SystemC-AMS modeling of an Electromechanical Harvester of
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university-logo Introduction & Goals Modeling the Conditioning Circuit and Resonator Results & Verification Conclusion SystemC-AMS modeling of an Electromechanical Harvester of Vibration Energy Ken CALUWAERTS 1 Dimitri GALAYKO 1 Philippe BASSET 2 1 LIP6, University of Paris-VI, France 2 University Paris-East, ESYCOM, France Behavioural Modeling And Simulation Conference, 2008 Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
Transcript of SystemC-AMS modeling of an Electromechanical Harvester of
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
SystemC-AMS modelingof an Electromechanical Harvester
of Vibration Energy
Ken CALUWAERTS1
Dimitri GALAYKO1
Philippe BASSET2
1LIP6, University of Paris-VI, France2University Paris-East, ESYCOM, France
Behavioural Modeling And Simulation Conference, 2008
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
Outline
1 Introduction & GoalsElectromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
2 Modeling the Conditioning Circuit and ResonatorTDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuitmodels
3 Results & VerificationGeneral resultsComparison with VHDL-AMS and MATLAB SimulinkFurther work
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
Electromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
1 Introduction & GoalsElectromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
2 Modeling the Conditioning Circuit and ResonatorTDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuitmodels
3 Results & VerificationGeneral resultsComparison with VHDL-AMS and MATLAB SimulinkFurther work
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
Electromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
Overview of the Harvester
Converts mechanicalenergy into electricalenergy to drive the load.
Heterogeneous: amechanical resonatorand a complex electricalconditioning ciruit
Power source forwireless sensornetworks
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
Electromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
Summary of circuit operation
When the switch is off: the charge pump transfers the chargesfrom the large Cres to the small Cstore.
When the switch is on: the flyback circuit transfers the harvestedenergy to the inductor and then to Cres.
The operating principle of the flyback: a Buck DC-DC converter
Strongly discontinuous behaviour due to the switchingKen Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
Electromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
Modeling challenges
1 Highly non-linear (exponential diodes) and switchingsystem
2 Processes with very different time constants: theflyback is ±300 times "quicker" than the chargepump,but happening only <0.1% of the time.
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
Electromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
1 Introduction & GoalsElectromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
2 Modeling the Conditioning Circuit and ResonatorTDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuitmodels
3 Results & VerificationGeneral resultsComparison with VHDL-AMS and MATLAB SimulinkFurther work
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
Electromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
Generalities
1 Extension of SystemC2 Environment for modeling analog and mixed systems3 Two operating modes: TDF (non-conservative) and
Linear Electrical Network (LinElec, conservative)4 The data rate (modeling time step) is constant for a
given block throughout the whole simulation.
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
Electromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
Non-conservative TDF modeling in SystemC-AMS
1 It is possible to implement Simulink-like FlowDiagrams.
2 A scheduler: each block is called at each time step.3 Particularity: absence of a non-linear solver.4 The time step of the blocks is a multiple of the "global"
system time step.
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
Electromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
Non-conservative TDF modeling: example
f (x, y)
xi
yiyi−1
f (x , y): algebraic functionx : a known input
The output evolution law:yi = f (xi , yi−1)
1 Example of an algebraic(memoryless) system withfeedback
2 A delay is necessary.3 If x changes slowly, the output
is correct.
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
Electromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
Linear Network modeling (LinElec)
1 Goal: modeling of linear electrical networks2 Allowed components: resistors, capacitors, inductors
and voltage/current sources3 At initialization, a network matrix is calculated and
inverted, then the network response is calculated inthe time domain.
4 Connections to and from TDF blocks are possible.
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
Electromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
Linear Network modeling: connection with the TDFdomain
ddt
∫Voltage
LinElec TDF1 A value calculated by the LinElec
solver can be used by a TDF block.2 The parameters of some linear
electrical components can bedynamically modified by a TDF block(e.g. changeable resistor).
3 Very important: at each parameterchange, the network matrix isrecalculated, which is atime-consuming operation.
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
Electromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
1 Introduction & GoalsElectromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
2 Modeling the Conditioning Circuit and ResonatorTDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuitmodels
3 Results & VerificationGeneral resultsComparison with VHDL-AMS and MATLAB SimulinkFurther work
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
Electromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
GoalsCreate a reusable model of the whole harvester inSystemC-AMS.
