Transcript 02-研究事例 - 片山研究室

片山研究室の無線制御研究
最近の学会発表より
名古屋大学 エコトピア科学研究所 情報・通信科学研究部門
（大学院 工学研究科 電子情報システム専攻 兼担）
片山 正昭
最近の学会発表より

複数機器同期のためのクロック配信
Power Supply Overlaid Communication and Common Clock Delivery for Cooperative Motion Control
IEEE International Symposium on Power Line Communications and Its Applications, pp.370-375
2011年4月



電力線通信
スペクトル拡散による信号重畳
複数機器同期への無線の同報性利用
A Wireless Cooperative Motion Control System with Mutual Use of Control Signals
IEEE International Conference on Industrial Electronics (ICIT), pp.25-30 2011年3月

非定常（周期定常）チャネルでのフィードバック制御
電力線通信を用いた回転型倒立振子の制御における周期定常雑音の影響評価
電子情報通信学会技術研究報告, RRRC2011-06,pp.19-24 2011年6月
Power Supply Overlaid Communication
and Common Clock Delivery
for Cooperative Motion Control
Fumikazu Minamiyama †* Hidetsugu Koga ‡
Kentaro Kobayashi †
Masaaki Katayama †
† Nagoya University, Japan
Hokuriku Electric Power Co., Japan
‡ YASKAWA Electric Corp., Japan
*
for Reduction of Wires
(DC)-PLC
SLV
SLV
SLV
SLV
SLV
Command
MST
SLV
SLV
MST: Master
SLV: Slave
4
Power
MST
Common
Clock
SLV
Communication of the Control Signal
Multi-Carrier Modulation
Down-Link ： OFDM, Up-Link ： OFDMA
Down-Link
COMMAND
M :Master
S-k : kth Slaves
5
Communication of the Control Signal
Multi-Carrier Modulation
Down-Link ： OFDM, Up-Link ： OFDMA
 OFDM
Up-Link
and OFDMA by TDD
RESPONSE
M :Master
S-k : kth Slaves
6
for Reduction of Wires
(DC)-PLC
SLV
SLV
SLV
SLV
SLV
Command
MST
SLV
SLV
MST: Master
SLV: Slave
7
Power
Common
Clock
SLV
MST
?
Common Clock for Synchronized motions
 Delivery of a high quality common clock signal
to each slave to inform the starting time of actions
SLV
Spread Spectrum（SS）
SLV
Command
Common
Clock
Power
MST
8
SLV
•
•
Continuous transmission
High resolution (<1 us)
Reception of the Common
RX for Common Clock at the slaves
MF
Common Clock
Threshold
Θ
MF Output
Q
t
t
Tt
9
High energy
2Tt
High resolution
Master Clock
t
Master Clock to Cue Slaves to Start
Control signal D ：Interval of Command
c
Command(OFDM)#0
Response(OFDMA)#0
Down-Link
Up-Link
Master Clock
0
1
2
・・・
Master Clock
MF
Θ
Crystal Oscillator
Action start time
10
Command(OFDM)#1
Re-load
>timer
Down-Link
18
>
19
ｔ
ｔ
Counter
（19 times）
Action start
time
Start the action
of Command #0
ｔ
Objective

Communication over the DC Power lines
inside the Robot.
 Command/Response
between a Master & Slaves
 Delivery of Common Clock
for Cooperative Motion
11
Channel characteristics
・Band Limited（＜３５MHｚ）
・Frequency Selective
AMPLITUDE
180
Phase[deg.]
Gain [dB]
0
-10
-20
-30
12
0
10
20
Frequency [MHz]
30
PHASE
0
-180
-360
-540
-720
0
10
20
Frequency [MHz]
30
Spectra of Signals
Control signal（OFDM(A)）: L=105 subcarriers
Common clock signal
2.19 5
25 34.69
[MHz]
Challenge:
cohabitation of control signal and clock
13
Down-Link
COMMAND
COMMON
M :Master
S-k : kth Slaves
CLOCK


14
SS
 OFDMA @Slaves
OFDMA  SS
@Slaves
Same Channel for SS & OFDM: Flat Interference
Up-Link
RESPONSE
COMMON
CLOCK


15
M :Master
S-k : kth Slaves
SS
 OFDMA @Master
OFDMA  SS
@Slaves
Different Channel for SS & OFDMA: Colored Interference
Solution of Mutual Interference
2.19 5
25 34.69
[MHz]
OFDM(A)  SS : Process Gain of SS
 SS  OFDM(A) : Interference Cancellation

