Designer’s Guide - Supporting Dimensional Analysis in ...École Polytechnique Fédérale de...

Supporting Dimensional Analysis in SystemC-AMS

Torsten Mähne Alain Vachoux

Laboratoire de Systèmes Microélectroniques (LSM)École Polytechnique Fédérale de Lausanne (EPFL)

Lausanne, Suisse

Behavioral Modeling and Simulation Conference (BMAS) 200917 to 18 September 2009, Doubletree Hotel, San Jose, California, USA

mailto:[email protected]

mailto:[email protected]

http://lsm.epfl.ch/

http://www.epfl.ch/

http://bmas-conf.org/

Table of Contents

Introduction

Modeling of Multi-Domain Systems

Integrating Dimensional Analysis into SystemC-AMS

Application Example

Conclusions and Outlook

References

T. Mähne, A. Vachoux (EPFL/STI/IEL/LSM) Dimensional Analysis in SystemC-AMS BMAS 2009 2 / 25

Introduction Heterogeneous SoCs Design Process Challenges

Heterogeneous SoCs Design Process Challenges

Processors

MOEMS sensors and actuators

Consumer peripherals

Copro-cessors

Memories:ROM, RAM,

FLASH,EEPROM,

FPGA Support devices:DMA, Timer, SPI,

PWM, UART,FPGA

Analog andmixed-signalcomponents:ADC, DAC,

Bandgap, VCO,OpAmp, radio

DSP

Clock:PLL,DLL

Businter-faces

I Component reuse and retargetingI Multiple engineering/physical domainsI Multiple Models of Computations (MoCs)I Conflicting naming conventions for (elec., mech., . . . ) quantities Strict interface specifications—not only value type Dimensional analysis: quantity<unit<dimension, system>, value_type> Check model assembly and calculation consistency


Introduction Motivation for Dimensional Analysis

Motivation (1/2): Loss of NASA’s Mars Climate Orbiter

Mars Climate Orbiter (MCO) was loston 23 September 1999 during its orbitentering maneuver.Details: http://marsprogram.jpl.nasa.gov/msp98/orbiter/

Statements by Arthur Stephenson(Chairman of MCO Mission FailureInvestigation Board, 10 November 1999):

I “The ‘root cause’ of the loss of thespacecraft was the failed translation ofEnglish units into metric units in asegment of ground-based,navigation-related mission software, asNASA has previously announced.”

I “The failure review board has identifiedother significant factors that allowedthis error to be born, and then let itlinger and propagate to the point whereit resulted in a major error in ourunderstanding of the spacecraft’s pathas it approached Mars.”


http://marsprogram.jpl.nasa.gov/msp98/orbiter/

http://marsprogram.jpl.nasa.gov/msp98/orbiter/


Motivation (2/2): Usage of Multiple Systems of Units

q1 u1u2u3u4u5u6u7u8u9u10v1 v2 v3 v4 v5

ROM144

Yaw rate sensorin−plane q3

q4

u1u2u3u4u5u6u7u8u9u10v1 v2 v3 v4 v5

ROM144

Yaw rate sensorout−of−plane

q2

SI

µSI

µSI

µSI

µSI

µSI

µSI

µSI

µSI

µ

1r3

r4

1

r3

1

σr, y

σr, x

σr, z

2r2

12r2

1

FM, y, 5

FM, y, 7

2r2

12r2

12r2

12r2

1

∂t∂

∂t∂

Conservationof the

angularmomentum

σr

ωr

αr

σi ωi αi

Mx

My

Mz

3

3

3

3

σr ωr αr

σr, z

Fz, 5

Fz, 6

Fz, 7

Fz, 8

Structuralcoupling

effect

3

∫

∂t∂

3

3

3

3

3

3

σi

αi

ωi

ωi, x

ωi, y

ωi, z

ωi, x

ωi, y

ωi, z

FM, z, 5 FM, z, 7 FM, z, 6 FM, z, 8

FQ, z ,8

FQ, z ,7

FQ, z ,6

FQ, z ,5

GND KA KI K2K1 CM C2 C1 T2 T1 AGND

Yaw rate sensor, full model (µMKSV system of units)

Yaw rate sensor driving and detection circuit (SI system of units)

