VHDL AMS Modeling of an Electric Power Steering System in a

Ansoft, LLC Proprietary

VHDL-AMS Modeling of an Electric

Power Steering System in a Multi-

Physics Simulation Environment.

SEKISUE, Takayuki

Ansoft Japan K.K.

Ansoft, LLC Proprietary

Presentation Goals

• Mechanical modeling in SIMPLORER

– About the mechanical system model’s description and the

usage.

– About the description of the motor drive part

• VHDL-AMS model

• System simulation with power unit

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Introduction

•

In the design of the electric equipment component, the
optimization of the equipment unit has been advanced.

•

On the other hand, modeling a complex phenomenon
and detailed operation is requested by making to high
performance in the design of the system that controls
them.

•

Cannot a new solution point be found by sharing the
simulation model as both cooperating?

– This presentation introduces the example of

simulating the subsystem as an example of EPS
control model and driving system.

– The example of simulating a necessary element

technology is referred to make it to high accuracy.

– And this introduces everything from each

simulation result to the power management as an
example of designing the total system.

Accept total

system

Subsystem
verification

Built-in

verification

Demand

definition

Optimize of

elements

Subsystem

design

Topology

layout

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• SIMPLORER can be applied not only for electrical circuits

but also Multi-domain system & circuit.

SIMPLORER OverView

OMEGA

3 ~

I1C

I1B

I1A

EQU

RTH_Chip

K := 1.5

CTH_J

C_TH := 1m

CTH_Chip

C_TH := 10m

RTH_Case

K := 0.2

CTH_Case

C_TH := 0.1

RTH_Sink_Conv

K := 1.02

THM1

THM2

THM3

RTH_Sink_Rad

K := 4.2

Tambient

VALUE := 300

Celsius

PEL

TR1

ROT2

TSF

tra

Wheel_dynamics

Thermal model design

Design of magnetic

components

Mechanical model design

Common mode- noise

SIMPLORER

ePhysics

Maxwell

Q3D

VHDL-AMS

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Steering assist system.

1. Steering

2. Torsion bar

Column shaft

3. Intermediate shaft

6.Assist motor

4.Rack & Pinion gear

Deceleration

gear

自動車工学入門：野崎博路著：山海堂 ISBN 4-381-08855-7

Steering

Torque sensor

Assist motor

Vehicle speed

Rack & Pinion

Slip angle

Side force

•

Change of the assistant gain by vehicle speed

• The moment of self aligning

=> These have not been considered yet

Diagram

Composition

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TR1

ROT2

TSF

ROT1 ROT2

TSF

ROT

ROT_V

ROT

ROT_V

TBar

Motion model of steering system.

Steer Angle

Torque detection

1. Steering

2. Torsion bar

3. Intermid shaft

4.Rack & Pinion gear

6.Assist motor

0.025[kgm2]

0.04[Nm s/rad]

130[Nm/rad]

12[kg]

6500[Ns/m]

210k [N/m]

Gear ratio 4

0.5m[kgm2]

• Reaction force imitates the set end with a high
rigidity spring.

• The detected torque of torsion bar refers from
assit motor.

Steer

inertia

Friction

Twist rigidity

Translation <> rotation

Rotor intertia

5. Reaction

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Steering angle and Steering torque

TR1

ROT2

TSF

ROT1 ROT2

TSF

ROT

ROT_V

ROT

ROT_V

TBar

-11.40

11.35

1.00

500.00m

トーションバー・トルク

TBar.TORQUE [Nm]

-10.00

10.00

1.00

500.00m

操舵量

S_ROTB1.PHI [deg]

Steering Angle
10[deg] 1Hz

Torsion bar
torque

• Input : steering angle 10[deg], 1[Hz]
• Confirm steering torque with out assist system

Steering angle [deg]

Torsion bar torque [deg]

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Modeling of motion system

DAMPING := .05 Nm*s/rad

C := 10 Nm/rad

VALUE := 10 rad/s

Angular speed source

Twist

Rigidity C

DAMPING

Inertia J

Rigidity

Viscous coeff.

1.44n

18.90

10.00

20.00

10.00

VM_ROT1.OMEGA [rad/s]

Velocity differential

Speed source

C: Rigidity over an angle difference of twist

Damping: Viscosity over a velocity differential

−

(

)

∫

−

Disturbance

Te =0

・Conservation law of torque.

