Automotive Electrical and
Electromechanical System Design
Dr.-Ing. Uwe Knorr
Product Marketing Director
Ansoft Corporation
Pittsburgh, PA
Challenge #1:
Multi-Domain Design
Mechanical
Electro-
Chemical
Hydraulic
Electrical
Controls
Magnetic
Pneumatic
Thermal
Multi-Domain Design
Multiple Domains are interconnected and influence
each other
The electrical content of vehicles increases
More and more controls are involved
Electrical systems closely interact with other
domains
Electro-Chemical
Electro-Mechanical
Electro-Magnetic
Electro-Thermal
Challenge #2:
Multi-Level Design
Accuracy
Complexity
Details
#ofComponents
)()(
)(
)()(
)()(
)(
)()(
1
1
111
1
1
111
ttp
dt
td
Rtitv
ttp
dt
td
Rtitv
d
q
qq
q
d
dd
ψω
ψ
ψω
ψ
⋅⋅++⋅=
⋅⋅−+⋅=
EQU
X Y
NL
XY1
NL1
I_main
sp
vset
vbus
vbus := VM1.V
D1
CONST
CONST GAIN
I LIMIT
VBUS
VSET
ERR
GAIN1
INTG1 SUM1 LIMIT1
+
V
VM1
I1
GAIN
GAIN2
engine2generator
INREG
OUTREG
GAIN
GAIN3
GAIN
GAIN4
VBUS<VSET
VBUS>=VSET
Multi-Level Design
Different analyses require different model accuracy
levels
Different analyses require different algorithms
Different accuracy levels require different modeling
languages
Model exchange from one level to the next higher
level requires model extraction
Design information must be exchanged between
different design groups
Challenge #3:
Multi-Organizational Design
Tier II
Component
Tier I
Subsystem
OEM
System
Multi-Organizational Design
Geometry, Material,
Structure
Fundamental Physics,
DC, AC, TR, FEA, Stress
TIER II
Circuits, Block Diagrams,
State Machines, C-Code,
Lookup Tables
Controls, Circuit Design,
Statistical, Optimization,
AC, Short Transients
TIER I
System Models with
lookup tables minimum
parameters
Statistical, Worst Case,
Drive Cycle, FMEA, Long
Transients
OEM
ModelAnalysis
Design Challenges Today
Control
Electrical
Mechanical
Component
Supplier
System
Integrator
Tier 1
Supplier
Circuit
System
Component
Hydraulics
Tier 2
Supplier
Thermal
Magnetic
Need for Integration
Integration
Control
Electrical
Mechanical
Component
Supplier
System
Integrator
Tier 1
Supplier
Circuit
System
Component
Multi-Domain
Multi-Level
Multi-Organization
EM Design Environment
SIMPLORER Simulation Data Bus
Simulator Coupling Technology
Circuit
Simulator
Block Diagram
Simulator
State Machine
Simulator
Simulink
MathCad
Maxwell2D/3D
Electromagnetism
Electro mechanics
C/C++
Interface
Model Database
Electrical, Blocks, States, Machines, Automotive, Hydraulic,
Mechanics, Power, Semiconductors…
VHDL-AMS
Simulator
Integrated Design Environment
WIN/2000
WIN/XP
WIN/NT
Pentium
>256MB
Compatibility
MS-Office compatible
Read and write Excel, Access
Copy & Paste to and from Word, PowerPoint,
Excel…
Windows Printing Support
Data Format compatible
ASCII
Access (*.mdb)
Excel (*.xls)
CSV (*.csv)
Comtrade (*.cfg)
SPICE (*.out)
TEK – Oscilloscope data (*.dat)
Post Processing
IEEE 488.2 Data
Interface (GPIB)
Graphical and
numerical data
analysis and
representation
Power Module
Channel Calculator
FFT
Presentation Mode
Matlab® and
Mathcad®
Integration
Component Characterization
2D, 3D, multi
dimensional
lookup table
#
L1
#C1
NL
NL_Charact
YZ
X
V3DLUT
E1
Y t
V_LUT
M3 ~B
A
C
IM1
Y t
M_LUT1
• Characteristics
• Stimuli
• Loads
Data Acquisition
Data Transfer
Data Processing
State Machines
Behavioral Modeling
Smart models, state
dependent step size
modification
Event driven
modification of
topologies &
parameters
Online measurement
of characteristic
values
Relay Model
com
no
drvm
drvp
Relay
E1 R1
E2
S1
LCoil := 250m
RSup := 680
ROn := 5m
tdbrk := 8m
tdmk := 12m
VPULL := 7
VDROP := 2
RCoil := 3
CCoil := 40n
E5
S3
E6
R3
Relay.Iin
Relay.Iout
t
14.00
-2.00
2.00
4.00
6.00
8.00
10.00
0 0.600.20 0.40
R1pNoRs1
Final Relay Model
Relay Macro
Symbol Editor
Relay Model
Rsup
LCoil
RCoil
ROn
S1
drvp
drvm
no
com
ON_DIS
DELAY_OFF_ON
DELAY_ON_OFFLCoil.I >= IPULL
LCoil.I <= IDROP
lon
loff
OFF_DIS
DEL: loff##tdbrk
DEL: lon##tdmk
EQU
IPULL := VPULL/RCoil.R
IDROP := VDROP/RCoil.R
A
+
AM1
+
V
VM1
CCoil
• Fast!
