control design for electronic power converters...control design for electronic power converters 10 /...
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Control Design for Electronic Control Design for Electronic
Power ConvertersPower Converters
PhD Thesis
by Carolina Albea
Supervised by Carlos Canudas de Wit and Francisco Gordillo
Grenoble, 14 October 2010
Control Design for Electronic Power Converters 2 / 49
OUTLOOKOUTLOOK
INTRODUCTION
FIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DC-DC Vdd-HOPPING CONVERTER
CONCLUSIONS & FUTURE WORK
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
Control Design for Electronic Power Converters 3 / 49
OUTLOOKOUTLOOK
INTRODUCTION INTRODUCTION
FIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DC-DC Vdd-HOPPING CONVERTER
CONCLUSIONS & FUTURE WORK
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
Control Design for Electronic Power Converters 4 / 49
INTRODUCTIONINTRODUCTION
Why are power converters important?
Relevant issues in power converters:Reliability of the power converters highly robust to achieve a high useful life
High efficiency: economic and environmental value of wastedcost of dissipated energyimproved profitability of the investment in the electronic market
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
… thus, automatic control has an special relevance.
Control Design for Electronic Power Converters 5 / 49
INTRODUCTIONINTRODUCTION
Classification: DC-DC converters. DC-AC converters. Inverter.AC-DC converters. Rectifier.AC-AC converters. Transformer.
DC-AC coverter
All level power
normal scale
4th order
Control objective: limit cycle
Boost Inverter
DC-DC converter
Low power level
micro- or nano-scales
1st order
Control objective: equilibrium
Vdd-Hopping Converter
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
Control Design for Electronic Power Converters 6 / 49
OUTLOOKOUTLOOK
INTRODUCTION
FIRST APPLICATION: FIRST APPLICATION: BOOST INVERTERBOOST INVERTER
SECOND APPLICATION: DC-DC Vdd-HOPPING CONVERTER
CONCLUSIONS & FUTURE WORK
INTRODUCTION INTRODUCTION
FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
Control Design for Electronic Power Converters 7 / 49
Boost Inverter in a practical case:Boost Inverter in a practical case: generates an alternating current and is an elevator.
BOOST
INVERTER
PHOTOVOLTAIC
ARRAY
DC 48V
ELECTRICAL
GRID
AC 220Vrms 50Hz
AC 220Vrms 50Hz
[Antonkopoulus et al, T. Inter. Journal of Electronics 92, Castaner et al. Book 03]
INTRODUCTION INTRODUCTION
FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1.1. MOTIVACIMOTIVACIÓÓNN2. SYSTEM3. CONTROL OBJECTIVES:
1. CONTROL LAW2. ANTY-SYNCRONIZATION3. ADAPTIVE CONTROL4. ATTRACTION DOMAIN
Control Design for Electronic Power Converters 8 / 49
[Caceres et al, T. Power Electronics 99]
BOOST INVERTER: BOOST INVERTER:
INTRODUCTION INTRODUCTION
FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN
2.2. SYSTEMSYSTEM3. CONTROL OBJECTIVES:
1. CONTROL LAW2. ANTY-SYNCRONIZATION3. ADAPTIVE CONTROL4. ATTRACTION DOMAIN
DC AC
DC-DC BOOSTCONVERTER
1
DC-DC BOOSTCONVERTER
2
LOAD
V1
V2
Vin Vout
Control Design for Electronic Power Converters 9 / 49
1.1. Control laws for the duty cycles of each DC-DC boost converter
1.2. Anti-synchronized voltage signals
2. Parameter adaptation for unknown and/or slowly varying loads
3. Set of initial voltage and current values that guarantee the system convergence.
INTRODUCTION INTRODUCTION
FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM
3.3. CONTROL OBJECTIVES:CONTROL OBJECTIVES:1. CONTROL LAW2. ANTY-SYNCRONIZATION3. ADAPTIVE CONTROL4. ATTRACTION DOMAIN
DCs with a desired positive voltages.
1. MAIN CONTROL OBJECTIVE: Generate an AC with a desired voltage.
Control Design for Electronic Power Converters 10 / 49
Control law for the duty cycle Control law for the duty cycle PWMPWM
TOOL: Energy shaping approach for oscillation generation [Aracil et al. IECON02, Gordillo et al. IWESA04]
Autonomuos & stable behaviour!!!!