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10 rad/s

C := 10 Nm/rad

DAMPING := .05 Nm*s/rad

J := 1 kg m %

C := 10 Nm/rad

DAMPING := .05 Nm*s/rad

J := 2 kg m %

2 DOF system

Angle

Rigidity C

Inertia

Velocity differential

Speed source

18.00

10.00

20.00

10.00

MASS_ROT2.OMEGA [rad/s]

• Series connection of elasticity
• Easy expansion to the multi body system.

(

)

(

)

(

)

∫

−

Damping

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Connecting in parallel

10 rad/s

C := 10 Nm/rad

DAMPING := .05 Nm*s/rad

J := 1 kg m %

Velocity differential

VALUE := 10 m/s

DAMPING := .05 N*s/m

C := .1 N/m

M := 1 kg

Velocity differential

• Consider damping to the speed difference in which section.

• Easy understanding where is the reference of a position and an angle

Rotational motion

Translational motion

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GAIN

N EG

NPG

TSP1

TSP4

TSP2

TSP5

TSP3

TSP6

COMP1

COMP2

COMP3

TRIANG1

Vref_u

Vref_v

Vref_w

PWM Generator

Vector control of IPM : Basic model

FREQ := 20k

AMPL := 1

SET: := ST4:=0

SET: := ST1:=1

TSP4.VAL=1

SET: := ST4:=0

SET: := ST1:=0

SET: := ST4:=0

SET: := ST1:=0

TSP1.VAL=1

SET: := ST1:=0
SET: := ST4:=1

Dead Time Control

ICA:

deadtime:=5u

Friction:=8e-3

3 ~

ST1

ST2

ST3

ST4

ST5

ST6

Vdc

DC_bus

AM1

AM2

AM3

Motor

theta

dq_abc

GAIN

Vref_u

Vref_v

Vref_w

EQU

Dw:=Friction*Motor.N*2*pi/60

theta

abc_dq

Input

PI_1

CONST

Omega

CONST

Idref

GAIN

Input

PI_2

Input

PI_3

GAIN

CONST

Psi

Omega

GAIN

VMA

VMB

VMC

DC_bus:=12

Motor.KE

Motor.L1D

Motor.P

GAIN

Motor.P

2 * PI/60.0

Motor.L1Q

P_Gain 0.5

I_Gain 2

0.6

20m

P_Gain 13

I_Gain 3

1/(DC_bus/2)

200

PWM carrier = 20kHz

q-axis voltage

compensation

Speed

control

q-axis

current control

d-axis

current control

12[V]

d-axis voltage

compensation

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Basic Component :

PM 3Phase synchronous motor（SYMP1）

3 ~

Rotor Speed [rpm]

OMEGA: Rotor Angular Velocity [rad/s]
MI:

Inner Torque [Nm]

PHI

Electrical Angle [rad]

PHIDEG

Electrical Angle [deg]

PHIM

Mechanical Angle [rad]

PHIMDEG Mechanical Angle [deg]

PHI := PolePairs * PHIM

LOAD:

Load torque [Nm]

R1:

Stator Resistance [Ohm]

L1D

d-axis Inductance [H]

L1Q

q-axis Inductance [H]

Rotor Flux [Wb]

Pole pairs

Rotor Moment of Inertia [kgm

]

PWRELEC:

Input Power [W]

PWRMECH:

Output Power [W]

PWRLOSS:

Losses [W]

Input parameters

Output parameters

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Basic Component :

PM 3Phase synchronous motor（SYMP1）

ωψ

⋅

−

⋅

(

)

{

}

⋅

−

⋅

Load

−

〜

dq-Axis Voltage Equation

dq-Axis Flux Linkage

Motor Torque

Equation of Motion

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Input parameters

3 ~

Temporary Load model

Friction := 10.0 e-3
Torque

⋅

= Friction

EQU

Dw:=Friction*Motor.n*2*pi/6

Dw := Friction * Motor.N * 2 * PI/60

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3 ~

Mo to r

theta

d q_ab

GAIN

Vref_u

Vref_v

Vref_w

theta

ab c_d q

Input

PI_1

Omega

CONST

Id re

GAIN

Input

PI_3

GAIN

CONST

Omega

GAIN

Motor.KE

Motor.L1D

GAIN

Motor.P

Motor.L1Q

P_Gain 0.5

I_Gain 2

P_Gain 13

I_Gain 3

1/(DC_bus /2)