• Easy model
generation
• Good numerical
behavior
Block Diagrams
Analog and Digital Controller Modeling
CONTR_OUT
op2 := 2.5
ymax2 := 1
op1 := -2.5
ymax1 := -1
-16.66m
N"GSMP_1" LIMITER
u_limit := 20
l_limit := 0
EXT
P_GAIN
KP := 50
I_GAIN
KI := 20
P
I
LIMIT
EXT
CONST
NSET
16.666667
Each block
can be
assigned an
individual
sampling time
or run with
system time
step
PI
C/C++
Code
NL
DC Motor Drive System
L_R
L_S
L_T
ET1
ET2
ET3
CD
1m
R_R
R_S
R_T
Yt
LOAD
CONTR_OUT
THRES2 := 2.5
VAL2 := 1
THRES1 := -2.5
VAL1 := -1
-16.66m
DCM.N P_GAIN
KP := 50
I_GAIN
KI := 20
LIMITER
UL := 20
LL := 0
10m
GAIN GAIN
I
LIMIT
CONST
N_REF
16.6667
0.3m
M
DCM
RA := 1.2
LA := 9.5m
KE := 0.544
J := 4m
A
+
AM1D1 D2 D3
D4 D5 D6
D7
TR
CONST
CLOCK
.1m
Wiper System
Wiper System – Result
Motor Torque and Load Torque
Motor Speed
N_REF
N
T
20.00
-10.00 -10.00
0 0
0
0
100.00m
100.00m
50.00m
50.00mT
15.00
0
0
10.00 10.00
0
0
100.00m
100.00m
50.00m
50.00m
Automotive Library
Power Storages
Wires
Battery - Basic Model
Battery
Fuel Cell
Wire - Thermal static
Wire - Thermal dynamic
Wire - Thermal dynamic II
Wire with Thermal Pin
Wire - Advanced
Wire - Advanced II
Gauge based
Fuses
Wire - Thermal static
Wire - Thermal dynamic
Wire - Thermal dynamic II
Wire with Thermal Pin
Wire - Advanced
Wire - Advanced II
Fuse - Single Element
Fuse - Double Element
Fuse - Advanced
PPTC (Three RC combinations)
PPTC (Two RC Combinations)
Lamps
Lamp - Filament
Lamp - Single Filament
Lamp - Double Filament
Lamp - Advanced
Relays
Relay - Normally Open
Relay - Normally Closed
Relay - One Pole, Two Throws
Relay - Two Poles, Two Throws
Relay - Two Poles, Cross-Strap
Spark Plugs
Spark Plug
Machines
Alternator - Transient Model
Alternator - Average Model
Alternator - Current Source
Starter
DC Machine
Mechanical Models
Inertia
Friction
Fan
Ideal Gearbox
Gearbox with Losses
PWM Models
PWM
PWM Switch
PWM Load
Flasher Switch
Connectors
Inline Terminal Pair
Eyelet Terminal
Engine Models
Engine - Speed Source
Engine - Dynamic Model
Applications:
• Electrical Distribution
System of Vehicles
• Power Management
• Drive Cycle Analysis
• FMEA
• Statistical Analyses
Industries:
• Automotive
Manufacturer
• EV/EHV
• Aerospace
• Defense
• Ship Building Industry
Automotive System Library
Automotive Library
Yt
Y t
Battery
- +
Engine Block Ground
Chassis
Ground
To Hazzard Flasher
To Head Lamp Switch
Lamp Switch
battery1
fuse1_5Amp
fuse2_15Amp
rlyno1
S1
TS1_HIGH_LOW_Beams_Switch
Low
High
Low High
High
Low
RH HeadLamp
LH HeadLamp
Tail
Lamps
Turn Signal
Y t
Y t
QuickGraph1
N0161.V
t
14.00
-2.00
2.00
6.00
10.00
0 60.0020.00 40.00
S2
S3
D1 D2
t
60s
itp11
itp19
Probe1
t
7.50
-2.50
0
5.00
0 60.0025.00 50.00
Exterior Lighting System
Inrush Currents
Turn Signal Voltages
Automotive Library
Benefits
Easy to use and intuitive graphical modeling
Easy parameterization using Wizard technology
Statistical analyses, optimization and parameter variations
Characterization tool for fuses
Multiple model levels for components
Web based example database with jump start projects
Animated symbols for easy visual inspection
Electro-Chemical Components
Lead Acid BatteryFuel Cell
Fuel
Cell
+-
Battery
- +
EV/EHV – Charging System
ST_r1
L1
0
0.1m
RLoad
RL
TR1
D1
ICA:
L1.I>=I_command
ST_r1.VAL>=0.99 and L1.I<I_command
On
SET: cs:=1
Off
SET: cs:=0
period := 20u
Off2
SET: RL:=10
t>3m t>12m
SET: RL:=5 SET: RL:=5
t>0.0025
SET: I_command:=10 SET: I_command:=15
VM1.V
t
6.10
5.10
5.20
5.30
5.40
5.50
5.60
5.70
5.80
5.90
6.00
0 20.00m2.50m 5.00m 7.50m 10.00m 12.50m 15.00m
+
V
VM1
L1.I
t
16.00
0
2.00
4.00
6.00
8.00
10.00
12.00
14.00
0 20.00m2.50m 5.00m 7.50m 10.00m 12.50m 15.00m
t0 20.00m2.50m 5.00m 7.50m 10.00m 12.50m 15.00m
Output Voltage
Input Voltage
Inductor Current
Transistor
Control modeled
using state
machines
Load resistance
and reference
current
modification
modeled using
state machines
Boost
Converter
Fuel
Cell
+ -
FUELCELL_A2
Battery
-+
LBATT_A2
Multi-Domain Design
• Hydraulics
• VHDL-AMS
• Mechanics
• Electro Mechanical
• Magnetics
• …
Hydraulic Library
1 0
3
r1
pk_1
50
Hydraulic Library
P1
PIPE
Level1
PIPE1
Sharp-Edge
Generic
OR_SE1
VOL_ACT1
MASS_TRB1
LIMIT_TRB1
F
LIMIT_TRB1.SUL
MASS_TRB1.S
t
15.00m
0
10.00m
0 1.000.50
Power Library
Power Library
Power System and Cable Models
Single Phase Power Supply
Ideal Three Phase Power Supply
Three Phase Power Supply with Impedance
WIRE - Gamma Model
Wire T-Model
Inverter Topologies
Line-commutated Converters
B2 Diode Bridge
B2 Fully Controlled
B2 Half-Controlled, Symmetrical
B2 Half-Controlled, Asymmetrical
B6 Diode Bridge
Two Level Inverter Equivalent Circuit