Energy functionDesired behaviour
INTRODUCTION INTRODUCTION
FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM
3.3. CONTROL OBJECTIVES:CONTROL OBJECTIVES:1.1. CONTROL LAWCONTROL LAW2. ANTY-SYNCRONIZATION3. ADAPTIVE CONTROL4. ATTRACTION DOMAIN
DC-DC BOOST
CONVERTER
1
PHASE
CONTROLLER
V
−V
t
V
−Vt
V
t
−Vt
V
−Vt LOAD
CONTROL
1
CONTROL
2
DC-DC BOOST
CONVERTER
2
x2
x4
x
ω
u1
u2
Vin
Vout
Control Design for Electronic Power Converters 11 / 49
Complete Complete boostboost inverterinverter
⎪⎪⎪⎪⎪
⎩
⎪⎪⎪⎪⎪
⎨
⎧
−+=
+−=
+−=
+−=
Rv
Rviu
dtdvC
Vvudt
diL
Rv
Rviu
dtdvC
Vvudt
diL
L
inL
L
inL
2122
22
222
2111
11
111
2
1
Model for one side
42112
211 1axaxxux
xux+−=
+−=&
&
]1,0[1 ∈uwith and CL
Ra
0
1=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
⎯⎯⎯⎯⎯⎯ →⎯
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡==
==
4
3
2
11
1
2
2
1
12
422
23
121
1
11
xxxx
iviv
inL
in
inL
in
Vvxi
CL
Vx
Vvxi
CL
Vx
L
L
[Caceres et Al, T. Power Electronics 99]
INTRODUCTION INTRODUCTION
FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM
3.3. CONTROL OBJECTIVES:CONTROL OBJECTIVES:1.1. CONTROL LAWCONTROL LAW2. ANTY-SYNCRONIZATION3. ADAPTIVE CONTROL4. ATTRACTION DOMAIN
Control Design for Electronic Power Converters 12 / 49
Control law from energy shaping approach [Albea et al. Control Engineering Practice 2010]
Open-loop system
)()( 2021012
2
0221
ζζζζωζ
ζζζ
−Γ−−−=
−=
k&
&
14212
2021012
4224
224
222
2
1 2)()(321
xaxxaxxkxaxxaxxaxau
−+−Γ+−+++−+
=ξξξξω&
32434
404223032
2422
242
224
2
2
14212
202111012
4224
224
222
2
1
2)()(321
2)()(321
xaxxaxxkxxaxaxxaxau
xaxxaxxkxxaxaxxaxau
−+−Γ+−+++−+
=
−+−Γ+−+++−+
=
ξξξξω
ξξξξω
&
&
)2(321
1421242
24
224
222
22
2021
xaxxaxxuxaxxaxxaxa
−+−++−+=
−=
&
&
&
ζ
ζζζ
Extension to the controller considering an inductive load [Albea et al. CDC07].
INTRODUCTION INTRODUCTION
FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM
3.3. CONTROL OBJECTIVES:CONTROL OBJECTIVES:1.1. CONTROL LAWCONTROL LAW2. ANTY-SYNCRONIZATION3. ADAPTIVE CONTROL4. ATTRACTION DOMAIN
Target system
Control Design for Electronic Power Converters 13 / 49
Simulations
INTRODUCTION INTRODUCTION
FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM
3.3. CONTROL OBJECTIVES:CONTROL OBJECTIVES:1.1. CONTROL LAWCONTROL LAW2. ANTY-SYNCRONIZATION3. ADAPTIVE CONTROL4. ATTRACTION DOMAIN
L1 = L2 = 250μH
C1 = C2 = 250μF
R = 100Ω, Vin = 48V
Vout = 220 2√2
sin(50 · 2πt)
V1 = 450 + 160 sin(50 · 2πt)
V2 = 450 − 160 sin(50 · 2πt)
Vin = 48V
fPWM = 50KHz, Ts = 0.1s
Control Design for Electronic Power Converters 14 / 49
Anti-synchronized voltage signals with a Phase Controller[Hsieh et al. Industrial Electronics 96, Albea et al. IECON06]
Aplication of PLL to the boost inverter
TOOL: Phase-locked loop PLL
INTRODUCTION INTRODUCTION
FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM
3.3. CONTROL OBJECTIVES:CONTROL OBJECTIVES:1. CONTROL LAW
2.2. ANTYANTY--SYNCRONIZATIONSYNCRONIZATION3. ADAPTIVE CONTROL4. ATTRACTION DOMAIN
DC-DC BOOST
CONVERTER
1
PHASE
CONTROLLER
V
−V
t
V
−Vt
V
t
−Vt
V
−Vt LOAD
CONTROL
1
CONTROL
2
DC-DC BOOST
CONVERTER
2
x2
x4
x
ω
u1
u2
Vin
Vout
Control Design for Electronic Power Converters 15 / 49
Simulations
THD=0.22%
INTRODUCTION INTRODUCTION
FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM
3.3. CONTROL OBJECTIVES:CONTROL OBJECTIVES:1. CONTROL LAW
2.2. ANTYANTY--SYNCRONIZATIONSYNCRONIZATION3. ADAPTIVE CONTROL4. ATTRACTION DOMAIN
Control Design for Electronic Power Converters 16 / 49
Synchronization with the electrical grid.