System of units converters

I MEMS yaw rate sensor behavioral model

I Sensor model using µMKSV system of units

I Control circuit model using SI system of units

Insertion of system of units converters



State of the Art: Dimensional Analysis in HDLs

I VHDL-AMS: Unit specification with attributes purely for presentationsubtype VELOCITY is REAL tolerance "DEFAULT_VELOCITY";attribute UNIT OF VELOCITY : subtype is "meter/second";attribute SYMBOL OF VELOCITY : subtype is "m/s";

I Modelica: SI unit specification (+ scale factors) in attributes of RealReal(unit="m.s-1") v = 2.0;

I Tool-specific dimensional analysis solutions, e.g., Dymola, Simulator XI Efforts to formalize and generalize physical unit checking

I F#: Units part of language and dimensional analysis built in compiler[<Measure>] type kg[<Measure>] type N = kg m/s^2let gravity = 9.808<m/s^2>let metresToFeet (l:float<m>) = l * 3.28084<ft/m>

I Extensible by declaring new units and system of unitsI No notion of dimension (classes of measurement units)I Programing language without dedicated supported for system modeling


Introduction AMS Extensions to SystemC

AMS Extensions to SystemC

Goal: Simulation of heterogeneous SoCs using several synchronised MoCsOSCI standardisation effort: based on SystemC-AMS (Fraunhofer IIS/EAS)

SynchronousData Flow (SDF)• Modules• Ports• Signals

Electrical LinearNetworks (Elec)• Primitives• Terminals• Nodes

SchedulerLinear DAE solver

Synchronization layer

SystemCmethodology-

specificelements

• Transaction LevelModeling (TLM)

• Cycle/bit AccurateModeling

• SystemCVerificationLibrary (SCV)

• etc.

OSCI SystemC 2.2 language standard (IEEE Std. 1666-2005) and simulation kernel

User-definedAMS extensions• Modules• Ports• Signals

(e.g., additional MoCs,simulator couplings)

AMS methodology-specific elementsQuantity/units specification, dimensional analysis, generic block diagram SDF modules

This work’s extensions to Fraunhofer’s SystemC-AMS

Our contribution: New modeling capabilities for formal/consistent descriptionof energy conserving multi-domain systems at a high level of abstraction.


http://www.systemc.org/

http://www.systemc-ams.org/

http://www.eas.iis.fraunhofer.de/index_en.html


Modeling of Multi-Domain Systems (1/2)

1. “Classic” domain-specific conservative model:R1

m

d

k

x

Ctrans(x), Ftrans(q,x)

vdrive(t)

iR1

− Implementation ofprimitives per domain

− SystemC-AMS offers onlylinear electrical primitives

2. Equivalent generic bond graph model:

1 C

e3(q3,q4)e4(q3,q4)

: 1

R : R2

I : I1

C : C1

R : R1

f2e2

e1 e3

f3f1

e4

f4

e5

e6

f6

e7

f5

f7

Se : e1(t)

+ Primitives parametrizableto domain

+ Causality analysis extractscomputational structure

− Not (yet) supported bySystemC-AMS

I Check model assembly, consistent equations dimensional analysis





m

d

k

x


vdrive(t)

iR1



2. Equivalent acausal bond graph model:

1 C

Ctrans(x)Ftrans(q,x)

: 1

R : d

I : m

C : k

Se : vdrive(t)

R : R1

iR1vR1

vdrive vtrans

iR1iR1

Ftrans

vm

Fd

Fm

vm

Fk

vm

vm









m

d

k

x


vdrive(t)

iR1



2. Equivalent causal bond graph model:

1 C

Ctrans(x)Ftrans(q,x)

: 1

R : d

I : m

C : k

Se : vdrive(t)

R : R1

iR1vR1

vdrive vtrans

iR1iR1

Ftrans

vm

Fd

Fm

vm

Fk

vm

vm








3. Derived block diagram:

g4

s1(t)

s3

s2

s5 s7

s11

s8

s10s13

∫∫

+−

f1(x,y) f2(x,y)

s4 s6

g1

+

g3

∫

∫

g2

s12

s9

s3(t)