Three Phase Two Level Inverter
Single Phase Two Level Inverter
Three Phase Three Level Inverter
Single Phase Three Level Inverter
Control Algorithms
Two Level Square Wave
Two Level Natural Sampling
Three Level Single Phase
Three Level Three Phase
Load Models
Three Level Single Phase NS
Three Level Three Phase NS
Four Quadrant Current Control
Four Quadrant Natural Sampling
B6 Thyristor Bridge
B6 Bridges - Inverse Parallel Connection
B12 Diode Bridge
B12 Thyristor Bridge Parallel Connection
B12 Thyristor Bridge Cascade
B24 Thyristor Bridge
Single Phase A.C. Chopper
Three Phase A.C. Chopper
DC Link
Three Phase RL Load
Logic
Dead Time
Applications:
• AC/DC Converters
• Inverters (DC/AC)
• Drive Systems
• Power Quality
• Alternative Power
Industries:
• Industrial Automation
• Drives Manufacturers
• EV/EHV
• Power Conversion
• Power Quality
Power Library
Us1
Us2
Us3
Us1
Us2
Us3
M
ω ω2
C
J1 J2
ω1
M 1 M 2
+
V
CONST
KONST1
SPR1
ein_aus
2L3_GTOS
g_r1
g_r2
g_s1
g_s2
g_t1
g_t2
2L_NSAMP
2-level natural sampling
Machine Characteristic
1.60k
-200.00
0
200.00
400.00
600.00
800.00
1.00k
1.20k
1.40k
-173.34 359.120 200.00
Stator Current
asm_k_g22.Is_d
asm_k_g22.Is_q
t
200.00
-1.40k
0
-1.20k
-1.00k
-800.00
-600.00
-400.00
-200.00
0 1.501.00
Rotor Current
asm_k_g22.Ir_d
asm_k_g22.Ir_q
t
1.40k
-200.00
0
200.00
400.00
600.00
800.00
1.00k
1.20k
0 1.501.00
CONST
Omega
Uf
Ua
M
ω
Torque
350.00
-150.00
0
-100.00
100.00
200.00
300.00
0 1.501.00
Direct inverter
driven squirrel
cage induction
machine with
2-level natural
sampling
control and
mechanical
load
Power Library
Benefits
Predefined macro models of frequently used power
electronic topologies
Includes common control algorithms
Auxiliary elements, such as power grid models and loads
System level models for rapid computation of overall
system behavior, power quality and control algorithms
Easy and intuitive graphical building blocks
Mechanical Elements Library
Rotational
Mass
Translational
Mass
Coordinate Transformation
Rotational-Rotational
Rotational-Translational
Translational-Rotational
SYMP Synchronous Machine Permanent Excitation
SYMP Synchronous Machine Permanent Excitation w Damper
Electrical Machines
DCMP DC-Machine Permanent Excitation
ASMS Slip Ring Induction Machine
Rigidity
Rigidity
Torque Source
Ground
Angular Velocity Source
Velocity Source
Ground
Force Source
Translational-Translational
Mechanical Systems
Applications:
• Drive Trains
• Electro-Hydraulic
Systems
• Electro-Mechanical
Systems
• Load Variations
Industries:
• Automotive Suppliers
• Drive Manufacturers
• Industrial Automation
• Defense
• Aerospace
Mechanical Elements Library
ET1
Square_wave1.VAL
M
DCMP
Dcmp1
J := 2m
STF
Stf1 M
DCMP
Dcmp2
J := 2m
M
DCMP
Dcmp3
J := 2m
STF
Stf2
J
Mas1
J := 10m
Dcmp1.VA
Dcmp2.VA
Dcmp3.VA
t
250.00
-250.00
0
-100.00
100.00
0 1.000.50
Dcmp1.OMEGA
Dcmp2.OMEGA
Dcmp3.OMEGA
Mas1.OMEGA
t
200.00
-200.00
0
-100.00
100.00
0 1.000.50
Mas1.MACX
t
1.25k
-1.25k
0
-500.00
500.00
0 1.000.50
Motor-generator
combination driving a
mass with limitations
Mechanical Elements Library
Benefits
Non-linear friction models incl. stick friction
Non-linear rigidity models incl. backlash
Fast computing 1D modeling approach based on
SIMPLORER C-Code interface
Electrical Machine model implementation with mechanical
pins provide connectivity between electrical and
mechanical world
Schematic based graphical modeling with mechanical
building blocks
VHDL-AMS
Block Diagram
Simulator
State Flow
Simulator
SIMPLORER Simulation Data Bus
MathCadSimulink Sim-Interface
External Simulators
Internal Simulators
Multi-Organizational Design
Digital
Solver
Circuit
Elements
Analog
Solver
AMS
VHDL-AMS
VHDL-AMS Schematic
Fully
supported by
SIMPLORER
Schematic
Embedded
Editor with
Syntax
coloring
allows to
create models
on sheet and
in the
ModelAgent
VHDL-AMS Code for a Resistor
ENTITY Resistor IS
PORT (
QUANTITY r : REAL := 1.0e+03; -- Default = 1 K
TERMINAL p,m : ELECTRICAL);
END ENTITY Resistor;
ARCHITECTURE Rbehav1 OF Resistor IS
QUANTITY voltage ACROSS current THROUGH p TO m;
BEGIN
current == voltage/r;
END behav;
mp
Resistor
r := 1.0e3
Rbehav1
r
Architecture 3
Architecture 2
Architecture 1
Entity and Architecture
Entity
Interface description of a
subsystem or physical
device
Specifies input and output
ports to the model
Architecture
Behavior description of the
model
Can be dataflow,
structural, procedural, etc
Modeling can deal with
both analog (continuous)
and digital (discrete)
domains
output ports
input ports
inout ports
Architecture 2
Architecture 1
Entity
VHDL-AMS Basic Library
OPEN!