INTRODUCTION INTRODUCTION
FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM
3.3. CONTROL OBJECTIVES:CONTROL OBJECTIVES:1. CONTROL LAW
2.2. ANTYANTY--SYNCRONIZATIONSYNCRONIZATION3. ADAPTIVE CONTROL4. ATTRACTION DOMAIN
Control Design for Electronic Power Converters 17 / 49
)ˆ(ˆˆ 224212 xxKaxxauxx −++−=&
Parameter adaptation for unknown and/or slowly varying loads (a=f(R0))[Albea et al. Control Engineering Practice]
))(ˆ(ˆ 2422 xxxxa −−= γ&
TOOL: Approximate stability guaranteed by singular perturbation analysis.
TOOL: Adaptive control
INTRODUCTION INTRODUCTION
FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM
3.3. CONTROL OBJECTIVES:CONTROL OBJECTIVES:1. CONTROL LAW2. ANTY-SYNCRONIZATION
3.3. ADAPTIVE CONTROLADAPTIVE CONTROL4. ATTRACTION DOMAIN
DC-DC BOOST
CONVERTER
1
PHASE
CONTROLLER
V
−V
t
V
−Vt
V
t
−Vt
V
−Vt LOAD
CONTROL
1
CONTROL
2
DC-DC BOOST
CONVERTER
2
OBSERVER
ADAPTiVE
CONTROL
x2
x4
x
x
ω
u1
u2
x2a
Vin
Vout
Control Design for Electronic Power Converters 18 / 49
Stabilty: timetime--scalescale separationseparationslow variables: fast variables:
yxPBa
Byaxx
xaxUxfx
T )~(~
~~~)~,()(
γ
α
−=
−−=
−=
&
&
&
Complete system
xax ~,~
STABILITY ANALYSIS
INTRODUCTION INTRODUCTION
FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM
3.3. CONTROL OBJECTIVES:CONTROL OBJECTIVES:1. CONTROL LAW2. ANTY-SYNCRONIZATION
3.3. ADAPTIVE CONTROLADAPTIVE CONTROL4. ATTRACTION DOMAIN
Control Design for Electronic Power Converters 19 / 49
STABILITY PROOF: singular perturbation analysis [Khalil, Kokotovic]
0~~
)( =⎥⎦
⎤⎢⎣
⎡==
ax
xz φ
)())(,()( xfxxxUxfx =−= φ&
*2
*22
11
~~
~~~
~~
yxadd
yaxxdd
xxdd
=
−−=
−=
τ
τ
τ)
1.-Find a stationary solution of the fastfast subsystem.
2.-Substitute this solution in the slowslow subsytem
3.-Check the boundary layer properties of the fast subsystem along oneparticular solution by using TikhonovTikhonov´ss TheoremTheorem.
INTRODUCTION INTRODUCTION
FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM
3.3. CONTROL OBJECTIVES:CONTROL OBJECTIVES:1. CONTROL LAW2. ANTY-SYNCRONIZATION
3.3. ADAPTIVE CONTROLADAPTIVE CONTROL4. ATTRACTION DOMAIN
Control Design for Electronic Power Converters 20 / 49
90% errorTime (sec) Estimated value R (Ω) Real value R (Ω)
0 1000 100
0.5 100 1000
SIMULATIONS:
Extension to the adaptive control law considering an inductive load [Albea et al. IFAC08].
INTRODUCTION INTRODUCTION
FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM
3.3. CONTROL OBJECTIVES:CONTROL OBJECTIVES:1. CONTROL LAW2. ANTY-SYNCRONIZATION
3.3. ADAPTIVE CONTROLADAPTIVE CONTROL4. ATTRACTION DOMAIN
Control Design for Electronic Power Converters 21 / 49
Set of initial voltage and current values that guarantee the system convergence.
Local stabilitySaturationPhysical constraints vc1 >0, vc2>0
]1,0[∈u
TOOLS:Lyapunov Theory employedin polynomial systems.[Levin et al. Automatic Control94, Romanchuk Automatica96, Tibken et al. CDC02]
Sum of Squares (SOS) optimization.SDPs.SOSTOOLS.
INTRODUCTION INTRODUCTION
FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM
3.3. CONTROL OBJECTIVES:CONTROL OBJECTIVES:1. CONTROL LAW2. ANTY-SYNCRONIZATION3. ADAPTIVE CONTROL
4.4. ATTRACTION DOMAINATTRACTION DOMAIN
Attraction
Domain
ATTRACTIONDOMAIN
CONSTRAINT
DESIRED LIMITCYCLE
SATURATIONS
ESTIMATEDATTRACTION
DOMAIN
Control Design for Electronic Power Converters 22 / 49
Max cst
are SOS; i=1,…,Niii xgxpcxV ε−+− )()())((
Problem formulation:
By numerical inspection, it was found: x(0)=(0,-0.1,0.2,5.8)T
which corresponds to V(xV(x)=33,02.)=33,02.
[Albea at al., NOLCOS07]
26.23*)( == cxV
Result:
Semi-definite positive polynomial. Positive polynomial constraints.