−−−

+ Fully causal static scheduling procedural execution+ Simulatable with SystemC-AMS’s Synchronous Data Flow (SDF) MoC− Energy conservation emulated− Hard to reuse in other context with different input/output roles Annotated units resolve symbol conflicts





k

vdrive(t)

iR1

vR1

vtrans Ftrans

Fd

Fm

vmFk

∫∫

+− q

C(x) F(q,x)

q x

1R1

+

d

∫

∫

1m

xm

pm

i(t)

−−−

Electrostatic transducer






k

vdrive(t)[V]

iR1 [A]

vR1 [V]

vtrans[V] Ftrans[N]

Fd [N]

Fm[N]

vm[m/s]Fk[N]

∫∫

+− q

C(x) F(q,x)

q[C] x[m]

1R1

+

d

∫

∫

1m

xm[m]

pm[Ns]

i(t)[A]

−−−

Electrostatic transducer[S] [Ns/m]

[kg−1][N/m]

[C/F] [N]



Integrating Dimensional Analysis into SystemC-AMS Boost.Units C++ Library for Dimensional Analysis

Boost.Units: C++ Library for Dimensional Analysis

I unit<Dim, System> type: to represent arbitrary composite unitI Dim: Static type list of base dimensions raised to a rational powerI System: Set of base dimensions and their measuresI Example: Energy is [M]1[L]2[T]−2, in SI: kg m2 s−2 = N m = J

I quantity<U, V> type: composed of unit U and value V typesI Code example:// Current quantity with double valuequantity<si::current> i = 0.1 * si::ampere;// Complex impedance quantityquantity<si::resistance, complex<double> >Z = complex<double>(4.0, 3.0) * si::ohm;// Assignment of product only to a complex voltage quantityquantity<si::electric_potential, complex<double> >v = Z * i;



Boost.Units Dimensional Analysis Examples (1/2)

I Accidental Summing of Different Quantity Types:quantity<si::electric_potential> v_1 = 5.0 * si::volt;quantity<si::velocity> v_2 = 3.0 * si::meter / si::second;// This won’t compile:quantity<si::electric_potential> v_tot = v_1 + v_2;

I Compiler error:fail_bmas2009_examples.cpp:16: error: no match for ‘operator+’ in ‘v_1 + v_2’

Cannot sum voltage quantity v_1 and speed quantity v_2



Boost.Units Dimensional Analysis Examples (2/2)

I Wrong implementation of Ohm’s law:quantity<si::resistance> R = 5.0e3 * si::ohm;quantity<si::electric_potential> v = 10.0 * si::volt;// This won’t compile:quantity<si::current> i = R * v;

I Compiler error (simplified, using namespace boost::units):fail_bmas2009_examples.cpp:10: error: conversion from’quantity<unit<list<dim<length_base_dimension, static_rational<4l, 1l> >,

list<dim<mass_base_dimension, static_rational<2l, 1l> >,list<dim<time_base_dimension,

static_rational<-6l, 1l> >,list<dim<current_base_dimension,

static_rational<-3l, 1l> >,dimensionless_type> > > >,

si::system, void>,double>’

to non-scalar type ’quantity<si::current, double>’ requested

Cannot convert from [Ω V] = [m4 kg2 s−6 A−3] to [A]


Integrating Dimensional Analysis into SystemC-AMS Integrating Boost.Units into SystemC-AMS

Integrating Boost.Units into SystemC-AMS

1. Parametrize signals and ports to new quantity<U, V> type:I Supported by DE and SDF MoCs, as ports and signals are templatesI Example:// Quantity SDF signalssca_sdf_signal<quantity<si::current> > i_sig;sca_sdf_signal<quantity<si::electric_charge> > q_sig;

2. Keep implemented modules generic enough:I Don’t reimplement similar behavior for each quantity type Write module templates to parametrize ports and parametersI Demonstrated with generic module library library scax_block_diagramI Example:// Integrator instantiationscax_bd::scax_integ_trapez<quantity<si::current> >i_integ("i_integ", 0.0 * si::coulomb);i_integ.in(i_sig);i_integ.out(q_sig);


Application Example Electromechanical Transducer with Mechanical Resonator

Electromechanical Transducer with ResonatorDomain-specific conservative model:

R1

m

d

k

x


vdrive(t)

iR1

Derived block diagram:

k

vdrive(t)[V]

iR1 [A]

vR1 [V]

vtrans[V] Ftrans[N]