VHDL – Digital Systems
A.val
B.val
C.val
SUM.y
CARRY.y
t0 40m2m 4m 6m 8m 10m 12m 14m 16m 18m 20m 22m 24m 26m 28m 30m 32m 34m 36m 38m
CLK
A
CLK
B
CLK
C
XOR2
XOR2
AND2
AND2
AND2
Two bit adder with Carry
Sum
Carry
OR3
VHDL – Digital Systems
Complete Automotive System Analysis across Domains
• ASICs
• Micro Controller
• FPGAs …
ECU
PTCU
MCU
VHDL
VHDL-AMS Multi Domain Design
L
dia := 1
len := 1/4
rho := MATH_PI
vol := 1
b := 1
k := 10
EQU
crank_radius:= 0.2
pipe_area:= 0.05
Fluidic
torque force pressure
flow_meter rhyd1 lhyd1
chyd1
spring_rotb damp_rotb T
fm_rotb
ω
+
vm_rotb
ω
+
v_rotb
mass_rotb
CONST CONST
1/pipe_areacrank_radius
P
Spped
damp_rotb.omega
t [s]
40
-40
0
-25
25
0 0.1k50
QuickGraph2
flow_meter.q
t [s]
1Meg
-1Meg
0
0 0.1k50
Mechanic
VHDL-AMS
Component
Providers
Subsystem
Providers -
Suppliers
OEM
System Simulation
Drive Cycles
Fuel Economy
Multi Organization Design
Power Train
Electrical System
Sensors …
VHDL - AMS
VHDL - AMS
Solenoids, Motors,
Battery, Sensors, Semiconductors,
Fuse …
DC Drive – VHDL-AMS Controller
L_R
0.3m
L_S
L_T
ET1
ET2
ET3
R_R
10m
R_S
R_T
t [s]
4.00e+001
0
2.00e+001
0
0
0.2
0.2
0.1
0.1
t [s]
1.50e+003
0
1.00e+003
0
0
0.2
0.2
0.1
0.1
motor
current
speed and
reference speed
LIMIT
LIMITER
LL := 0
UL := 20
GAIN
CONTR_OUT
THRES1 := -2.5
VAL1 := -1
THRES2 := 2.5
VAL2 := 1
CONST
N_REF
1000
M
DCM
J := 4m
LA := 9.5m
RA := 1.2
KE := 0.544
A
AM1
t [s]
1.00e+003
0
5.00e+002
0
0
0.2
0.2
0.1
0.1
DCM.MI [N·m]
TLoad.VAL
t [s]
2.00e+001
-1.00e+001
0
0
0
0.2
0.2
0.1
0.1
motor torque
and
load torque
DC Link
Voltage and
Current
D7
TR
TLoad
3
Bridge1
PIC
VHDL-AMS
DC Drive – VHDL-AMS Controller
ODE
Non-
Electrical
Elements
External
Simulators
Electrical
Components
µ-Controller
Code
C/C++ Interface
C/C++ Interface
®
System Simulation
The Multi Domain Simulator
C/C++ make
Dynamic
Link
Library
.dll
Symbol
Library
Symbol Editor
DC Drive – C-Code Controller
L_R
0.3m
L_S
L_T
ET1
ET2
ET3
R_R
10m
R_S
R_T
DCM.IA [A]
t [s]
3.00e+001
0
2.00e+001
0
0
0.2
0.2
0.1
0.1
DCM.N [rpm]
N_REF.VAL
t [s]
1.50e+003
0
1.00e+003
0
0
0.2
0.2
0.1
0.1
motor
current
speed and
reference speed
LIMIT
LIMITER
LL := 0
UL := 20
GAIN
CONTR_OUT
THRES1 := -2.5
VAL1 := -1
THRES2 := 2.5
VAL2 := 1
CONST
N_REF
1000
M
DCM
J := 4m
LA := 9.5m
RA := 1.2
KE := 0.544
A
AM1
Bridge1.Vout [V]
Bridge1.Iout [A]
t [s]
1.00e+003
0
5.00e+002
0
0
0.2
0.2
0.1
0.1
DCM.MI [N·m]
TLoad.VAL
t [s]
2.00e+001
-1.00e+001
0
0
0
0.2
0.2
0.1
0.1
motor torque
and
load torque
DC Link
Voltage and
Current
D7
TR
TLoad
3
Bridge1
PIC
PIC1
IGain := 2
PGain := 3
C-Code
DC Drive – C-Code Controller
SIM2SIM
SIMPLORER to Simulink Interface
SIMPLORER
Simulink
• Co-Simulation Interface
• Link blocks in both
packages
• Using SIMPLORER's
external simulator
integration interface and
S-function in Matlab
• Co-Simulation Interface
is an open API that can
be used for other
simulation packages
Drive System Control
L_R
0.3m
L_S
L_T
ET1
ET2
ET3
R_R
10m
R_S
R_T
GAIN
P_GAIN
KP := 3
I
I_GAIN
KI := 2
LIMIT
LIMITER
LL := 0
UL := 20
CONTR_OUT
THRES1 := -2.5
VAL1 := -1
THRES2 := 2.5
VAL2 := 1
CONST
N_REF
1000
M
DCM
J := 4m
LA := 9.5m
RA := 1.2
KE := 0.544
A
+
AM1
D7
TR
CONST
CLOCK
.1m
3
Bridge1
TLoad
Drive System Control
L_R
0.3m
L_S
L_T
ET1
ET2
ET3
R_R
10m
R_S
R_T
M
DCM
J := 4m
LA := 9.5m
RA := 1.2
KE := 0.544
D7
TR
3
Bridge1
TLoad
SiM2SiMSIMPLORER Link Interface

SiM2SiM
50
SIM2SIM1
SIM2SIM1.CS
Drive System Control
Complete Vehicle Simulation
SIMPLORER – Advisor Link
SIMPLORER – Advisor Link
SIMPLORER Single Voltage Electrical Automobile System Template
voltage
regulator curve
Regulator
Generator
p
mGeneratorPower
p
m
BatteryPower
RearDefrost FrontHVAC
Engine BrakeLightsMisc ExternalLights
HeatedSeats
FrontWipers
RearWipers Radio
TurnSignalRadiatorFan
RearHVAC
generic
generator
generator
Battery
Loads
Starter
p
m
®
Simulation properties:
Step width max 100m
Step width min 100u
Simulation end time 1369
GAIN
Battery
-+
pm
LoadPower
+
V
VM1
A
+
AM1
generic
generator
generator1
SiM2SiMSIMPLORER Link Interface

SiM2SiM
50
Results
Generator Current
AM1.I
t
100.00
-50.00
0
0 793.91500.00
Speed in RPM
Speed
t
4.00k
-2.00k
0
2.50k
0 793.91500.00
Bus Voltage
VM1.V
t
13.00
11.50
12.00
0 793.91500.00
Load Power
LoadPower
t
500.00
-1.50k
0
-1.00k
0 793.91500.00
Complete Set of Analyses
DC Analysis
NINV
INV
OUT
+
-
NSC_LM_7411
NINV
INV
OUT
+
-
NSC_LM_7412
NINV
INV
OUT
+
-
NSC_LM_7413
R1
10k
R2
10k
R3
10k
R4
10k
Rp
15916
R1p
10k
C1
100p
C2
1n
E1 +
V VM
Rfp
30k
R9
30k
R
15916
OP: -0.00100994 V
OP: -0.00405477 V
OP: -7.9752e-006 V
OP: 0.999992 V
OP: 0.998936 V
OP: 3.99573 V
OP: 0.000980576 V
OP: -3.98873 V
OP: 1 V
E1 1
R1
500m
L1
R2 16
L2
C1 132.6u
31.83m
3.18m
OP: 0 V
OP: 0.969697 V
OP: 0.969697 V
OP: 1 V
Complete Set of Analyses
Bode
C1.VGain
Phase
100
100
1k
1k
200
200
300
300
400
400
500
500
600
600
700
700
800
800
900
900
100
100
1k
1k
200
200
300
300
400
400
500
500
600
600
700
700
800
800
900
900
-28.01
-20.00
0.00
20.00
-28.01
-20.00
0.00
20.00
0.00
0.79
1.57
2.36
3.14
0.00
0.79
1.57
2.36
3.14
f [Hz]
f [Hz]
[dB]
[rad]
AC Analysis
Experiments
1D, 2D & 3D Parameter Sweep
Monte Carlo
Sensitivity
Worst Case
Optimization
Simplex Algorithm
Successive Approximation
Genetic Algorithms
Electrical Mechanical
ThermalMagneticLogic
Hydraulic
Component
Circuit
Sub-System
System
OEM
Supplier
VHDL-AMS
Block Diagrams/State Machines
FEA
Disconnected Technologies
Circuits
FEA
VHDL-AM
S
Circuits
Block
D
iagram
s/
State
M
achines
Integrated Technologies
Simulator
Coupling
Matlab/
Simulink
MathCAD
Co-Simulation
Advisor
…
Integrated Design Environment
Efficiency
Com
m
unication
Accuracy
Standards

Automotive electrical and electromechanical system design

  • 1.