INTRODUCTION INTRODUCTION
FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM
3.3. CONTROL OBJECTIVES:CONTROL OBJECTIVES:1. CONTROL LAW2. ANTY-SYNCRONIZATION3. ADAPTIVE CONTROL
4.4. ATTRACTION DOMAINATTRACTION DOMAIN
Control Design for Electronic Power Converters 23 / 49
OUTLOOKOUTLOOK
INTRODUCTION
FIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: SECOND APPLICATION: DCDC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTER
CONCLUSIONS & FUTURE WORK
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
Control Design for Electronic Power Converters 24 / 49
ARAVIS Project sponsored by ARAVIS Project sponsored by MinalogicMinalogic polepole
Current tecnology: 90nm, 65nm and, even, 45nm can not be applied any more to the technology of 32nm.
WHY???Technology variability
phenomenon
1.1. MOTIVACIMOTIVACIÓÓNN2. SYSTEM3. CONTROL OBJECTIVES4. PRELIMINARY CONTROL STUDY5. ENERGY AWARE CONTROL6. APPROXIMATE STABILITY ANALYSIS7. PARAMETER UNCERTAINTY AND DELAYS
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
Control Design for Electronic Power Converters 25 / 49
Three technology keys:Three technology keys:ReRe--configurable structure configurable structure w.r.tw.r.t. applicability requirements . applicability requirements [Pinheiro et al. COSLP01].
Dynamic management of the power consumption and activity Dynamic management of the power consumption and activity Asynchronous technique Asynchronous technique [Marculescu et al. ISCA02].
Cluster
Vdd - Hopping
ProgrammableRing
Energy Controller
Voltage Controller
QoSController
Speed1, No. of Instructions1, Deadlines1
Cluster
Energy Controller
Speed2, No. of Instructions2, Deadlines2
Processing Nodes Processing Nodes
f, Vddf, Vdd
Vdd - Hopping
ProgrammableRing
Voltage Controller
[Hellerstein et al. Book04, Cervin et al. RTS02, Ríos et al. PATMOS05].
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1.1. MOTIVACIMOTIVACIÓÓNN2. SYSTEM3. CONTROL OBJECTIVES4. PRELIMINARY CONTROL STUDY5. ENERGY AWARE CONTROL6. APPROXIMATE STABILITY ANALYSIS7. PARAMETER UNCERTAINTY AND DELAYS
Control Design for Electronic Power Converters 26 / 49
DCDC--DCDC VddVdd--Hopping Converter: Hopping Converter: [S. Miermot et al. LNCS07]
System control model
uRuR k =)(
⎪⎩
⎪⎨⎧
====
=∑=
n
i
ni
RRRR
Mu
L21
1
where
and
M1 R1
M2 R2
Mn−1 Rn−1
Mn Rn
Vh
IMPEDANCE
Z(vc)
vc
Il(vc)
CONTROL
uk
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
CONTROL
CLK
LPM
+
−
Vh Vl
SetofPMOS
vce
uk
vr
Objective: Good performance during transient periods.
1. MOTIVACIÓN
2.2. SYSTEMSYSTEM3. CONTROL OBJECTIVES4. PRELIMINARY CONTROL STUDY5. ENERGY AWARE CONTROL6. APPROXIMATE STABILITY ANALYSIS7. PARAMETER UNCERTAINTY AND DELAYS
Control Design for Electronic Power Converters 27 / 49
DCDC--DC converter circuitDC converter circuit
Error equation
cr vve −=where rhrkrk vVvbuvebue && ++−+++−= δββ )()(
Converter model – 1st order
δβ −−+−= kchcc uvVbvv )(&
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
⎪⎪⎩
⎪⎪⎨
⎧
>=
>=
01
01
0CRb
CRL
β 0>=C
Ileakδand depend on the load parameter.
depends on PMOS resistance and load parameter.
IleakC rL
Il
Icap Idyn + Ishort
IMPEDANCE
ImpedanceImpedance[PhD thesis 2008 S. Miermot]
1. MOTIVACIÓN
2.2. SYSTEMSYSTEM3. CONTROL OBJECTIVES4. PRELIMINARY CONTROL STUDY5. ENERGY AWARE CONTROL6. APPROXIMATE STABILITY ANALYSIS7. PARAMETER UNCERTAINTY AND DELAYS
Control Design for Electronic Power Converters 28 / 49
STABILITY OF THE STABILITY OF THE CLOSEDCLOSED--LOOP LOOP
SYSTEMSYSTEM
Vdd-Hopping
+PSS Two voltagesources
Objectives in VLSI:1. High energy-efficiency.2. Small current peaks.3. Fast transient periods.4. Robustness w.r.t. parameter uncertainty.5. Robustness w.r.t delays6. Simple implementation
CONTROL !!!!!