CONST

TR ef

GAIN

1/(1.5 * Motor.KE * Motor.P)

Check : Motor torque control

-50.00u

935.00m

500.00m

60.00m

20.00m

40.00m

モータトルク [Nm]

Motor.MI [(kg m)/s]

• Convert the reference torque into iq
• Check the following capability and steady-state error at reference torque = 1[Nm]

(

)

{

}

⋅

−

⋅

Motor torque

Motor Torque [Nm]

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Parametric : searching gains for torque control

-10.00m

1.84

1.00

60.00m

20.00m

40.00m

モータートルク [Nm] /KP

-5.00m

940.00m

500.00m

60.00m

20.00m

40.00m

モータトルク [Nm] / KI

KP valid

KI fixed=3

KP fixed=13

KI valid

KP = 0.1

0.2
0.8

1
2
8

10
20

KP = 20

KP=0.1

KI = 0.1

0.2
0.8

1
2
8

10
20

KI = 20

KI = 0.1

KP = 2

Check : KP
following capability

Check : KI

Steady state error

• Gain KP influences the following capability.
• In this case, KP >= 2 is required.

Motor Torque [Nm] / KP

Motor Torque [Nm] / KI

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TR1

ROT2

TSF

ROT1 ROT2

TSF

ROT

ROT_V

ROT

ROT_V

TBar

The load model system and motor torque

3 ~

Torque Source

• The load torque in standard SML motor model is defined as a simple signal.
• How much torque should we refer as load ?

The parameter display of a SML motor model.

Motor torque

Where can we get the load torque ??

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Intricate case : Described as individual system.

3 ~

Motor

Omega

GAIN

Motor.P

ROT1

ROT2

TSF

ROT

ROT_V

ROTB_ROT3

Motor.J

OMEGA

LOAD

• Load torque from axis.
• Add rotor inertia.

• Motor speed is compelled to axis

• Motor torque is compelled to axis

• Note that the direction of the torque meter.
• Don’t forget that the addition of rotor inertia at the terminal.

• Though thinking the motor to be a torque source…

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Improvement motor model : using VHDL-AMS

shaft

Motor

LIBRARY

IEEE;

USE

IEEE.ELECTRICAL_SYSTEMS.ALL;

USE

IEEE.MECHANICAL_SYSTEMS.ALL ;

USE

IEEE.MATH_REAL.ALL;

ENTITY

SYMP

GENERIC

(

L1d : INDUCTANCE :=

0.042

;

L1q : INDUCTANCE :=

0.042

;

…..

3 ~

・ Equal 3PH synchronous motor model included in AMS library.

• Improve the AMS model to create the shaft output to connect mechanical model.

Copy the definition and create subsheet.

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• Addition of a rotation system terminal

• Quantity definition

• Equation of motion

Improvement of VHDL-AMS motor model.

PORT

(

TERMINAL

a, b, c : ELECTRICAL;

TERMINAL

shaft : ROTATIONAL_V ;

shaft

Motor

QUANTITY

omega

across

load

through

shaft

ROTATIONAL_V_REF ;

mi ==

3.0

2.0

* P * (psi1d * i1q - psi1q * i1d);

j * omega‘dot == mi + load ;

mi : motor torque
P : pole pairs
psi1d, psi1q : d,q axis flux

load

omega

• “shaft

ROTATIONAL_V_REF” expresses the direction which

load torque flows.

Note that the direction is opposite with “load” of a standard model.

⇒ With equation of motion, “load” should be added.

shaft

omega

load

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Integrate Steering model and electrical system.