Fd [N]

Fm[N]

vm[m/s]

Fk[N]

+− q

C(x) F(q,x)

q[C] x[m]

1R1

+

d

∫

∫

1m

xm[m]

pm[Ns]

i(t)[A]

−−−

Electrostatic transducer[S] [Ns/m]

[kg−1][N/m]

[C/F] [N]

itrans[A] vtrans[m/s]

∫ ∫


Application Example Interface of the Electromechanical Transducer Model

Electromechanical Transducer Using double

struct elmech_transducer : public sc_core::sc_module // Electrical and mechanical portssca_sdf_in<double> i_in; // Current input [A]sca_sdf_out<double> v_out; // Voltage output [V]sca_sdf_in<double> v_in; // Velocity input [m/s]sca_sdf_out<double> F_out; // Force output [N]// Parametrize module// v_func: Transducer voltage [V] function v = f(q, x)// F_func: Transducer force [N] function F = f(q, x)// q_0: Initial charge [C]// x_0: Initial displacement [m]elmech_transducer(const sc_core::sc_module_name& name,function<double (double, double)> v_func,function<double (double, double)> F_func,double q_0 = 0.0,double x_0 = 0.0); // ...

;


Application Example Interface of the Electromechanical Transducer Model

Electromechanical Transducer Using quantity<U, V>

struct elmech_transducer : public sc_core::sc_module // Typedefs for common quantity typestypedef quantity<si::electric_potential> voltage_t;typedef quantity<si::force> force_t; // ...// Electrical and mechanical portssca_sdf_in<current_t> i_in;sca_sdf_out<voltage_t> v_out;sca_sdf_in<velocity_t> v_in;sca_sdf_out<force_t> F_out;// Parametrize moduleelmech_transducer(const sc_core::sc_module_name& name,function<voltage_t (charge_t, displacement_t)> v_func,function<force_t (charge_t, displacement_t)> F_func,charge_t q_0 = 0.0 * si::coulomb,displacement_t x_0 = 0.0 * si::meter); // ...

;


Application Example Parametrization of the Electromechanical Transducer Model

Transducer Voltage Function Defined in Testbench

I Version using double:// Transducer capacitance formula v_trans(q, x)// v_trans: Voltage [V]; q: Charge [F]; x: Displacement [m]function<double (double, double)>v_trans_func = _1 / (C_trans_0 * (1.0 - (_2 / overlap)));

Compiler cannot check formula consistency and parameter order!I Version using quantity<U, V>:typedef quantity<si::electric_potential> voltage_type;typedef quantity<si::electric_charge> charge_type;typedef quantity<si::length> displacement_type;// Transducer capacitance formula v_trans(q, x)function<voltage_type (charge_type, displacement_type)>v_trans_func = _1 / (C_trans_0 * (1.0 - (_2 / overlap)));

Compiler can fully check formula consistency and parameter order!


Application Example Simulation Results

Simulation Results

-2

0

2

4

6

v /

V

vdrive

-4

-2

0

2

4

v /

V

vR1

vtrans

-40

0

40

80

120

160

F /

µN

Ftrans

-800

-400

0

400

800

F /

µN

Fd

Fk

Fm

-8

-4

0

4

8

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x /

µm

t / ms

xm


Application Example Compilation and Simulation Times Comparison

Compilation and Simulation Times Comparison

Language/Simulator Feature tcompile tsimulate

SystemC-AMS 0.15 RC5 quantity<U, V> 19.07 s 11.76 s(+ SystemC 2.2.0, g++ 4.3.2 -O2) double 9.69 s 11.38 s

VHDL-AMS free quantity 0.79 s 18.76 s(ADVance MS 2008.2) branch quantity 0.84 s 18.43 s

I Simulated time: 2.4 msI Fixed time step: 10 nsI Platform: Intel Pentium 4 3 GHz, 1 MB Cache, 2 GB RAM,

Debian Lenny, Linux 2.6.26 (i386)




Conclusions:I Quantities check model assembly and calculation consistencyI Boost.Units increases compilation time, not simulation timeI Generic block diagram library for SDF MoC enables high-level

description of analog behavior and keeps link to physical domain

Current work and outlook:I Scalability of demonstrated approach?I Filter Boost.Units compiler errorsI Develop Bond Graph MoC applying these techniques


References

References

Boost Library Documentation, 1998-2009.http://www.boost.org/doc/libs.