16
Reduction of Influence of SS to OFDM(A)
Receiver for Common Clock (RXt)
Command
MF
Common
Clock
Θ
Master
Clock
Regenerated Common Clock
REGENE.
Receiver for Control Signal (RXc)
ー
DEMODULATOR
Interference
Cancellation (IC)
17
Command
Data
System Parameters
Number of Slaves K
3
Channel
Measured
Noise
None
Common Clock Signal
Carrier Frequency
15 [MHz]
Chip Interval
0.1[ms]
PN Sequence
(Interval N)
M sequences ＋ 0 padding
（2048(=211) [bit]）
The Lowest Carrier Frequency
2.19 [MHz]
Symbol duration Time
3.2 [ms]
The number of Subcarriers /Allocation
106/Slave with High Gain
Modulation
QPSK
Control Signal
18
System Requirement
Working Hours a year
1.0512×107 ｓ
(8h/day×365)
Accuracy of Self-Running OSC
±100ppm
• a pair losses of two successive command packets < once a year
• a misdetection of a start cure
< once a year
• cue with timing error more than 1us
< once a year
Requirements for Communication Part
[Reception performance]
Common Clock Signal（SS） ：
Control Signal（OFDM（A）) ：
Prob. of False Alarm
Prob. of Miss Detection
Symbol Error Rate (SER)
Required Conditions for Reception Performance
Prob. of False Alarm ef
Prob. of Miss Detection em
SER for Control Signal es
20
2.1 x 10-7
3.2 x 10-1
3.19 x 10-8
Down-Link
COMMAND
COMMON
M :Master
S-k : kth Slaves
CLOCK


21
SS
 OFDMA @Slaves
OFDMA  SS
@Slaves
Same Channel for SS & OFDM: Flat Interference
Common Clock Signal
Receiver of Common Clock Signal (RXt)
Control Signal
+
Common Clock
Signal
Threshold
MF
Q
Probability Distribution Function
MF Output
Prob. of False Alarm
Q
T0
T0+NTt
Q：Threshold for detection
22
t
PDF
Prob. of Miss Detection
Reception Performance
of the Common Clock Signal (Down-Link)
Prob. False Alarm ef
5
x10-7
gd =
4
Control signal power (OFDM)
Common clock signal power (SS)
Q:small
3
slave0,1,2
(gd=14.5dB)
2.1
Q=41.7
Q=45.0
Q:large
1
0
23
Q:Threshold of common clock
Requirement
0
0.1
0.2
0.32
0.4
Prob. Miss detection em
0.5
Reception Performance
of the Common Clock Signal (Down-Link)
Prob. False Alarm ef
5
x10-7
slave1
gd=15dB
4
3
slave0,1,2
(gd=14.5dB)
2.1
gd =
Control signal power (OFDM)
Common clock signal power (SS)
Required Condition
Q=42.6
gd < 14.5 dB
Q=43.4
1
0
24
Q:Threshold of common clock
Requirement
0
0.1
0.2
0.32
0.4
Prob. Miss detection em
0.5
Reception Performance
of the Control Signal (Down-Link)
average SER
10 0
(QPSK)
w/o IC
10-2
10-3
★
10-6
10-8
with IC
0
5
gd [dB]
10
14.5
20
・In the case of using IC，at the gｄ=14.5[dB]
SER <10-8 （ required SER = 3×10-8)
25
Up-Link
RESPONSE
COMMON
CLOCK