LDVSLocal Dynamic VoltageScaling Architecture
GALSGlobally Asynchronous
and Locally Synchronous Systems
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM
3.3. CONTROL OBJECTIVESCONTROL OBJECTIVES4. PRELIMINARY CONTROL STUDY5. ENERGY AWARE CONTROL6. APPROXIMATE STABILITY ANALYSIS7. PARAMETER UNCERTAINTY AND DELAYS
Control Design for Electronic Power Converters 29 / 49
Set of controllers using sameramp reference: [Albea et al., IECON08]
Controller 1: linear controller.Controller 2: feedback linearization.Controller 3: Lyapunov-based design.
Disipated total energy (μJ)Intuitive control 7.2
Control No.1. 6.8
Control No.2. 6.2
Control No.3. 4.8
Lyapunov controller
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM3. CONTROL OBJECTIVES
4.4. PRELIMINARY CONTROL STUDYPRELIMINARY CONTROL STUDY5. ENERGY AWARE CONTROL6. APPROXIMATE STABILITY ANALYSIS7. PARAMETER UNCERTAINTY AND DELAYS
)(1 esignuu kk += −
An intuitive control law with a ramp reference: [S. Miermot et al. LNCS07]
Switching limitation!!!
No switching limitation!!!From comparison Better voltage and current performance with developed
controllers.
Control Design for Electronic Power Converters 30 / 49
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−+
+−+= −
)(
ˆ*
***
11
k
kkk
rkhs
srrrsNk veVbT
TvvvTroundsatu
δβ
High-performance Lyapunov controller:
TOOL: Lyapunov TOOL: Lyapunov theory. theory. .
TOOL: Optimal control TOOL: Optimal control for minimizing current peaks and dissipated energy.
krskk evT 11~~ γββ −= −
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
ukOPTIMALREFERENCE
CONTROL
ADAPTIVECONTROL
v∗ vc
β
+
-SYSTEM
1. MOTIVACIÓN2. SYSTEM3. CONTROL OBJECTIVES
4.4. PRELIMINARY CONTROL STUDYPRELIMINARY CONTROL STUDY5. ENERGY AWARE CONTROL6. APPROXIMATE STABILITY ANALYSIS7. PARAMETER UNCERTAINTY AND DELAYS
Control Design for Electronic Power Converters 31 / 49
INTUITIVE CONTROL LAW [S. Miermot et al. LNCS07]
)(1 esignuu kk += −
HIGH-PERFORMANCE LYAPUNOV CONTROLLER
Advantages:Dissipated energy 0.5μJ (93% energy saving w.r.t. intuitive controller.).Minimum current peaks.Fast transient periods.
Disadvantages:Complex implementationComplex implementation
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM3. CONTROL OBJECTIVES
4.4. PRELIMINARY CONTROL STUDYPRELIMINARY CONTROL STUDY5. ENERGY AWARE CONTROL6. APPROXIMATE STABILITY ANALYSIS7. PARAMETER UNCERTAINTY AND DELAYS
Control Design for Electronic Power Converters 32 / 49
( )σ211 KeKroundsatu Nk +=
From Controller No.1: linear controller with a step reference:
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
Design of Energy Design of Energy EwareEware controller.controller.
Lemma 1: Consider the interval
If ξ is chosen in I, then the following inequalities are satisfiedand
Notice that
01 >K
⎥⎥⎦
⎤
⎢⎢⎣
⎡
++
++=
)(22,
2 βω
ωβ
ωβ
h
ll
k
n
n
k
n
k
bububu
I
0)(2>
+ βω
hk
n
bu
0)( 21 <−+ KbuKhk β
)(
)()(2
2
2
1
lh
n
lh
kn
VVbK
VVbbu
K l
−=
−
+−=
ω
βξω
02 >KNotice that
1. MOTIVACIÓN2. SYSTEM3. CONTROL OBJECTIVES4. PRELIMINARY CONTROL STUDY
5.5. ENERGY AWARE CONTROLENERGY AWARE CONTROL6. APPROXIMATE STABILITY ANALYSIS7. PARAMETER UNCERTAINTY AND DELAYS
Control Design for Electronic Power Converters 33 / 49
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x 10−6
0
5
10
15
20
25a)
NT
rans
t(s)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x 10−6
0.8
0.9
1
1.1
1.2b)
V(V
)
t(s)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x 10−6
0
0.1
0.2
c)
I(A
)
t(s)
WITH STEP REFERENCE SIGNAL
( )σ211 KeKroundsatu Nk +=
BEWARE!!!!!