ICA:

deadtime:=5u

Friction:=8e-3

ST1

ST2

ST3

ST4

ST5

ST6

Vdc

DC_bus

AM1

AM2

AM3

theta

dq_abc

GAIN

Vref_u

Vref_v

Vref_w

EQU

Dw:=Friction*Motor.n*2*pi/60

theta

abc_dq

Input

PI_1

Omega

C ON ST

Idref

GAIN

Input

PI_3

GAIN

C ONST

Psi

Omega

GAIN

VMA

VMB

VMC

DC bus:=12

Motor.ke

Motor.l1d

GAIN

Motor.p

Motor.l1q

P_Gain 0.5

I_Gain 2

P Gain 13/*20*/

I Gain 3 /*0.2*/

1/(DC_bus/2)

C ON ST

TRef

TBar.TORQUE

GAIN

1/(1.5 * Motor.ke * Motor.p)

TR1

ROT2

TSF

ROT1

ROT2

TSF

ROT

ROT_V

ROT

ROT_V

TBar

shaft

Motor

FM_ROT1

Reference
Torque

CONST

TRef

TBar.TORQUE

1) Connect motor shaft terminal to steering model.

2) Add torque reference value into a control block.

• Refer to torsion bar torque.

(1)

(2)

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Integrated model : Simulation result.

10.00

5.00

500.00m

200.00m

400.00m

操舵量 [d...

S _ROT B 1.PHI [deg

-36.00

38.50

500.00m

200.00m

モータトルク [Nm]

Motor.mi

-5.00m

9.45

5.00

200.00m

100.00m

モータトルク [Nm]

Motor.mi

ICA:

deadtime:=5u

Friction:=8e-3

ST1

ST2

ST3

ST4

ST5

ST6

Vdc

DC_bus

AM1

AM2

AM3

theta

dq_abc

GAIN

Vref_u

Vref_v

Vref_w

EQU

Dw:=Friction*Motor.n*2*pi/60

theta

abc_dq

Input

PI_1

Omega

CONST

Idref

GAIN

Input

PI_3

GAIN

CONST

Psi

Omega

GAIN

VMA

VMB

VMC

DC_bus:=12

Motor.ke

Motor.l1d

GAIN

Motor.p

Motor.l1q

P_Gain 0.5

I_Gain 2

P Gai n 13/*20*/

I Gain 3 /*0.2*/

1/(DC_bus/2)

CONST

TRef

TBar.TORQUE

GAIN

1/(1.5 * Motor.ke * Motor.p)

TR1

ROT2

TSF

ROT1

ROT2

TSF

ROT

ROT_V

ROT

ROT_V

TBar

shaft

Motor

FM_ROT1

Steering Angle [deg]

Time < 200ms

Whole time

Motor Torque [Nm]

•

Oscillation !!

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Frequency response of mechanics

TBar

D2D

D2D1

Steering Inertia

BodePlotSel3

TBar.TORQUE

Gain

Phase

100

200

400

100

200

400

-75.00

-50.00

-25.00

0.00

25.00

-75.00

-50.00

-25.00

0.00

25.00

0.00

45.00

90.00

135.00

180.00

0.00

45.00

90.00

135.00

180.00

f [Hz]

[dB]

[deg]

Inertia of Motor

• The resonance point by the inertia
of motor is seen in 100Hz.

• other point 8Hz caused by the
steering inertia.

Transfer ratio : Steering Torque/Motor Torque

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Oscillation control / phase compensation

Input

PI_3

GA IN

C ON ST

Omeg a

Motor.ke

Motor.l1d

P Gain 13 /*20*/

I Gain 3 /*10 */

C ON ST

TR ef

TBar.TORQUE

GA IN

1/(1.5 * Motor.ke * Motor.p)

G(s)

GS1

-10.00

10.00

1.00

500.00m

操舵量

S _ROT B 1.P HI [deg

-7.60

7.55

1.00

500.00m

モータトルク [Nm]

Motor.mi

-1.00m

1.03

500.00m

30.00m

10.00m

20.00m

モータトルク [Nm]

Motor.mi

Motor Torque

(Zoom ）

( )

⎟

⎠

⎞

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

Primary progress compensation

• The oscillation frequency of the mechanical system was avoided and
the torque assistance was attained.

Steering Angle 10[deg]

Motor Torque [Nm]

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VHDL-AMS model can use AC simulation.