Broman, D., et al.: Design considerations for dimensional inference and unit consistencychecking in Modelica.In Proceedings of the 6th International Modelica Conference, Bielefeld, Germany, 2008.

IEEE: IEEE Standard 1666-2005, SystemC Language Reference Manual, Mar. 2006.http://standards.ieee.org/reading/ieee/std/dasc/1666-2005.pdf.

Karnopp, D.C., et al.: System Dynamics: Modeling and Simulation of Mechatronic Systems.Wiley, 4th ed., Jan. 2006.

Maehne, T., et al.: Development of a bond graph based model of computation for SystemC-AMS.In Proc. 4th IEEE PRIME 2008 Conference, Istanbul, Turkey, 2008. IEEE.

Mähne, T., et al.: Creating virtual prototypes of complex MEMS transducers using reduced-ordermodelling methods and VHDL-AMS.In Applications of Specification and Design Languages for SoCs. Springer, 2006.

OSCI: Draft Standard SystemC AMS Extensions Language Reference Manual, Dec. 2008.http://www.systemc.org/members/download_files/check_file?agreement=AMS_draft1_120308.

Vachoux, A., C. Grimm, and K. Einwich: Extending SystemC to support mixeddiscrete-continuous system modeling and simulation.In Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS) 2005.


http://www.boost.org/doc/libs

http://standards.ieee.org/reading/ieee/std/dasc/1666-2005.pdf

http://www.systemc.org/members/download_files/check_file?agreement=AMS_draft1_120308

The End

The End

Thank you for your attention!


Appendix AMS Extensions to SystemC



Open-source SystemC-AMS prototype byFraunhofer IIS/EAS

SynchronousData Flow (SDF)• Modules• Ports• Signals

Electrical LinearNetworks (Elec)• Primitives• Terminals• Nodes



SystemCmethodology-

specificelements




• etc.


User-definedAMS extensions• SC networks• Conservative

non-lin. networks• Simulator

couplings

Proprietaryextensions

AMS methodology-specific elementsSDF module libraries, schematic entry

I White paper and Draft 1 LRM availableI Proof-of-concept implementation under way driven





Appendix AMS Extensions to SystemC



Timed Data Flow(TDF)

• Modules• Ports• Signals

Electrical LinearNetworks (ELN)• Primitives• Terminals• Nodes



SystemCmethodology-

specificelements




• etc.

Linear SignalFlow (LSF)

• Primitives• Ports• Signals


User-definedAMS extensions• Modules• Ports• Signals

(e.g., additional MoCs,simulator couplings)

AMS methodology-specific elementsElements for AMS design refinement, etc.

OSCI AMS Extensions to SystemC LRM Draft 1Envisionedextensions

I White paper and Draft 1 LRM availableI Proof-of-concept implementation under way driven





Appendix Integrating Dimensional Analysis into SystemC-AMS

scax_block_diagram Library Overview (1/2)

Name Description

scax_source<T,TimeType> SDF samples source module using a waveformfunction: f : TimeType→ T

scax_sink<T> SDF samples sink module

scax_scale<T1,T2> Scale module

scax_sum<T> Summing module with variable input number

scax_mul<T1,T2> Multiplier module with two inputs

scax_integ_trapez<T> Trapezoidal integrator module

scax_dot_secant<T> Differentiator module using asymmetric evaluation ofNewton’s difference quotient


Appendix Integrating Dimensional Analysis into SystemC-AMS

scax_block_diagram Library Overview (2/2)

Name Description

scax_func1<T1,T2> Time-independent function module withone input: f : T1→ T2

scax_func2<T1,T2,T3> Time-independent function module with twoinputs: f : T1 × T2→ T3

scax_func3<T1,T2,T3,T4> Time-independent function module withthree inputs: f : T1 × T2 × T3→ T4

scax_func1t<T1,T2,TimeType> Time-dependent function module with oneinput: f : T1 × TimeType→ T2

scax_func2t<T1,T2,T3,TimeType> Time-dependent function module with twoinputs: f : T1 × T2 × TimeType→ T3


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