26
M :Master
S-k : kth Slaves
SS
 OFDMA @Master
OFDMA  SS
@Slaves
Different Channel for SS & OFDMA: Colored Interference
Reception Performance
of the Common Clock Signal (Up-Link)
False Alarm Prob. ef
5
x10-7
Q:Threshold of common clock
Control signal power(OFDMA)
gu =Common clock signal power(SS)
4
Required Condition
3
2.1
1
g u<15dB
Q:small
Q=53.5
slave0,1,2
(gu=15dB)
Q=59.1
Q:large
Requirement
0
27
0
0.1
0.2
0.32
0.4
Miss detection Prob. em
0.5
Reception Performance
of the Control Signal (Up-Link)
10 0
(QPSK)
average SER
w/o IC
10-2
10-5
10-6
10-8
★
with IC <10-8
0
5
gd [dB]
10
15
20
・In the case of using IC，at the gｄ=15[dB],
SER <10-8 （ required SER = 3×10-8)
28
Conclusions
Propose
 A multiple servo control communication system
in which the power supply overlaid communications
 Delivery of a common clock
for cooperative motion control
Result
 Control signals and master clock can coexist
in actually channel.
29
ICIT-SSST2011 March 15th Auburn Univ. Alabama
A Wireless Cooperative Motion Control System
with Mutual Use of Control Signals
Tsugunori Kondo
Kentaro Kobayashi
Masaaki Katayama
Nagoya University, Japan
Cooperative Motion Control System
Cooperative motion
Multiple machines work
at the same time
with each other.
31
..
Control of moving machines
Relocation of machines
Saving of space
..
Robot group control
Assembly lines
Partner robots
Performance of Wireless Cooperative Control
Packet errors
Control performance
of each machine
(stability, etc.)
New measurement of performance is
“the synchronization of all machines”.
32
..
..
Synchronization
of all machines
Conventional Control Signal Transmission
Conventional method
One input and one output.
..
..
33
Mutual Use of Control Signals
Conventional method
One input and one output
..
..
The nature of wireless
Proposed method
Multiple input
and one output
We consider to use the control signals of the other machines.
34
Purpose
A wireless control method
for a cooperative motion system
Mutual use of the control signals
Improvement of control performance and
synchronization
New measurement of performance
Synchronization of all machines
35
Rotary Inverted Pendulum
The pendulums are controlled to make
their arm angles  [k ] follow the target value
while keeping the pendulums
in an upright position (  [k ] =0).
 [k ]
 [k ]
Basic model
Bipedal walking robot
Crane
Rocket launching pad
Underactuated system
One actuator for two degrees of freedom
u [k ] :Control information (torque)
x[k ] :State information
x[ k ] = [ [ k ] [ k ]  [ k ]  [ k ]]
36
Rotary Inverted Pendulum
uˆ [ k ]
u [k ]
Controller xˆ [ k ]
TRx
TRx
u [k ] :Control information (torque)
x[k ] :State information
x[ k ] = [ [ k ] [ k ]  [ k ]  [ k ]]
x[k ]
Plant
 [k ]
Plant
 [k ]
In wireless channels, packet errors may occur.
xˆ [ k ] =
：Success
x[k ]
xˆ [k  1] ：Failure
uˆ [ k ] =
：Success
u[k ]
uˆ [k  1] ：Failure
Success：Input the transmitted signal
Failure：Reuse the last received value
37
Cooperative Motion Model
 1[ k ]
Controller1
Plant 1
 2[k ]
1 [ k ]
Plant 2
Controller2
 3[k ]
2[k ]
Plant 3
3[k ]
Controller3
A example of
synchronized motion
1 [ k ] =    2 [ k ]
1 [ k ] =  3 [ k ]
Top view
 1, 2 , 3 [ k ] = 0 (The pendulum maintains an upright position.)
38
System Model
Wireless channel
Controller
1
Controller
u 1[k ]
xˆ 1 [ k ]
u 2[k ]
2
xˆ 2 [ k ]
Controller
u 3[k ]
3
xˆ 3 [ k ]
TRx
1
TRx
2
TRx
3
TRx
1
TRx
2
TRx
3
u [k ] :Control information (torque)
x[k ] :State information
x[ k ] = [ [ k ] [ k ]  [ k ]  [ k ]]
39
uˆ 1 [ k ]
x 1[k ]
uˆ 2 [ k ]
x 2[k ]
uˆ 3 [ k ]
x 3[k ]
Plant
1
Plant
2
Plant
3
Independent Transmission Scheme
Wireless channel
Controller
1
Controller
u 1[k ]
TRx
1
TRx
1
xˆ 1 [ k ]
u 2[k ]
2
uˆ 1 [ k ]
x 1[k ]
uˆ 2 [ k ]
Plant
1
TRx
2
TRx
2
x 2[k ]
Plant
2
TRx
3
ˆ
TRx u 3 [ k ]
x 3[k ]
3
Plant
3
xˆ 2 [ k ]
Controller
3
xˆ [ k ] =
u 3[k ]
xˆ 3 [ k ]
:Success
x[k ]
xˆ [k  1] :Failure
uˆ [ k ] =
:Success
u[k ]
uˆ [k  1] :Failure
Success :Input the transmitted signal
Failure :Reuse the last received value
40
Proposed Transmission Scheme (signal input)
ˆ 2 [k ]
u
Rx 2 3
TRx
1
TRx
1
ˆ 3[k ]
