Title Personal lighting control with occupancy and daylight adaptation Marco Rossi1 2 English 1.4 MB 68
```                            Table of contents
List of figures
1 Introduction
1.1 Philips' lighting commercial products
1.2 Buildings and lighting systems nowadays
1.3 Lux: illuminance unit of measure
1.4 Contribution
1.5 Lighting control systems' state of art
1.6 Thesis structure
2 System model
2.1 Analytical model
3 Control algorithms
3.1 Reference set-points at light sensors
3.2 Reference stand-alone controller
3.2.1 Generalized stand-alone controller
3.2.2 Stand-alone controller parameters
3.3 MIMO lighting control algorithm
3.3.1 Lighting control algorithm using unconstrained optimization
3.3.2 Lighting control algorithm using constrained optimization
4 Numerical results
4.1 Office lighting model and parameter description
4.2 Unconstrained optimization behaviour
4.2.1 All-occupied scenario
4.2.2 One-occupied scenario
4.2.3 Explanation and energy savings
4.3 Sensor-driven lighting control
4.3.1 Overshoot/undershoot and settling time
4.3.2 Achieved illuminance and energy savings
4.3.3 All zones occupied
4.3.4 One zone occupied
4.4 Sensor-driven personal lighting control
5 Conclusions and future works
References
Appendix A TrueTime Toolbox
A.1 Wired network description and parameters
```
##### Document Text Contents
Page 1

Personallightingcontrolwith
MarcoRossi
1
;
2
1
PhilipsResearch,HighTechCampus,Eindhoven,TheNetherlands
2
MasterDegreeinAutomationEngineering
Supervisors
:
AngeloCenedese
1
,AshishPandharipande
2

Page 2

Page 34

22
Controlalgorithms
Substitutingthemodel
y
(
k
+
1
)=
G
u
(
k
)+
d
(
k
+
1
)
in(
3.15
)andsolvingthenorm,
thecostfunctioncanberewrittenasfollows:
f
(
u
(
k
))=

l
u
(
k
)
T
G
T
G
u
(
k
)+
2
l
u
(
k
)
T
G
T
(
d
(
k
+
1
)

r
)+(
1

l
)(
u
(
k
)
T
1
)
2
+(

)

;
(3.17)
where
1
=[
1
:::
1
]
T
and
(

)
indicatestermsthatdonotdependon
u
(
k
)
.Thelastterm
in(
3.17
)canalsobewrittenas:
(
1

l
)(
u
(
k
)
T
1
)
2
=(
1

l
)(
u
(
k
)
T
1
)(
1
T
u
(
k
))=(
1

l
)
u
(
k
)
T
(
11
T
)
u
(
k
)
;
since
u
(
k
)
T
1
isascalarterm,sothatthecostfunction(
3.15
)becomes:
f
(
u
(
k
))=

l
u
(
k
)
T
G
T
G
u
(
k
)+
2
l
u
(
k
)
T
G
T
(
d
(
k
+
1
)

r
)+(
1

l
)
u
(
k
)
T
(
11
T
)
u
(
k
)

:
(3.18)
Takingthederivativeof(
3.18
)withrespecttovector
u
(
k
)
andequatingittozeroit
yields:
l
G
T
G
u
(
k
)+
l
G
T
(
d
(
k
+
1
)

r
)+(
1

l
)(
11
T
)
u
(
k
)=
0
;
(3.19)
andsolvingnowtheequationin
u
(
k
)
,itispossibletoobtainthefollowingoptimum
dimmingvector:
u
?
(
k
)=(
G
T
G
+
1

l
l
11
T
)

1
G
T
(
r

d
(
k
+
1
))
:
(3.20)
Generallyitisnotpossibletoassumethatthedaylighttermin(
3.20
)isexplicitly
known.Howeverundertheassumptionthatdaylightchangesslowly,similarlyto
Section(
3.2.2
),wecanestimatethedaylightvaluefromthepreviousiteration:
d
(
k
+
1
)
ˇ
d
(
k
)=
y
(
k
)

G
u
(
k

1
)
:
(3.21)
Thensubstituting(
3.21
)in(
3.20
)thiscontrollawisobtained:
u
?
(
k
)=(
G
T
G
+
1

l
l
11
T
)

1
G
T
(
e
(
k
)+
G
u
(
k

1
))
:
(3.22)
Where
e
(
k
)=
r

y
(
k
)
isthevectoroferrorsatthetimeinstant
k
.

Page 35

3.3MIMOlightingcontrolalgorithm
23
Inderivingthiscontrollaw,thephysicallimitsoftheluminairedimminglevels
werenotaccountedfor.Tomakesurethatthecontrolleroutputislimitedbetween0
and1asaturationfunctionisappliedtothesolution(
3.22
),asshownin(
3.7
).
3.3.2Lightingcontrolalgorithmusingconstrainedoptimization
constraintsonlightsensorsvaluesanddimminglevelsexplicitly.Thenconsiderthe
optimizationproblemin(
3.16
(
y
(
k
+
1
)=
G
u
(
k
)+
d
(
k
+
1
)

r
;
0

u
(
k
)

1
;
(3.23)
wheretheaboveinequalitiesholdcomponent-wise,
0
and
1
arevectorswitheach
component0and1respectively.Theoptimumdimmingvector
u
?
(
k
)
isthusobtained
bysolvingthefollowingoptimizationproblematiteration
k
:
u
?
(
k
)=
argmin
u
(
k
)

l
jj
G
u
(
k
)+
d
(
k
+
1
)

r
jj
2
2
+(
1

l
)
jj
u
(
k
)
jj
2
1

;
(3.24)
(
y
(
k
+
1
)=
G
u
(
k
)+
d
(
k
+
1
)

r
;
0

u
(
k
)

1
;
(3.25)
Notethattheaboveoptimizationproblemalwayshasafeasiblesolutionforthe
ﬁsensor-drivenlightingcontrol"scenario,giventhat
d
(
k
)

0
and
G
1

r
holdsdue
tothecalibrationstep.Notealsothattheilluminationerroriscapturedinboththe
termofthecostfunctionaswellasintheconstraint.Thisensuresthatthe
attainedlightsensorvaluesattheoptimumsolutionwillbeclosetotheset-points,as
opposedtoanoptimizingsolutionwherethistermisnottakenintoaccountinthecost
function(
l
=
0case).
Again,intheoptimizationframework,thedaylighttermin(
3.24
)andin(
3.25
)
isnotexplicitlyknown.However,undertheassumptionthatthedaylightchanges
slowly,thistermmaybeestimatedagainusing(
3.21
).
Notethatthecostfunctionin(
3.24