    Automotive Electrical and ElectromechanicalSystem Design Dr.-Ing. Uwe Knorr Product Marketing Director Ansoft Corporation Pittsburgh, PA
  • 2.
  • 3.
    Multi-Domain Design Multiple Domainsare interconnected and influence each other The electrical content of vehicles increases More and more controls are involved Electrical systems closely interact with other domains Electro-Chemical Electro-Mechanical Electro-Magnetic Electro-Thermal
  • 4.
    Challenge #2: Multi-Level Design Accuracy Complexity Details #ofComponents )()( )( )()( )()( )( )()( 1 1 111 1 1 111 ttp dt td Rtitv ttp dt td Rtitv d q qq q d dd ψω ψ ψω ψ ⋅⋅++⋅= ⋅⋅−+⋅= EQU XY NL XY1 NL1 I_main sp vset vbus vbus := VM1.V D1 CONST CONST GAIN I LIMIT VBUS VSET ERR GAIN1 INTG1 SUM1 LIMIT1 + V VM1 I1 GAIN GAIN2 engine2generator INREG OUTREG GAIN GAIN3 GAIN GAIN4 VBUS<VSET VBUS>=VSET
  • 5.
    Multi-Level Design Different analysesrequire different model accuracy levels Different analyses require different algorithms Different accuracy levels require different modeling languages Model exchange from one level to the next higher level requires model extraction Design information must be exchanged between different design groups
  • 6.
    Challenge #3: Multi-Organizational Design TierII Component Tier I Subsystem OEM System
  • 7.
    Multi-Organizational Design Geometry, Material, Structure FundamentalPhysics, DC, AC, TR, FEA, Stress TIER II Circuits, Block Diagrams, State Machines, C-Code, Lookup Tables Controls, Circuit Design, Statistical, Optimization, AC, Short Transients TIER I System Models with lookup tables minimum parameters Statistical, Worst Case, Drive Cycle, FMEA, Long Transients OEM ModelAnalysis
  • 8.
    Design Challenges Today Control Electrical Mechanical Component Supplier System Integrator Tier1 Supplier Circuit System Component Hydraulics Tier 2 Supplier Thermal Magnetic
  • 9.
    Need for Integration Integration Control Electrical Mechanical Component Supplier System Integrator Tier1 Supplier Circuit System Component Multi-Domain Multi-Level Multi-Organization
  • 10.
    EM Design Environment SIMPLORERSimulation Data Bus Simulator Coupling Technology Circuit Simulator Block Diagram Simulator State Machine Simulator Simulink MathCad Maxwell2D/3D Electromagnetism Electro mechanics C/C++ Interface Model Database Electrical, Blocks, States, Machines, Automotive, Hydraulic, Mechanics, Power, Semiconductors… VHDL-AMS Simulator
  • 11.
  • 12.
    Compatibility MS-Office compatible Read andwrite Excel, Access Copy & Paste to and from Word, PowerPoint, Excel… Windows Printing Support Data Format compatible ASCII Access (*.mdb) Excel (*.xls) CSV (*.csv) Comtrade (*.cfg) SPICE (*.out) TEK – Oscilloscope data (*.dat)
  • 13.
    Post Processing IEEE 488.2Data Interface (GPIB) Graphical and numerical data analysis and representation Power Module Channel Calculator FFT Presentation Mode Matlab® and Mathcad® Integration
  • 14.
    Component Characterization 2D, 3D,multi dimensional lookup table # L1 #C1 NL NL_Charact YZ X V3DLUT E1 Y t V_LUT M3 ~B A C IM1 Y t M_LUT1 • Characteristics • Stimuli • Loads Data Acquisition Data Transfer Data Processing
  • 15.
    State Machines Behavioral Modeling Smartmodels, state dependent step size modification Event driven modification of topologies & parameters Online measurement of characteristic values
  • 16.
    Relay Model com no drvm drvp Relay E1 R1 E2 S1 LCoil:= 250m RSup := 680 ROn := 5m tdbrk := 8m tdmk := 12m VPULL := 7 VDROP := 2 RCoil := 3 CCoil := 40n E5 S3 E6 R3 Relay.Iin Relay.Iout t 14.00 -2.00 2.00 4.00 6.00 8.00 10.00 0 0.600.20 0.40 R1pNoRs1 Final Relay Model Relay Macro Symbol Editor
  • 17.
    Relay Model Rsup LCoil RCoil ROn S1 drvp drvm no com ON_DIS DELAY_OFF_ON DELAY_ON_OFFLCoil.I >=IPULL LCoil.I <= IDROP lon loff OFF_DIS DEL: loff##tdbrk DEL: lon##tdmk EQU IPULL := VPULL/RCoil.R IDROP := VDROP/RCoil.R A + AM1 + V VM1 CCoil • Fast! • Easy model generation • Good numerical behavior
  • 18.