uˆ 1 [ k ] u
x1[k ]
ˆ 1 [k ]
u
Rx 1 3
TRx
2
TRx
2
ˆ 3[k ]
uˆ 2 [ k ] u
x 2 [k ]
TRx
3
Plant
2
ˆ 1 [k ]
u
Rx 1 2
TRx
3
Plant
1
ˆ 2 [k ]
uˆ 3 [ k ] u
x 3 [k ]
Plant
3
Each plant receives each other’s control information
41
Proposed Scheme (selection of the signal)
ˆ 2 [k ]
u
Rx 2 3
TRx
1
TRx
1
ˆ 3[k ]
uˆ 1 [ k ] u
x1[k ]
ˆ 1 [k ]
u
Rx 1 3
TRx
2
TRx
2
ˆ 3[k ]
uˆ 2 [ k ] u
x 2 [k ]
TRx
3
ˆ 2 [k ]
uˆ 3 [ k ] u
x 3 [k ]
e.g. Feedback loop No.1
42
plant
2
ˆ 1 [k ]
u
Rx 1 2
TRx
3
Plant
1
plant
3
Proposed Scheme (selection of the signal)
ˆ 2 [k ]
u
Rx 2 3
TRx
1
TRx
1
ˆ 3[k ]
ˆ 1 [k ] u
u
x1[k ]
ˆ 1 [k ]
u
Rx 1 3
TRx
2
TRx
2
ˆ 3[k ]
uˆ 2 [ k ] u
x 2 [k ]
TRx
3
ˆ 2 [k ]
uˆ 3 [ k ] u
x 3 [k ]
ˆ 1[k ] = u1[k ] :If 1 success
u
43
plant
2
ˆ 1 [k ]
u
Rx 1 2
TRx
3
Plant
1
plant
3
Proposed Scheme (selection of the signal)
ˆ 2 [k ]
u
Rx 2 3
TRx
1
TRx
1
ˆ 3[k ]
uˆ 1 [ k ] u
x1[k ]
ˆ 1 [k ]
u
Rx 1 3
TRx
2
TRx
2
ˆ 3[k ]
uˆ 2 [ k ] u
x 2 [k ]
plant
2
ˆ 1[k  1] - uˆ 2 [k uˆ11][k ]
u
Select
Rx 1 2
the most
ˆ 1[k  1]uˆ -[ kuˆ] 3[uˆk [k1]]
plant
u
2
3
similar
signal
TRx
3
x 3 [k ]
3
TRx
3
ˆ 1 [k ] =
u
44
Plant
1
u 2 [k ] signal is used
:If 1 fail
u 3 [k ] signal is used
or
Proposed Scheme (selection of the signal)
ˆ 2 [k ]
u
Rx 2 3
TRx
1
TRx
1
ˆ 3[k ]
uˆ 1 [ k ] u
x1[k ]
ˆ 1 [k ]
u
Rx 1 3
TRx
2
TRx
2
ˆ 3[k ]
uˆ 2 [ k ] u
x 2 [k ]
TRx
3
plant
2
ˆ 1 [k ]
u
Rx 1 2
TRx
3
Plant
1
ˆ 2 [k ]
uˆ 3 [ k ] u
x 3 [k ]
plant
3
ˆ 1[k ] = u 2 [k ]signal is used
u
:If 1and3 fail
45
Proposed Scheme (selection of the signal)
ˆ 2 [k ]
u
Rx 2 3
TRx
1
TRx
1
ˆ 3[k ]
uˆ 1 [ k ] u
x1[k ]
ˆ 1 [k ]
u
Rx 1 3
TRx
2
TRx
2
ˆ 3[k ]
uˆ 2 [ k ] u
x 2 [k ]
TRx
3
plant
2
ˆ 1 [k ]
u
Rx 1 2
TRx
3
Plant
1
ˆ 2 [k ]
uˆ 3 [ k ] u
x 3 [k ]
plant
3
:If 1and2 fail
ˆ 1[k ] = u 3 [k ]signal is used
u
46
Proposed Scheme (selection of the signal)
ˆ 2 [k ]
u
Rx 2 3
TRx
1
TRx
1
Rx 1 3
TRx
2
TRx
2
ˆ 3[k ]
uˆ 1 [ k ] u
x1[k ]
ˆ 1[k  1]
u
ˆ 1 [k ]
u
ˆ 3[k ]
uˆ 2 [ k ] u
x 2 [k ]
TRx
3
ˆ 2 [k ]
uˆ 3 [ k ] u
x 3 [k ]
ˆ 1 [k ] = u
ˆ 1[k  1] :If all fail
u
47
plant
2
ˆ 1 [k ]
u
Rx 1 2
TRx
3
Plant
1
plant
3
Proposed Transmission Scheme (input)
Main controller
u1[k ]
Controller
1
TRx
ˆ 1[k ] 1
x
TRx
1
u 2 [k ]
Controller
2
TRx
2
TRx
2
TRx
ˆ 3 [k ] 3
x
TRx
3
ˆ 2 [k ]
x
u 3[k ]
Controller
3
48
The state information of each
controller is available to every other
Proposed Scheme (selection of the signal)
Main controller
u1[k ]
Controller
1
TRx
ˆ 1[k ] 1
x
TRx
1
u 2 [k ]
controller
2
TRx
2
TRx
2
TRx
ˆ 3 [k ] 3
x
TRx
3
ˆ 2 [k ]
x
u 3[k ]
controller
3
e.g. Feedback loop No.1
49
Proposed Scheme (selection of the signal)
Main controller
u1[k ]
Controller
1
TRx
ˆ 1[k ] 1
x
TRx
1
u 2 [k ]
controller
2
TRx
2
TRx
2
TRx
ˆ 3 [k ] 3
x
TRx
3
ˆ 2 [k ]
x
u 3[k ]
controller
3
ˆ 1[k ] = x1[k ] :If 1 success
x
50
Proposed Scheme (selection of the signal)
Main controller
u1[k ]
Controller
1
TRx
ˆ 1[k ] 1
x
TRx
1
u 2 [k ]
controller
2
TRx
2
TRx
2
TRx
ˆ 3 [k ] 3
x
TRx
3
ˆ 2 [k ]
x
u 3[k ]
controller
3
ˆ 1[k ]
x
51
x 2 [k ]signal is used
Select
or
the most
=
x3[k ]signal is used xˆ 1[k  1] - xˆ 3[k  1] similar signal
ˆ 1[k  1] - xˆ 2 [k  1]
x
Proposed Scheme (selection of the signal)
Main controller
u1[k ]
Controller
1
TRx
ˆ 1[k ] 1
x
TRx
1
u 2 [k ]
controller
2
TRx
2
TRx
2
TRx
ˆ 3 [k ] 3
x
TRx
3
ˆ 2 [k ]
x
u 3[k ]
controller
3
:If 1and3 fail
ˆ 1[k ] = x 2 [k ] signal is used
x
52
Proposed Scheme (selection of the signal)
Main controller
u1[k ]
Controller
1
TRx
ˆ 1[k ] 1
x
TRx
1
u 2 [k ]
controller
2
TRx
2
TRx
2
TRx
ˆ 3 [k ] 3
x
TRx
3
ˆ 2 [k ]
x
u 3[k ]
controller
3
:If 1and2 fail
ˆ 1[k ] = x3[k ] signal is used
x
53
Proposed Scheme (selection of the signal)
Main controller
u1[k ]
Controller
1
TRx
ˆ 1[k ] 1
x
TRx
1
ˆ 1[k  1]
x
u 2 [k ]
controller
2
TRx
2
TRx
2
TRx
ˆ 3 [k ] 3
x
TRx
3
ˆ 2 [k ]
x
u 3[k ]
controller
3
ˆ 1[k  1] :If all fail
ˆ 1[k ] = x
x
54
Simulation
1. Control performance :The rate at which the pendulum collapses
2. Synchronization performance :The difference among arm angles
Packet loss :Random
Top view
Desired
value
Pendulum angle(  )
Arm angle( 1 , 3 )
Arm angle(  2 )
Plant 1
Plant 2
0 [rad]
 [rad]
0