This current peak can
damage the physical system
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM3. CONTROL OBJECTIVES4. PRELIMINARY CONTROL STUDY
5.5. ENERGY AWARE CONTROLENERGY AWARE CONTROL6. APPROXIMATE STABILITY ANALYSIS7. PARAMETER UNCERTAINTY AND DELAYS
Control Design for Electronic Power Converters 34 / 49
CONTROL WITH CURRENT PEAK CONSTRAINTS[Albea et al. CCA09]
( )σαα 211
1
1KeKsatroundsatu
Mkkmkk
uu
Nk += +
+−
−
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x 10−6
0
5
10
15
20
25a)
NT
rans
t(s)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x 10−6
0.8
0.9
1
1.1
1.2b)
V(V
)
t(s)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x 10−6
0
0.05
0.1
0.15
c)
I(A
)
t(s)
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM3. CONTROL OBJECTIVES4. PRELIMINARY CONTROL STUDY
5.5. ENERGY AWARE CONTROLENERGY AWARE CONTROL6. APPROXIMATE STABILITY ANALYSIS7. PARAMETER UNCERTAINTY AND DELAYS
max0 II Δ≤Δ< max0
max IuR
vVI k
chigh Δ≤Δ−
≤Δ−
Maximum current peaks constraint:
considering vc is continuous
Control Design for Electronic Power Converters 35 / 49
( )σαα 211
1
1KeKsatroundsatu
Mkkmkk
uu
Nk += +
+−
−
( ) kkkkN
k eKeeKsatroundusatuMkmk
21111 )( +−+= −−αα
DISCRETIZATION OF CONTROL WITH CURRENT PEAK CONSTRAINTS
⎪⎩
⎪⎨⎧
=
−=
TKK
KKK
22
211 2
4. Rounding
mechanism
ek
Vref
Vc
Δumk
ΔuMk
satN1
q−1us
k−1
usk
ΔuskΔuk
ΔI
ADC
ADC
ek−1
K1
K2
Vrk
Vck
q−1
3. On-line
saturation
mechanisms
2. On-line
current limits
mechanism
1. Error Tracking Filter
Δusk
usk
5.Output saturation
mechanism
Control patent pending under the name:ENergyENergy--AwaReAwaRe ControlControl(ENARC)
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM3. CONTROL OBJECTIVES4. PRELIMINARY CONTROL STUDY
5.5. ENERGY AWARE CONTROLENERGY AWARE CONTROL6. APPROXIMATE STABILITY ANALYSIS7. PARAMETER UNCERTAINTY AND DELAYS
Control Design for Electronic Power Converters 36 / 49
INTUITIVE CONTROL LAW [S. Miermot et al. LNCS07]
)(1 esignuu kk += −
ENARC
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
TOTAL ENERGY DISSPATEDIntuitive controller 7.2 μJ
ENARC 0.3 μJ
Advantages:96% energy saving .Easy implementation.Small current peaks.Fast transient periods.
1. MOTIVACIÓN2. SYSTEM3. CONTROL OBJECTIVES4. PRELIMINARY CONTROL STUDY
5.5. ENERGY AWARE CONTROLENERGY AWARE CONTROL6. APPROXIMATE STABILITY ANALYSIS7. PARAMETER UNCERTAINTY AND DELAYS
Control Design for Electronic Power Converters 37 / 49
[Albea et al., CCA09]
2K1KTheorem 1: System with the
controller is globally asymptotically stable, if and are positives.
δββ +−+++−= )()( hrkrk Vvbuvebue&σ21 KeKuk +=
2
22
2)(
)(2K
vVbeV
rh
σσ −+
−=
Proof: Lyapunov function candidate:
P2
e
σ
Ω1
1ΩThe stability is established by LaSalle’s invariant principle, since the
maximum invariant set in with corresponds to the single point . Therefore, every solution starting in approaches as
0),( =σeV&),0(2 σσ === eP 1Ω
.∞→t 2P
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM3. CONTROL OBJECTIVES4. PRELIMINARY CONTROL STUDY5. ENERGY AWARE CONTROL
6.6. APPROXIMATE STABILITY ANALYSISAPPROXIMATE STABILITY ANALYSIS7. PARAMETER UNCERTAINTY AND DELAYS
Control Design for Electronic Power Converters 38 / 49
2K1K
2
max0
2
max0
2
σσ
σKsatu
IvV
RK
IvV
RKkch
ch
Δ−
+
Δ−
−=
Theorem 2: System with the controller globally asymptotically stable, if and are positives.
δββ +−+++−= )()( hrkrk Vvbuvebue& σα
α 211
1KeKsatu
Mkkmkk
uuk += +
+−
−
Remark: The equilibrium of the system are in Region I.
Region II
Region III
Region I
e
σ
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM3. CONTROL OBJECTIVES4. PRELIMINARY CONTROL STUDY5. ENERGY AWARE CONTROL
6.6. APPROXIMATE STABILITY ANALYSISAPPROXIMATE STABILITY ANALYSIS7. PARAMETER UNCERTAINTY AND DELAYS
2Ω
By La Salle’s invariance principle, we can conclude the statement of the Theorem, since there exists a set limited by the level curve for sufficiently large and the saturation limits, which is compact and positively invariant.