    Block Diagrams Analog andDigital Controller Modeling CONTR_OUT op2 := 2.5 ymax2 := 1 op1 := -2.5 ymax1 := -1 -16.66m N"GSMP_1" LIMITER u_limit := 20 l_limit := 0 EXT P_GAIN KP := 50 I_GAIN KI := 20 P I LIMIT EXT CONST NSET 16.666667 Each block can be assigned an individual sampling time or run with system time step PI C/C++ Code NL
  • 19.
    DC Motor DriveSystem L_R L_S L_T ET1 ET2 ET3 CD 1m R_R R_S R_T Yt LOAD CONTR_OUT THRES2 := 2.5 VAL2 := 1 THRES1 := -2.5 VAL1 := -1 -16.66m DCM.N P_GAIN KP := 50 I_GAIN KI := 20 LIMITER UL := 20 LL := 0 10m GAIN GAIN I LIMIT CONST N_REF 16.6667 0.3m M DCM RA := 1.2 LA := 9.5m KE := 0.544 J := 4m A + AM1D1 D2 D3 D4 D5 D6 D7 TR CONST CLOCK .1m Wiper System
  • 20.
    Wiper System –Result Motor Torque and Load Torque Motor Speed N_REF N T 20.00 -10.00 -10.00 0 0 0 0 100.00m 100.00m 50.00m 50.00mT 15.00 0 0 10.00 10.00 0 0 100.00m 100.00m 50.00m 50.00m
  • 21.
    Automotive Library Power Storages Wires Battery- Basic Model Battery Fuel Cell Wire - Thermal static Wire - Thermal dynamic Wire - Thermal dynamic II Wire with Thermal Pin Wire - Advanced Wire - Advanced II Gauge based Fuses Wire - Thermal static Wire - Thermal dynamic Wire - Thermal dynamic II Wire with Thermal Pin Wire - Advanced Wire - Advanced II Fuse - Single Element Fuse - Double Element Fuse - Advanced PPTC (Three RC combinations) PPTC (Two RC Combinations) Lamps Lamp - Filament Lamp - Single Filament Lamp - Double Filament Lamp - Advanced Relays Relay - Normally Open Relay - Normally Closed Relay - One Pole, Two Throws Relay - Two Poles, Two Throws Relay - Two Poles, Cross-Strap Spark Plugs Spark Plug Machines Alternator - Transient Model Alternator - Average Model Alternator - Current Source Starter DC Machine Mechanical Models Inertia Friction Fan Ideal Gearbox Gearbox with Losses PWM Models PWM PWM Switch PWM Load Flasher Switch Connectors Inline Terminal Pair Eyelet Terminal Engine Models Engine - Speed Source Engine - Dynamic Model Applications: • Electrical Distribution System of Vehicles • Power Management • Drive Cycle Analysis • FMEA • Statistical Analyses Industries: • Automotive Manufacturer • EV/EHV • Aerospace • Defense • Ship Building Industry Automotive System Library
  • 22.
    Automotive Library Yt Y t Battery -+ Engine Block Ground Chassis Ground To Hazzard Flasher To Head Lamp Switch Lamp Switch battery1 fuse1_5Amp fuse2_15Amp rlyno1 S1 TS1_HIGH_LOW_Beams_Switch Low High Low High High Low RH HeadLamp LH HeadLamp Tail Lamps Turn Signal Y t Y t QuickGraph1 N0161.V t 14.00 -2.00 2.00 6.00 10.00 0 60.0020.00 40.00 S2 S3 D1 D2 t 60s itp11 itp19 Probe1 t 7.50 -2.50 0 5.00 0 60.0025.00 50.00 Exterior Lighting System Inrush Currents Turn Signal Voltages
  • 23.
    Automotive Library Benefits Easy touse and intuitive graphical modeling Easy parameterization using Wizard technology Statistical analyses, optimization and parameter variations Characterization tool for fuses Multiple model levels for components Web based example database with jump start projects Animated symbols for easy visual inspection
  • 24.
    Electro-Chemical Components Lead AcidBatteryFuel Cell Fuel Cell +- Battery - +
  • 25.
    EV/EHV – ChargingSystem ST_r1 L1 0 0.1m RLoad RL TR1 D1 ICA: L1.I>=I_command ST_r1.VAL>=0.99 and L1.I<I_command On SET: cs:=1 Off SET: cs:=0 period := 20u Off2 SET: RL:=10 t>3m t>12m SET: RL:=5 SET: RL:=5 t>0.0025 SET: I_command:=10 SET: I_command:=15 VM1.V t 6.10 5.10 5.20 5.30 5.40 5.50 5.60 5.70 5.80 5.90 6.00 0 20.00m2.50m 5.00m 7.50m 10.00m 12.50m 15.00m + V VM1 L1.I t 16.00 0 2.00 4.00 6.00 8.00 10.00 12.00 14.00 0 20.00m2.50m 5.00m 7.50m 10.00m 12.50m 15.00m t0 20.00m2.50m 5.00m 7.50m 10.00m 12.50m 15.00m Output Voltage Input Voltage Inductor Current Transistor Control modeled using state machines Load resistance and reference current modification modeled using state machines Boost Converter Fuel Cell + - FUELCELL_A2 Battery -+ LBATT_A2
  • 26.
    Multi-Domain Design • Hydraulics •VHDL-AMS • Mechanics • Electro Mechanical • Magnetics • …
  • 27.
  • 28.
  • 29.
    Power Library Power Library PowerSystem and Cable Models Single Phase Power Supply Ideal Three Phase Power Supply Three Phase Power Supply with Impedance WIRE - Gamma Model Wire T-Model Inverter Topologies Line-commutated Converters B2 Diode Bridge B2 Fully Controlled B2 Half-Controlled, Symmetrical B2 Half-Controlled, Asymmetrical B6 Diode Bridge Two Level Inverter Equivalent Circuit Three Phase Two Level Inverter Single Phase Two Level Inverter Three Phase Three Level Inverter Single Phase Three Level Inverter Control Algorithms Two Level Square Wave Two Level Natural Sampling Three Level Single Phase Three Level Three Phase Load Models Three Level Single Phase NS Three Level Three Phase NS Four Quadrant Current Control Four Quadrant Natural Sampling B6 Thyristor Bridge B6 Bridges - Inverse Parallel Connection B12 Diode Bridge B12 Thyristor Bridge Parallel Connection B12 Thyristor Bridge Cascade B24 Thyristor Bridge Single Phase A.C. Chopper Three Phase A.C. Chopper DC Link Three Phase RL Load Logic Dead Time Applications: • AC/DC Converters • Inverters (DC/AC) • Drive Systems • Power Quality • Alternative Power Industries: • Industrial Automation • Drives Manufacturers • EV/EHV • Power Conversion • Power Quality
  • 30.