0 [rad]
Period of arm motion (T)
10 [s]
Precision level
10-3[rad]
Falling down range of pendulum
 /6[rad]
55
Plant 3
Every 5 seconds,
the desired values
are flipped.
The motion of plants
1and3 is equal
Simulation
1. Control performance :The rate at which the pendulum collapses
2. Synchronization performance :The difference among arm angles
Packet loss :Random
Top view
Desired
value
Pendulum angle(  )
Arm angle( 1 , 3 )
Arm angle(  2 )
Plant 1
Plant 2
0 [rad]
 [rad]
0

0 [rad]
Period of arm motion (T)
10 [s]
Precision level
10-3[rad]
Falling down range of pendulum
 /6[rad]
56
Plant 3
Every 5 seconds,
the desired values
are flipped.
The motion of plants
1and3 is equal
Rotary Inverted Pendulum
uˆ [ k ]
u [k ]
Controller xˆ [ k ]
TRx
TRx
u [k ] :Control information (torque)
x[k ] :State information
x[ k ] = [ [ k ] [ k ]  [ k ]  [ k ]]
x[k ]
Plant
 [k ]
Plant
 [k ]
In wireless channels, packet errors may occur.
xˆ [ k ] =
:Success
x[k ]
xˆ [k  1] :Failure
uˆ [ k ] =
:Success
u[k ]
uˆ [k  1] :Failure
Success：Input the transmitted signal
Failure：Reuse the last received value
57
Pendulum angle [rad]
Pendulum Angle
Low packet loss (p=0.01)
Ts
T
Controller
T
Transmission Success
Transmission Failure
Time [s]
：Packet transmission rate
(20Hz)
The pendulum can maintain its upright position.
58
Plant
Pendulum Angle
Pendulum angle [rad]
The pendulum is considered to fall down
when its angle goes over  /6 or below -  /6 rad
High packet loss (p=0.2)
Ts
T
Controller
Plant
T
Transmission Success
Transmission Failure
Time [s]
transmission rate
1 /：Packet
Ts
(20Hz)
Packet errors occur before the pendulum can restore its upright position.
59
The pendulum falls down.
Pendulum angle [rad]
Pendulum Angle
High packet loss (p=0.2)
Ts
T
Plant
Controller
T
Transmission Success
Transmission Failure
Time [s]
transmission rate
1 /：Packet
Ts
(50Hz)
If packet transmission rate is high,
the pendulum can maintain its upright position.
60
Transmission Rate / Loss Rate
uˆ [ k ]
u [k ]
in 100s
Controller xˆ [ k ]
TRx
TRx
x[k ]
Plant
 [k ]
Plant
 [k ]
Trade-off between
the packet transmission rate
and the packet loss rate [1]
[1] R.Kohinata,T.Yamazato and M.Katayama,
“Influence of channel errors on a wireless-controlled rotary inverted pendulum”
61
Transmission Rate vs Loss Rate
Each point :At least one of the pendulums falls down
in a simulation of 1000 runs of 1000[s]
Packet loss rate
0.3
0.3
0.25
0.25
0.2
0.2
0.15
0.15
0.1
0.1
Proposed
Independent
0.05
0.05
00
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.02
0.04
0.06
0.08
0.1
0.12
Packet
period [s]
(10Hz)
（25Hz）
The proposed scheme is especially effective
when packet transmission rates are low.
62
Simulation
1. Control performance :The rate at which the pendulum collapses
2. Synchronization performance :The difference among arm angles
Packet loss :Random
Top view
Desired
value
Pendulum angle(  )
Arm angle( 1 , 3 )
Arm angle(  2 )
Plant 1
Plant 2
0 [rad]
 [rad]
0