System stability : mechanics + controls

shaft

Motor

D2D

ROT

ROT_V

TBar

D2D1

theta

GAIN

theta

Input

CONST

GAIN

Input

GAIN

CONST

GAIN

CONST

GAIN

G(s)

dq_abc

1/(DC_bus/2)

Vref_u

Vref_v

Vref_w

abc_dq

PI_1

P_Gain 0.5

I_Gain 2

Omega

Idref

Motor.l1q

PI_3

P_Gain 13/*13*/

I_Gain 3 /*3*/

Motor.l1d

Psi

Motor.ke

Omega

Motor.p

TRef

TBar.TORQUE

1/(1.5 * Motor.ke * Motor.p)

GS1

ICA:

Friction:=8e-3

deadtime:=5u

DC_bus:=12

Vref_u

Vref_v

Vref_w

BodePlotSel9

dq_abc.d

dq_abc.q

Gain

Phase

100

10k

100k

100

10k

100k

136.82

0.00

50.00

100.00

136.82

0.00

50.00

100.00

44.85

-180.00

-135.00

-90.00

-45.00

0.00

44.85

-180.00

-135.00

-90.00

-45.00

0.00

f [Hz]

[dB]

[deg]

Transfer characteristic of control system

10.00u

1.00

200.00u

2.00m

20.00m

1.00

100.00k

20.00 200.00 2.00k

2DGraphSel5

dq_ab...

-3.14

3.14

1.00

100.00k

10.00 100.00 1.00k

2DGraphSel5

dq_ab...

GAIN

PHASE

Transfer characteristic of control system ( KP dependency)

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The modeling of side-force by a tire.

Slip rate

Side angle

Traction force, Side fo

rce [kgf]

Perpendicular load 380[kgf]

Side force

Slip rate

Slip

Vehicle speed

Slip angle

Rotational

Speed of tire

Load

Force of Rack F

Diagram of side force of Tire

Gap of a rack and rotational center : R
Sidewall equivalent radius : Rc

Ref. ISBN 4-381-08855-7

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VHDL-AMS code

)

(

)

(

Slip

lookup

−

∫

)

(

−

⋅

begin

T == R * F ;
V == omg * R ;

(vv'dot <

0.0

)

use

slip_rate == (vv-ww)/vv ;

else

slip_rate == (ww-vv)/ww ;

end use

;

beta == omg'integ ;
mur == lookup_SideFC(slip_rate,

abs

(beta)) ;

Fs == mur * mass *

9.8

* sign(beta);

J * omg'dot == (T- Fs*R) ;

end architecture

beh ;

Slip rate

• VHDL-AMS model expresses definitional equations directly.

Friction Coeff.

Equations

Translation <> Rotation

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Nonlinear side force model

-4.20

4.00

1.00

500.00m

TBar.TORQUE [Nm]

SPRING_ROTB2.TORQUE [Nm]

-4.20

4.00

1.00

500.00m

トーションバー・トルク

TBar.TORQUE [Nm]

SPRING_ROTB2.TORQUE [Nm]

Motor.mi

-4.20

4.00

1.00

500.00m

トーションバー・トルク

TBar.TORQUE [Nm]

SPRING_ROTB2.TORQUE [Nm]

Motor.mi

TR1

ROT2

TSF

tra

Wheel_dynamics

-35.00

34.80

-20.00

20.00

1.00

500.00m

タイヤ横力 [kgf]

Steering torque = side force torque

Steering torque reduces as 1/2

• Nonlinear side force mapping.
• Confirm reducing steering force by assist motor.

w/o Power Assist

with Assist

Side force of Tire [N]

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System Simulation

CONST

TRef

TBarAMS.m

TR1

ROT2

TSF

ROT1

ROT2

TSF

ROT

ROT_V

ROT

ROT_V

FM_ROT1

G(s)

ハンドル

操舵量

トーションバー

インタミ

ラック・ピニオン

反力

ピニオン

GAIN

1/2

AssistGain

WM_T

WM1

shaft

dcn

dcp

INV

Ave

Motor

tra

Tire

GAIN

DATAPAIRS1

Battery

SYM

100 %

MRV

Pulley_ratio

Engine

VM_Eng

ECU

DCp

Fuel_Calc

Name

Value

Fuel_Calc.fc

9.7746m

DCp

Energy Balanced Model

Mechanics

Power supply

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Components

•

Motor + Inverter

– Energy balanced model written by VHDL-AMS.