    Power Library Us1 Us2 Us3 Us1 Us2 Us3 M ω ω2 C J1J2 ω1 M 1 M 2 + V CONST KONST1 SPR1 ein_aus 2L3_GTOS g_r1 g_r2 g_s1 g_s2 g_t1 g_t2 2L_NSAMP 2-level natural sampling Machine Characteristic 1.60k -200.00 0 200.00 400.00 600.00 800.00 1.00k 1.20k 1.40k -173.34 359.120 200.00 Stator Current asm_k_g22.Is_d asm_k_g22.Is_q t 200.00 -1.40k 0 -1.20k -1.00k -800.00 -600.00 -400.00 -200.00 0 1.501.00 Rotor Current asm_k_g22.Ir_d asm_k_g22.Ir_q t 1.40k -200.00 0 200.00 400.00 600.00 800.00 1.00k 1.20k 0 1.501.00 CONST Omega Uf Ua M ω Torque 350.00 -150.00 0 -100.00 100.00 200.00 300.00 0 1.501.00 Direct inverter driven squirrel cage induction machine with 2-level natural sampling control and mechanical load
  • 31.
    Power Library Benefits Predefined macromodels of frequently used power electronic topologies Includes common control algorithms Auxiliary elements, such as power grid models and loads System level models for rapid computation of overall system behavior, power quality and control algorithms Easy and intuitive graphical building blocks
  • 32.
    Mechanical Elements Library Rotational Mass Translational Mass CoordinateTransformation Rotational-Rotational Rotational-Translational Translational-Rotational SYMP Synchronous Machine Permanent Excitation SYMP Synchronous Machine Permanent Excitation w Damper Electrical Machines DCMP DC-Machine Permanent Excitation ASMS Slip Ring Induction Machine Rigidity Rigidity Torque Source Ground Angular Velocity Source Velocity Source Ground Force Source Translational-Translational Mechanical Systems Applications: • Drive Trains • Electro-Hydraulic Systems • Electro-Mechanical Systems • Load Variations Industries: • Automotive Suppliers • Drive Manufacturers • Industrial Automation • Defense • Aerospace
  • 33.
    Mechanical Elements Library ET1 Square_wave1.VAL M DCMP Dcmp1 J:= 2m STF Stf1 M DCMP Dcmp2 J := 2m M DCMP Dcmp3 J := 2m STF Stf2 J Mas1 J := 10m Dcmp1.VA Dcmp2.VA Dcmp3.VA t 250.00 -250.00 0 -100.00 100.00 0 1.000.50 Dcmp1.OMEGA Dcmp2.OMEGA Dcmp3.OMEGA Mas1.OMEGA t 200.00 -200.00 0 -100.00 100.00 0 1.000.50 Mas1.MACX t 1.25k -1.25k 0 -500.00 500.00 0 1.000.50 Motor-generator combination driving a mass with limitations
  • 34.
    Mechanical Elements Library Benefits Non-linearfriction models incl. stick friction Non-linear rigidity models incl. backlash Fast computing 1D modeling approach based on SIMPLORER C-Code interface Electrical Machine model implementation with mechanical pins provide connectivity between electrical and mechanical world Schematic based graphical modeling with mechanical building blocks
  • 35.
    VHDL-AMS Block Diagram Simulator State Flow Simulator SIMPLORERSimulation Data Bus MathCadSimulink Sim-Interface External Simulators Internal Simulators Multi-Organizational Design Digital Solver Circuit Elements Analog Solver AMS VHDL-AMS
  • 36.
    VHDL-AMS Schematic Fully supported by SIMPLORER Schematic Embedded Editorwith Syntax coloring allows to create models on sheet and in the ModelAgent
  • 37.
    VHDL-AMS Code fora Resistor ENTITY Resistor IS PORT ( QUANTITY r : REAL := 1.0e+03; -- Default = 1 K TERMINAL p,m : ELECTRICAL); END ENTITY Resistor; ARCHITECTURE Rbehav1 OF Resistor IS QUANTITY voltage ACROSS current THROUGH p TO m; BEGIN current == voltage/r; END behav; mp Resistor r := 1.0e3 Rbehav1 r
  • 38.
    Architecture 3 Architecture 2 Architecture1 Entity and Architecture Entity Interface description of a subsystem or physical device Specifies input and output ports to the model Architecture Behavior description of the model Can be dataflow, structural, procedural, etc Modeling can deal with both analog (continuous) and digital (discrete) domains output ports input ports inout ports Architecture 2 Architecture 1 Entity
  • 39.
  • 40.
    VHDL – DigitalSystems A.val B.val C.val SUM.y CARRY.y t0 40m2m 4m 6m 8m 10m 12m 14m 16m 18m 20m 22m 24m 26m 28m 30m 32m 34m 36m 38m CLK A CLK B CLK C XOR2 XOR2 AND2 AND2 AND2 Two bit adder with Carry Sum Carry OR3
  • 41.
    VHDL – DigitalSystems Complete Automotive System Analysis across Domains • ASICs • Micro Controller • FPGAs … ECU PTCU MCU VHDL
  • 42.
    VHDL-AMS Multi DomainDesign L dia := 1 len := 1/4 rho := MATH_PI vol := 1 b := 1 k := 10 EQU crank_radius:= 0.2 pipe_area:= 0.05 Fluidic torque force pressure flow_meter rhyd1 lhyd1 chyd1 spring_rotb damp_rotb T fm_rotb ω + vm_rotb ω + v_rotb mass_rotb CONST CONST 1/pipe_areacrank_radius P Spped damp_rotb.omega t [s] 40 -40 0 -25 25 0 0.1k50 QuickGraph2 flow_meter.q t [s] 1Meg -1Meg 0 0 0.1k50 Mechanic
  • 43.
    VHDL-AMS Component Providers Subsystem Providers - Suppliers OEM System Simulation DriveCycles Fuel Economy Multi Organization Design Power Train Electrical System Sensors … VHDL - AMS VHDL - AMS Solenoids, Motors, Battery, Sensors, Semiconductors, Fuse …
  • 44.
