LEDs reduction.
Figure 70
GCALinv & GC2Sinv matrices calculation block and subsystems.
Figure 71
Plant model of the system used in simulation development mode.
Figure 72
RGBA colour control. Transient response I.
Figure 73
RGBA colour control. Transient response II.
Figure 74
RGBA colour control. Simulated transient and steady state response for
some RA values.
Figure 75
RGBA colour control. AM transient response.
Figure 76
Spectral power density of resultant light using RGB and RGBA colour
control.
Figure 77
Spectral power density for some RA values.
Figure 78
Multiple primary LED lamp colour controller with inherent brightness
limitation.
Figure 79
RGBA colour control. AM transient response for some RA values.
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B List of tables
Table 1
MTI04 gain.
Table 2
Spectrometer measurements of the mixed light of amber-red LEDs.
Table 3
Individual spectrometer measurements of amber LED and red LED lights.
Table 4
Calculated brightness and chromaticity coordinates of amber-red mixed
light using individual spectrometer measurements of each LED.
Table 5
Deviation between measured and calculated characteristics of amber-red
mixed light.
Table 6
Amber-red LED characteristics as a result of interpolation (blue) and
spectrometer measurements (black).
Table 7
Calculated brightness and chromaticity coordinates of amber-red mixed
light using individual interpolated characteristics of each LED.
Table 8
Deviation between measured and
characteristics of amber-red mixed light.
Table 9
Brightness and chromaticity coordinates of RBGA mixed light .
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calculated
by
interpolation
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