2Ω 1),( ceV =σ&
1c
Control Design for Electronic Power Converters 39 / 49
CONTROL
Vdd-HOPPING
vr e uk
vc
+
-
R0
LOAD
RL, C
K1 K2z−2 z−1
Load dynamic resistance (RL(t)) from 55.53Ω to 72.46Ω
Load capacitance from 1nF to 1pF
PMOS characteristic from 25Ω to 38Ω
System frequency from 125MHz to 600MHZ
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
Parameter uncertaintyParameter uncertainty
DelayDelay
1. MOTIVACIÓN2. SYSTEM3. CONTROL OBJECTIVES4. PRELIMINARY CONTROL STUDY5. ENERGY AWARE CONTROL6. APPROXIMATE STABILITY ANALYSIS
7.7. PARAMETER UNCERTAINTY AND DELAYSPARAMETER UNCERTAINTY AND DELAYS
Synchronization issuesSynchronization issuesTradeTrade--off between off between energy consumption energy consumption and performanceand performance
TWO PROBLEMS:TWO PROBLEMS:
Control Design for Electronic Power Converters 40 / 49
,
1
kk
hkhk
kk
wwhkkk
xKxuxLz
wBBuAxx
φ===
++=
−−
−+
]0,[ hk −∈∀
SUBOPTIMAL CONSTANT TUNING: KSUBOPTIMAL CONSTANT TUNING: K11, K, K22
The considered model is: delay
perturbations L2, i.e., energy bounded
uncertain matrices
PROBLEMS FOR THIS DELAYPROBLEMS FOR THIS DELAY--TIME SYSTEM:TIME SYSTEM:
1.-Asymptotically stability.
2.-Perturbation rejection.
3.-Robustness w.r.t. parameter uncertainty.
TOOL: HTOOL: H∞∞ control theory applied control theory applied to timeto time-- delay systems.delay systems. To develop of LMIs through Lyapunov-Krasovskiimethod.
` [Cao et al. Circuit and Systems 02, Fridman et al European Journal of Control 05, Moon et al. International Journal of Control 01]
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM3. CONTROL OBJECTIVES4. PRELIMINARY CONTROL STUDY5. ENERGY AWARE CONTROL6. APPROXIMATE STABILITY ANALYSIS
7.7. PARAMETER UNCERTAINTY AND DELAYSPARAMETER UNCERTAINTY AND DELAYS
kkkkN
k eKeeKusatu 21111 )( +−+= −−
Control Design for Electronic Power Converters 41 / 49
KK11, K, K22
Asymptotic stability & disturbance rejection.
System robustness w.r.t.:
• delays
• parameter uncertainty
.2,1,,...,1
0)21(
,0)2(
00
2
1)(
1)(2
2
)()()(11
)()()()(2
)(1
)(
==
≥⎥⎦
⎤⎢⎣
⎡+−∗
≥⎥⎦
⎤⎢⎣
⎡−∗
<
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
−∗∗∗
−−∗∗
−−+−∗+−−ΓΓ
=Γ
−
−
iNjPu
YcPNuN
Yc
Q
ShR
QBYDBTDBRhQPQBSYDBTDB
ii
jji
j
jji
jjj
j i
i
γ
ω
ω
T
i
TT
i
T
i
TT
jTjTjj
TjjTi
jji
Tjjj
BDYBTQAQP
LLYDBBDYTDBBDTQQAAQ)()(
1)(
11)(
2
)()()()(11
)()(1
)(1
2
2−
−−
++−+=Γ
+++++−+=Γ
where
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM3. CONTROL OBJECTIVES4. PRELIMINARY CONTROL STUDY5. ENERGY AWARE CONTROL6. APPROXIMATE STABILITY ANALYSIS
7.7. PARAMETER UNCERTAINTY AND DELAYSPARAMETER UNCERTAINTY AND DELAYS
Control Design for Electronic Power Converters 42 / 49
0.8R0 1.2R0
0 0.2 0.4 0.6 0.8 1
x 10−6
01020
a)
NT
rans
t(s)
0 0.2 0.4 0.6 0.8 1
x 10−6
0.81
1.2b)
V(V
)
t(s)
0 0.2 0.4 0.6 0.8 1
x 10−6
00.02
d)
I(A
)
t(s)
0 0.2 0.4 0.6 0.8 1
x 10−6
01020
a)
NT
rans
t(s)
0 0.2 0.4 0.6 0.8 1
x 10−6
0.81
1.2b)
V(V
)
t(s)
0 0.2 0.4 0.6 0.8 1
x 10−6
00.02
d)I(
A)
t(s)
Delay & time-varying load RL
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM3. CONTROL OBJECTIVES4. PRELIMINARY CONTROL STUDY5. ENERGY AWARE CONTROL6. APPROXIMATE STABILITY ANALYSIS
7.7. PARAMETER UNCERTAINTY AND DELAYSPARAMETER UNCERTAINTY AND DELAYS
Control Design for Electronic Power Converters 43 / 49
400MHz 200MHz
0 0.2 0.4 0.6 0.8 1
x 10−6
01020
a)
NT
rans
t(s)
0 0.2 0.4 0.6 0.8 1
x 10−6
0.81
1.2b)
V(V
)
t(s)
0 0.2 0.4 0.6 0.8 1
x 10−6
0
0.05
d)
I(A
)
t(s)
0 0.2 0.4 0.6 0.8 1
x 10−6
01020
a)
NT
rans
t(s)
0 0.2 0.4 0.6 0.8 1
x 10−6
0.81
1.2b)
V(V
)
t(s)
0 0.2 0.4 0.6 0.8 1
x 10−6
00.02
d)I(
A)
t(s)
Delay & time-varying load RL
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM3. CONTROL OBJECTIVES4. PRELIMINARY CONTROL STUDY5. ENERGY AWARE CONTROL6. APPROXIMATE STABILITY ANALYSIS