0 [rad]
Period of arm motion (T)
10 [s]
Precision level
10-3[rad]
Falling down range of pendulum
 /6[rad]
63
Plant 3
Every 5 seconds,
the desired values
are flipped.
The motion of plants
1and3 is equal
Arm Angle (no packet loss)
 ideal_1
 ideal_2
Arm angle [rad]
Every 5 seconds,
the desired values are flipped.
Time [s]
64
Desired value 1
Output 1 ideal_1
Time [s]
Desired value 2
Output 2  ideal_2
Arm angle [rad]
Arm Angle (Independent)
Packet loss rate :0.05
Output 1(  1 )
Output 2( 2 )
Output 3(  3 )
65
Arm angle [rad]
Arm angle [rad]
Time（s）
Arm angle [rad]
Arm Angle (Proposed)
Packet loss rate :0.05
66
Arm angle [rad]
Arm angle [rad]
Time（s）
1
Output 1(
)
2
Output 2(
)
3
Output 3(
)
Arm angle [rad]
Output 1 1
Output 2 2
Synchronization error
of arm angle [rad]
Synchronization Error of Arm Angle
Time [s]
Time [s]
Synchronization error:
1 [ k ]   2 [ k ]  
The difference between the two arm angles
67
Independent
Time [s]
Synchronization error
of arm angle [rad]
Synchronization error
of arm angle [rad]
Synchronization Error of Arm Angle
Synchronization error
between output 1 and output 2
Proposed
Time [s]
1 [ k ]   2 [ k ]  
The proposed scheme reduces the synchronization error.
68
Distribution of Worst Synchronization Error
The distribution of worst synchronization errors
in a simulation run of 1000[s] (number of trials :1000)
700
Packet loss rate :0.05
Number of times
600
600
500
Independent
Proposed
400
400
300
200
200
100
0.4以上
～0.4
～0.35
～0.3
～0.25
～0.2
～0.15
～0.1
～0.05～0.1～0.15～0.2～0.25～0.3～0.35～0.4～0.45～0.45～0.5～0.55～0.6 over
～0.05
0
0
Synchronization error range [rad]
Average and variance of the synchronization error
of the proposed scheme are smaller than independent scheme.
69
Synchronization Error for Packet Transmission Rate
The average of worst synchronization errors
in a simulation run of 1000[s] (number of trials :1000)
Average of worst
synchronization error
[rad]
10
1
Packet loss rate :0.05
Independent
101-1
Proposed
0.1-2
10
0.01
10-310
10
20
30
40
20
30
40
Packet transmission rate [Hz]
The proposed scheme reduces the synchronization error
for whole packet transmission rate.
70
Synchronization Error for Packet Loss Rate
The average of worst synchronization errors
in a simulation run of 1000[s] (number of trials :1000)
Average of worst
synchronization error
[rad]
101-1
Independent
0.1-2
10
Proposed
Packet transmission rate :20Hz
10
0.01-3
00
0.025
0.05
0.075
0.025
0.05
0.075
Packet loss rate
0.1
0.1
The proposed scheme reduces the synchronization error
for whole packet loss rate.
71
Conclusions
For wireless cooperative motion of machines
Proposal
Mutual use of control signals
New measurement of the machine synchronization
The control performance of each machine is improved.
The synchronization performance of machines is improved.
72
2011年度 RRRC（2011.06.17）
電力線通信を用いた回転型倒立振子の制御における
周期定常雑音の影響評価
○カリソセサル 小林健太郎 岡田啓 片山正昭
名古屋大学
工場内の機器の制御通信