Previous workStudy of the system and development of a VHDL-AMSmodel, presented at BMAS 2007.
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
TDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuit models
1 Introduction & GoalsElectromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
2 Modeling the Conditioning Circuit and ResonatorTDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuitmodels
3 Results & VerificationGeneral resultsComparison with VHDL-AMS and MATLAB SimulinkFurther work
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
TDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuit models
The resonator is modeled as a second-order lumped-parameterlinear system:
−kx − µx + Ft(VCvar , x) + maext = mx
x is the mass displacement from the equilibrium position
m is the mass
k is the stiffness of the spring
µ is the viscous damping constant of the resonator
Ft is the force generated by the capacitive transducer Cvar
aext is the acceleration of the external vibrations
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
TDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuit models
TDF Model of the resonator∫ ∫
−µ
1/m
x
aextm
xx
Vvar
Cvar
Ft(VCvar, x)
Ft
−
k
Timed Data Flow implementation of the above equation:each operator is a SystemC-AMS TDF module.
The block has one electrical input (Vvar ), one mechanicalinput (aext ) and one electrical output (Cvar ).
The loop requires one delay step.
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
TDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuit models
1 Introduction & GoalsElectromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
2 Modeling the Conditioning Circuit and ResonatorTDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuitmodels
3 Results & VerificationGeneral resultsComparison with VHDL-AMS and MATLAB SimulinkFurther work
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
TDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuit models
Modeling electrical networks with SystemC-AMS
Difficulty: only linear networks can be natively modeled bySystemC-AMS.
"Natural" solution: model a non-linear network as a TDFsystem.
For this, the system of equations should be represented asa TDF diagram.
The problem: blocks with strong non-linearity and strongdiscontinuities due to switching.
Impossible to have a convergence with the existing TDFsolver.
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
TDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuit models
A SystemC-AMS LinElec diode model: Approach I
p n
TDF: V = Vnp − Vnn
LIN. ELEC.
I = Iss(exp(kT
eV )− 1)
A current source controlled by thevoltage on its terminals, withexponential relation between thecurrent and the voltage.
This implementation contains aloop, thus a one-step delay isnecessary.
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
TDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuit models
SystemC-AMS Lin Elec diode model: drawbacks ofapproach I
i(t)
e(t)
R
t
t
i(t)
e(t)
Bad solution: if the diode voltagebecomes positive, during onestep the diode generates a verylarge (exponential) current.
This current injection stronglydisturbs the state of the reactiveelements.
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
TDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuit models
SystemC-AMS LIN ELEC diode model: approach II
np
if V > 0, R = RON ,
else R = ROF F
TDF: V = Vnp − Vnn
LIN. ELEC.
1 Model a diode as a resistive switch,i.e., as a voltage-controlled resistor.
2 A TDF module calculates the stateof the diode (its resistance).
3 State (resistance) is updated after anecessary delay step.
4 The current value is still bad duringone step, but the error is notexponential and can be tolerated.
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
TDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuit models
Lin Elec diode: conclusions
Completely "embedded": usable as a normal Lin Eleccomponent.
The current value is erroneous during one step, thus, thesimulation step should be small enough to tolerate.
A more complex diode model can be realized in a similarway, using a series-connected voltage source and resistor,both voltage-controlled.
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
TDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuit models
Lin Elec diode: calculating the diode’s state
Simple state calculation
SCA_TDF_MODULE( E l e c t r i c a l _ d i o d e _ f u n c t i o n ) {sca_td f_ in <double > vo l tage ;sca_tdf_out <double > res i s tance ;void process ( ) {
res i s tance . w r i t e ( vo l tage . read () >0.?1e−9:1e10 ) ;}void s e t _ a t t r i b u t e s ( ) {
cu r ren t . set_delay ( 1 ) ;}
} ;
More complex state calculation
void process ( ) {double v o l t = round_to_n_decimals ( vo l tage . read , < prec is ion > ) ;double cu r ren t = < r e a l i s t i c cu r ren t diode law using v o l t > ;i f ( cu r ren t = = 0 . | | v o l t < 0 . 1 ) / / spec ia l cases
res i s tance . w r i t e (1e10 ) ;else
res i s tance . w r i t e ( v o l t / cu r ren t ) ;}
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
TDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuit models
1 Introduction & GoalsElectromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
2 Modeling the Conditioning Circuit and ResonatorTDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuitmodels
3 Results & VerificationGeneral resultsComparison with VHDL-AMS and MATLAB SimulinkFurther work
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
TDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuit models
Conditioning circuit
LIN. ELEC.TDF
Resonator
Vvar
Vvar
Cvar
Coupled electromechanicaloperation
There is a loop: a delay step isnecessary.