7.7. PARAMETER UNCERTAINTY AND DELAYSPARAMETER UNCERTAINTY AND DELAYS
Control Design for Electronic Power Converters 44 / 49
1pF initial K1 & K2 1pF suboptimal K1 & K2
0 0.2 0.4 0.6 0.8 1
x 10−6
01020
a)
NT
rans
t(s)
0 0.2 0.4 0.6 0.8 1
x 10−6
0.81
1.2b)
V(V
)
t(s)
0 0.2 0.4 0.6 0.8 1
x 10−6
00.02
d)
I(A
)
t(s)
0 0.2 0.4 0.6 0.8 1
x 10−6
01020
a)
NT
rans
t(s)
0 0.2 0.4 0.6 0.8 1
x 10−6
0.81
1.2b)
V(V
)t(s)
0 0.2 0.4 0.6 0.8 1
x 10−6
00.02
d)I(
A)
t(s)
Delay & time-varying load RL
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTERCONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
1. MOTIVACIÓN2. SYSTEM3. CONTROL OBJECTIVES4. PRELIMINARY CONTROL STUDY5. ENERGY AWARE CONTROL6. APPROXIMATE STABILITY ANALYSIS
7.7. PARAMETER UNCERTAINTY AND DELAYSPARAMETER UNCERTAINTY AND DELAYS
Control Design for Electronic Power Converters 45 / 49
OUTLOOKOUTLOOK
INTRODUCTION
FIRST APPLICATION: BOOST INVERTER
SECOND APPLICATION: DC-DC Vdd-HOPPING CONVERTER
CONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTER
CONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
Control Design for Electronic Power Converters 46 / 49
CONCLUSIONSCONCLUSIONS
Vdd-Hopping converter:
Dissipated energy is reduced
Current peaks are limited
Fast transient periods
Simple implementation
Robustness w.r.t. delay
Robustness w.r.t. uncertain parameters
Approximate system stability
Boost inverter:
To get desired behavior by:
a two nonlinear controllers.
anti-synchronizing both voltage signals.
Autonomous and stable system.
Adaptation for unknown and/or slowly varying loads
Set of initial voltage and current values that guarantee the system convergence.
Automatic control contributes to the:
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTER
CONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
Control Design for Electronic Power Converters 47 / 49
FUTURE WORK & OPEN LINESFUTURE WORK & OPEN LINES
Boost inverter:
Physical implementation.
Adaptive control extension considering not all states are measured.
Global stability analysis to the system with the adaptive controller for a infinite time interval.
Less conservative solution for estimating the attraction region.
Extension of the estimated attraction region considering the phase controller and the adaptive mechanism.
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTER
CONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
Boost inverter Microcontroller eZdsp F2812
Voltage conversions
Control Design for Electronic Power Converters 48 / 49
FUTURE WORK & OPEN LINESFUTURE WORK & OPEN LINES
Vdd-Hopping converter:
Implementation in VHDL-AMS.
A better numerical solution for obtaining an optimal voltage reference for the Lyapunov controller
Extension of the stability analysis of the closed-loop system in discrete-time
Extension of the suboptimal tuning approach for the control gains considering the saturations.
INTRODUCTION INTRODUCTION FIRST APPLICATION: BOOST INVERTERFIRST APPLICATION: BOOST INVERTERSECOND APPLICATION: DCSECOND APPLICATION: DC--DC DC VddVdd--HOPPING CONVERTERHOPPING CONVERTER
CONCLUSIONS & FUTURE WORKCONCLUSIONS & FUTURE WORK
Control Design for Electronic Power Converters 49 / 49
PUBLICATIONS & PUBLICATIONS & RESEARCH ACTIVITIESRESEARCH ACTIVITIES
4 publications in international journals, 1 accepted in « Control Engineering Practice »1 submitted to « Control System technology »2 under preparations to « Circuit and Systems »
8 publications in international conferences,
4 publications in national conferences,
1 French national patent.
Control Design for Electronic Power Converters 50 / 49
Thank you, gracias, merci.Thank you, gracias, merci.
Questions and comments?Questions and comments?