工場内
 多くの通信線が邪魔になる
通信線を一緒にすると
配線とコストが減る
制御情報
状態情報
制御器側
制御対象側
電力線を用いた制御の既存研究例

パルス幅変調(PWM) を用いて制御されてい
るモータの電源線上のフィードバックループ
としてもPLC を用いることを検討

N. Ginot, M.A. Mannah, C. Batard, and M. Machmoum,
“Application of power line communication for data transmission over pwm
network,” IEEE Transactions on Smart Grid, vol.1, pp.178–185, Sept. 2010.

電力線通信の雑音が制御品質に与える評
価が明らかされてない
電力線通信路の雑音（波形の例）
電圧[V]
5
0
周期定常雑音
（瞬時電力が周期
的に変化する）
TAC/2
平均電力：1.00
商用電源
-5
0
4
8
12
16
20
時間[ms]
※[1]より
雑音の周期 TAC/2=1/120秒
※[1] M. Katayama, T. Yamazato, H. Okada, “A Mathematical
Model of Noise in Narrowband Power-Line Communication
Systems,”
IEEE Journal on Selected Areas in Communications, vol. 24, No.
定常雑音波形の例
電圧[V]
5
0
-5
0
平均電力：1.00
4
8
12
時間[ms]
16
20
目的
電力線通信を用いたフィードバック制御システム
（の制御品質）に対する
雑音の周期定常性の影響を明らかにする
システムモデル