    DC Drive –VHDL-AMS Controller L_R 0.3m L_S L_T ET1 ET2 ET3 R_R 10m R_S R_T t [s] 4.00e+001 0 2.00e+001 0 0 0.2 0.2 0.1 0.1 t [s] 1.50e+003 0 1.00e+003 0 0 0.2 0.2 0.1 0.1 motor current speed and reference speed LIMIT LIMITER LL := 0 UL := 20 GAIN CONTR_OUT THRES1 := -2.5 VAL1 := -1 THRES2 := 2.5 VAL2 := 1 CONST N_REF 1000 M DCM J := 4m LA := 9.5m RA := 1.2 KE := 0.544 A AM1 t [s] 1.00e+003 0 5.00e+002 0 0 0.2 0.2 0.1 0.1 DCM.MI [N·m] TLoad.VAL t [s] 2.00e+001 -1.00e+001 0 0 0 0.2 0.2 0.1 0.1 motor torque and load torque DC Link Voltage and Current D7 TR TLoad 3 Bridge1 PIC VHDL-AMS
  • 45.
    DC Drive –VHDL-AMS Controller
  • 46.
  • 47.
    C/C++ Interface ® System Simulation TheMulti Domain Simulator C/C++ make Dynamic Link Library .dll Symbol Library Symbol Editor
  • 48.
    DC Drive –C-Code Controller L_R 0.3m L_S L_T ET1 ET2 ET3 R_R 10m R_S R_T DCM.IA [A] t [s] 3.00e+001 0 2.00e+001 0 0 0.2 0.2 0.1 0.1 DCM.N [rpm] N_REF.VAL t [s] 1.50e+003 0 1.00e+003 0 0 0.2 0.2 0.1 0.1 motor current speed and reference speed LIMIT LIMITER LL := 0 UL := 20 GAIN CONTR_OUT THRES1 := -2.5 VAL1 := -1 THRES2 := 2.5 VAL2 := 1 CONST N_REF 1000 M DCM J := 4m LA := 9.5m RA := 1.2 KE := 0.544 A AM1 Bridge1.Vout [V] Bridge1.Iout [A] t [s] 1.00e+003 0 5.00e+002 0 0 0.2 0.2 0.1 0.1 DCM.MI [N·m] TLoad.VAL t [s] 2.00e+001 -1.00e+001 0 0 0 0.2 0.2 0.1 0.1 motor torque and load torque DC Link Voltage and Current D7 TR TLoad 3 Bridge1 PIC PIC1 IGain := 2 PGain := 3 C-Code
  • 49.
    DC Drive –C-Code Controller
  • 50.
    SIM2SIM SIMPLORER to SimulinkInterface SIMPLORER Simulink • Co-Simulation Interface • Link blocks in both packages • Using SIMPLORER's external simulator integration interface and S-function in Matlab • Co-Simulation Interface is an open API that can be used for other simulation packages
  • 51.
    Drive System Control L_R 0.3m L_S L_T ET1 ET2 ET3 R_R 10m R_S R_T GAIN P_GAIN KP:= 3 I I_GAIN KI := 2 LIMIT LIMITER LL := 0 UL := 20 CONTR_OUT THRES1 := -2.5 VAL1 := -1 THRES2 := 2.5 VAL2 := 1 CONST N_REF 1000 M DCM J := 4m LA := 9.5m RA := 1.2 KE := 0.544 A + AM1 D7 TR CONST CLOCK .1m 3 Bridge1 TLoad
  • 52.
    Drive System Control L_R 0.3m L_S L_T ET1 ET2 ET3 R_R 10m R_S R_T M DCM J:= 4m LA := 9.5m RA := 1.2 KE := 0.544 D7 TR 3 Bridge1 TLoad SiM2SiMSIMPLORER Link Interface  SiM2SiM 50 SIM2SIM1 SIM2SIM1.CS
  • 53.
  • 54.
  • 55.
  • 56.
    SIMPLORER – AdvisorLink SIMPLORER Single Voltage Electrical Automobile System Template voltage regulator curve Regulator Generator p mGeneratorPower p m BatteryPower RearDefrost FrontHVAC Engine BrakeLightsMisc ExternalLights HeatedSeats FrontWipers RearWipers Radio TurnSignalRadiatorFan RearHVAC generic generator generator Battery Loads Starter p m ® Simulation properties: Step width max 100m Step width min 100u Simulation end time 1369 GAIN Battery -+ pm LoadPower + V VM1 A + AM1 generic generator generator1 SiM2SiMSIMPLORER Link Interface  SiM2SiM 50
  • 57.
    Results Generator Current AM1.I t 100.00 -50.00 0 0 793.91500.00 Speedin RPM Speed t 4.00k -2.00k 0 2.50k 0 793.91500.00 Bus Voltage VM1.V t 13.00 11.50 12.00 0 793.91500.00 Load Power LoadPower t 500.00 -1.50k 0 -1.00k 0 793.91500.00
  • 58.
    Complete Set ofAnalyses DC Analysis NINV INV OUT + - NSC_LM_7411 NINV INV OUT + - NSC_LM_7412 NINV INV OUT + - NSC_LM_7413 R1 10k R2 10k R3 10k R4 10k Rp 15916 R1p 10k C1 100p C2 1n E1 + V VM Rfp 30k R9 30k R 15916 OP: -0.00100994 V OP: -0.00405477 V OP: -7.9752e-006 V OP: 0.999992 V OP: 0.998936 V OP: 3.99573 V OP: 0.000980576 V OP: -3.98873 V OP: 1 V
  • 59.
    E1 1 R1 500m L1 R2 16 L2 C1132.6u 31.83m 3.18m OP: 0 V OP: 0.969697 V OP: 0.969697 V OP: 1 V Complete Set of Analyses Bode C1.VGain Phase 100 100 1k 1k 200 200 300 300 400 400 500 500 600 600 700 700 800 800 900 900 100 100 1k 1k 200 200 300 300 400 400 500 500 600 600 700 700 800 800 900 900 -28.01 -20.00 0.00 20.00 -28.01 -20.00 0.00 20.00 0.00 0.79 1.57 2.36 3.14 0.00 0.79 1.57 2.36 3.14 f [Hz] f [Hz] [dB] [rad] AC Analysis
  • 60.
    Experiments 1D, 2D &3D Parameter Sweep Monte Carlo Sensitivity Worst Case Optimization Simplex Algorithm Successive Approximation Genetic Algorithms
  • 61.
  • 62.
  • 63.