•

Power sources

– Battery : Automotive Library (Lead Acid battery)
– Alternator : Automotive Library (Averaged Model)
– Engine : Torque source (Throttle controlled torque source with

Torque-RPM lookup table)

– ECU : Analog PI control ( to keep RPM as idle )

MRV

X Y

Trq_per_ro

AxWM

ThrPct

DAMP_ROT1

INPUT
Power

Motor Power OUT

Motor Losses

Inverter Losses

Engine model

RPM vs. Torque

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High Accuracy Estimation of Efficiency

for Inverter Losses

for Motor Losses

• Device Level IGBT and Diodes

• Easy estimation by

RMxprt

Vce

Loss:ON

Loss:Off

200

Lcoil

Rcoil

ICA:

Rcoil := 178m

Lcoil

Lcoil :=2.46m

Pp := 4

Turns := 9

Pars := 2

500u

200

E G

AMuIfw

AMuIC

WiHE

WdHA

WiHC

WdHC

ViHC

VdHC

UiHC

UdHC

ViHE

VdHA

UiHE

UdHA

VccP

VccN

WiLC

WdLC

ViLC

VdLC

UiLC

UdLC

WiLE

WdLA

ViLE

VdLA

UiLE

UdLA

Sheet7

• Parasitic LCR with

Q3D

• Core Loss from

Maxwell 2D/3D

Speed

Efficiency

FEA

sourceA1

sourceA2

sourceB1

sourceB2

sourceC1

sourceC2

Magnet01

Magnet02

400 V

RA Ohm

LL H

LDUM H

Core Loss vs. time

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Energy Balanced model verification.

Motor Rotation Speed [RPM]

Motor Torque [Nm]

shaft

dcn

dcp

shaft

dcn

dcp

INV

Ave

Input :

Reference Torque

Equation

⋅

inv

motor

ref

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Simulation result : Battery Voltage

wEPS

woEPS

180.0

25.0

50.0

75.0

100.0

125.0

150.0

2.500

12.500

3.100

2.600

12.600

2.700

12.700

2.800

12.800

2.900

12.900

3.000

13.000

(1)

(2)

(1) : t= 30 : start EPS control
(2) : t=150 : end EPS control

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Simulation result : Engine Speed

wEPS

woEPS

180.0

25.0

50.0

75.0

100.0

125.0

150.0

700.0

100.0

200.0

300.0

400.0

500.0

600.0

wEPS

wo...

60.00

70.00

62.50

65.00

67.50

625.0

650.0

630.0

635.0

640.0

645.0

(1)

(2)

(1) : t= 30 : start EPS control
(2) : t=150 : end EPS control

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Fuel Consumption

wEPS

woEPS

180.0

25.0

50.0

75.0

100.0

125.0

150.0

700.0

100.0

200.0

300.0

400.0

500.0

600.0

MRV

Engine

VM Eng

ECU

Fuel Calc

• 4 cycle engine
• Displacement : 1800[cc]
• ideal Air-Fuel ratio : 14.7
• Specific gravity : C

7.5

13.5

Engine rotational speed

Total Fuel consumption @2.5[min]

]

[

With EPS

26.8

WO EPS

26.1

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Summary

• The construction method of the mechanical load model by

using SIMPLORER.

• By using VHDL-AMS, modeling with high degree of

freedom or more was able to be made easily.

• In addition, it introduced the continuousness to the system

simulation of power consumption and components
simulation.

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Conclusions

•

SIMPLORER can be as a communications tool that the designer of an
electric equipment and the designer of the regulating system guess the
function from the viewpoint of power consumption.

•

The equipment designer can optimize it by sharing the model under a more
concrete environment.

•

For a system designer, over-specked apparatus is presumed and the whole
cost can be reduced.

•

The model construction in standard language VHDL-AMS has a high ability
for such a demand, and the importance increases.

自動車工学入門：野崎博路著：山海堂 ISBN 4-381-08855-7

自動車工学 –基礎- ：：（社）自動車技術会 ISBN 4-915219-30-5

車両システムのダイナミクスと制御：（社）日本機会学会：養賢堂： ISBN 4-8425-9901-4

電動機制御工学〜可変速ドライブの基礎〜：松瀬貢規著：電気学会/オーム社 ISBN 978-4-88686-255-6

Ansoft, LLC Proprietary

• Thank you

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