電力線を介したフィードバックシステム 状態情報
制御情報
目標値
状態情報
システムモデル

電力線を介したフィードバックシステム 状態情報
制御情報
目標値
状態情報
[k]
回転型倒立振子
[k]
システムモデル（伝送手法）
制御情報
u[k]
送信した制御情報
ut [n]
TX
r[k]
電力線
通信路
ur[n]
u[k]
RX
制御
対象
制御器
RX
xr[n]
x[k]
Ts
電力線
通信路
TX
xt [n]
x[k]
Tp
x[k]
システムモデル（伝送手法）
受信した制御情報
u[k]
ut [n]
TX
r[k]
電力線
通信路
ur[n]
推定した制御情報
u[k]
RX
制御
対象
制御器
RX
xr[n]
x[k]
Tp
電力線
通信路
TX
xt [n]
x[k]
Ts
x[k]
システムモデル（伝送手法）
受信した制御情報
u[k]
ut [n]
TX
r[k]
電力線
通信路
ur[n]
推定した制御情報
u[k]
RX
制御
対象
制御器
RX
x[k]
xr[n]
電力線
通信路
TX
xt [n]
x[k]
x[k]
システムモデル（伝送手法）
Ts
Tp
u[k]
ut [n]
TX
r[k]
電力線
通信路
ur[n]
u[k]
RX
制御
対象
制御器
RX
x[k]
xr[n]
電力線
通信路
TX
xt [n]
送信した状態情報
x[k]
状態情報
x[k]
システムモデル（伝送手法）
Ts
Tp
u[k]
ut [n]
TX
r[k]
電力線
通信路
ur[n]
u[k]
RX
制御
対象
制御器
RX
x[k]
xr[n]
電力線
通信路
推定した状態情報
TX
xt [n]
x[k]
受信した状態情報
x[k]
システムモデル（伝送手法）
u[k]
ut [n]
TX
r[k]
電力線
通信路
ur[n]
u[k]
RX
制御
対象
制御器
RX
x[k]
xr[n]
電力線
通信路
推定した状態情報
TX
xt [n]
x[k]
受信した状態情報
x[k]
パケット損失率の時変性
パケッ ト 損失率 Pe[n]
1
γ=2 dB
周期定常
定常
0.8
γ:SNR
パケット長：４０ビット
変調方式：BPSK
0.6
0.4
γ=6 dB
0.2
0
0
4
8
12
時間 [ms]
16
パケッ ト 損失率対時間
20
パケット損失率の時変性
パケッ ト 損失率 Pe[n]
1
γ=2 dB
周期定常
定常
0.8
0.6
電力線の
雑音レベル
が高くなる時
0.4
γ=6 dB
0.2
0
0
4
8
12
時間 [ms]
16
パケッ ト 損失率対時間
20
パケット損失率の時変性
パケッ ト 損失率 Pe[n]
1
γ=2 dB
周期定常
定常
0.8
0.6
電力線の
雑音レベル
が低くなる時
0.4
γ=6 dB
0.2
0
0
4
8
12
時間 [ms]
16
パケッ ト 損失率対時間
20
シミュレーションパラメータ
変調方式
BPSK
パケット長さ
40 ビット
デジタルシステムのサンプリング周
波数
1024 Hz
電源の周波数
60 Hz
シミュレーション時間
100 秒
シミュレーション回数
100と1000 回
振子の角度の目標値
0 [rad]
アームの動作周期
10 秒
アームの角度の目標値
0⇔π
安定領域
±π/6 [rad]
シミュレーションパラメータ
変調方式
BPSK
パケット長さ
40 ビット
デジタルシステムのサンプリング周
波数
1024 Hz
電源の周波数
60 Hz
シミュレーション時間
100 秒
シミュレーション回数
100と1000 回
振子の角度の目標値
0 [rad]
アームの動作周期
10 秒
アームの角度の目標値
0⇔π
安定領域
±π/6 [rad]
安定領域
振子
振子がこの角度
を超えたら、転倒
と考える
π/6 π/6
回転倒立型振子のパラメーター
振子の重りの質量
0.004 [kg]
振り上げ棒の質量
0.025 [kg]
振り上げ棒の長さ
0.241 [m]
アームの長さ
0.152 [m]
アームの慣性モーメント
0.00121 [kgm2]
重力加速度
9.81 [m/s2]
入力と出力の信号（定常雑音の場合）
振子転倒
入力と出力の信号（周期定常雑音の場合）
振子・アーム安定
平均SNRに対する制御品質の評価（定常雑音の場合）
雑音：定常
平均SNRに対する制御品質の評価（周期定常雑音の場合）
雑音：周期定常
平均SNRに対する制御品質の評価
雑音：定常
雑音：周期定常
周期定常雑音下より定常雑音下の方が特性が悪い
パケットレートに対する制御品質の評価（定常雑音の場合）
雑音：定常
パケットレートに対する制御品質の評価（周期定常雑音の場合）
雑音：周期定常
パケットレートに対する制御品質の評価
雑音：定常
雑音：周期定常
周期定常雑音下より定常雑音下の方が特性が悪い
振子の帯域幅
ローパスフィルタの帯域幅
目標値の信号
アームの角度
f c
上がり時間
0.35

f c  0.4 Hz
1
最小の目標値の周期
f
c
= 2 . 5s
制御信号伝送タイミングと制御品質の関係
雑音：周期定常
パケットレート：120Hz
制御信号の伝送タイミングと制御品質関係
雑音：周期定常
今回のシミュレーションはパ
ケット伝送タイミングは試行毎
にランダムにした
まとめ
今回のシステムでは同じSNRで定常雑音と周期
定常雑音を比較すると、周期定常雑音下の方が
制御品質が良い
「雑音周期＜システムの要求最小伝送周期」であ
るため
 周期定常雑音下ではパケット伝送タイミングの選
択に配慮が必要