The mechanical part’s time step is100 times higher than theconditioning ciruit’s: the simulationruns 8 times faster (less matrixreinitialization).
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
General resultsComparison with VHDL-AMS and MATLAB SimulinkFurther work
1 Introduction & GoalsElectromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
2 Modeling the Conditioning Circuit and ResonatorTDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuitmodels
3 Results & VerificationGeneral resultsComparison with VHDL-AMS and MATLAB SimulinkFurther work
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
General resultsComparison with VHDL-AMS and MATLAB SimulinkFurther work
Global system operation
top: evolution of the voltage onCstore during about 5 cycles. Theswitch closes at 11V and opensat 6V (on VCstore ).
bottom: voltage accumulation onCres with no load connected.
The steep non-linear behavior iscorrectly modeled when theswitch changes state.
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
General resultsComparison with VHDL-AMS and MATLAB SimulinkFurther work
1 Introduction & GoalsElectromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
2 Modeling the Conditioning Circuit and ResonatorTDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuitmodels
3 Results & VerificationGeneral resultsComparison with VHDL-AMS and MATLAB SimulinkFurther work
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
General resultsComparison with VHDL-AMS and MATLAB SimulinkFurther work
Verification of the results
The SystemC-AMS model is compared to a VHDL-AMSand a Simulink model.
The VHDL-AMS model was presented at BMAS 07.Different diode models had to be used for the simulationsto work.
VHDL-AMS a diode law with 3 regions (linear on/off zones,quadratic transition).Simulink a quadratic diode law.SystemC-AMS a two state diode law.
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
General resultsComparison with VHDL-AMS and MATLAB SimulinkFurther work
Summmary of results
Table: Relative differences in comparison with VHDL-AMS
VCstore VCres ILSystemC-AMS 0.495% 1.468% 0.595%
Simulink 0.886% 0.316% 0.100%
Table: Simulation time for 1 second of system operation (in min.)
SystemC-AMS Simulink VHDL-AMS145 3.5 5.75
The same system was modeled in VHDL-AMS, Simulinkand SystemC.
The relative difference was less than 2 %.
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
General resultsComparison with VHDL-AMS and MATLAB SimulinkFurther work
1 Introduction & GoalsElectromechanical Harvester of Vibration EnergySystemC-AMS: overviewGoals and previous work
2 Modeling the Conditioning Circuit and ResonatorTDF Model of the Mechanical ResonatorLin Elec Model of the Conditioning CircuitConnecting the Resonator and Conditioning Circuitmodels
3 Results & VerificationGeneral resultsComparison with VHDL-AMS and MATLAB SimulinkFurther work
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
General resultsComparison with VHDL-AMS and MATLAB SimulinkFurther work
Further work
Find the parameters for optimal energy gain, i.e. refine theswitch model (VHDL-AMS/Simulink).
Implement a higher level load (i.e. a processor) and usethe system as power source (SystemC-AMS only).
Find a TDF approximation of the conditioning circuit, tospeed up the simulation (SystemC-AMS only).
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
university-logo
Introduction & GoalsModeling the Conditioning Circuit and Resonator
Results & VerificationConclusion
Summary
By combining TDF and Lin Elec modules we simulatednon-linear Lin Elec components using the linear solver ofSystemC-AMS.
This allowed us to correctly model a (heterogeneous)electromechanical system (<2% rel. diff. with VHDL-AMS).
The fixed time step slows down the simulation.
Ken Caluwaerts, Dimitri Galayko, Philippe Basset SystemC-AMS modeling of a Vibration Energy Harvester
