37 Rotary Inverted Pendulum Failure:Reuse the last received value :Success :Failure :Success Success:Input the transmitted signal :Failure Controller TRx Plant TRx In wireless channels, packet errors may occur. Plant :Control information (torque) :State information 38 Cooperative Motion Model A example of synchronized motion Top view Controller1 Plant 1 Plant 2 Plant 3 Controller2 Controller3 (The pendulum maintains an upright position.) 39 System Model Controller 1 TRx 1 Plant 1 Wireless channel TRx 1 Controller 2 TRx 2 Plant 2 TRx 2 Controller 3 TRx 3 Plant 3 TRx 3 :Control information (torque) :State information 40 Independent Transmission Scheme Failure :Reuse the last received value :Success :Failure :Success Success :Input the transmitted signal Controller 1 TRx 1 Plant 1 Wireless channel TRx 1 Controller 2 TRx 2 Plant 2 TRx 2 Controller 3 TRx 3 Plant 3 TRx 3 :Failure
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Rotary Inverted Pendulum Cooperative Motion Modelkatayama/2011-0805/5-先端研究...37 Rotary Inverted Pendulum Failure:Reuse the last received value :Success :Failure :Success
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37
Rotary Inverted Pendulum
Failure:Reuse the last received value
:Success :Failure
:Success
Success:Input the transmitted signal
:Failure
Controller TRx Plant TRx
In wireless channels, packet errors may occur.
Plant
:Control information (torque) :State information
38
Cooperative Motion Model
A example of synchronized motion
Top view
Controller1 Plant 1
Plant 2
Plant 3 Controller2
Controller3
(The pendulum maintains an upright position.)
39
System Model
Controller 1
TRx 1
Plant 1
Wireless channel
TRx 1
Controller 2
TRx 2
Plant 2
TRx 2
Controller 3
TRx 3
Plant 3
TRx 3
:Control information (torque) :State information
40
Independent Transmission Scheme
Failure :Reuse the last received value
:Success :Failure
:Success
Success :Input the transmitted signal
Controller 1
TRx 1
Plant 1
Wireless channel
TRx 1
Controller 2
TRx 2
Plant 2
TRx 2
Controller 3
TRx 3
Plant 3
TRx 3
:Failure
41
Proposed Transmission Scheme (signal input)
TRx 1
TRx 1
TRx 2
TRx 3
TRx 2
TRx 3
Plant 2
Plant 3
Rx 2 3
Rx 1 3
Rx 1 2
Plant 1
Each plant receives each other’s control information.
42
Proposed Scheme (selection of the signal)
TRx 1
TRx 1
TRx 2
TRx 3
TRx 2
TRx 3
plant 2
plant 3
Rx 2 3
Rx 1 3
Rx 1 2
Plant 1
e.g. Feedback loop No.1
43
:If 1 success =
TRx 1
TRx 1
TRx 2
TRx 3
Plant 1
Rx 2 3
Proposed Scheme (selection of the signal)
TRx 2
TRx 3
plant 2
plant 3
Rx 1 3
Rx 1 2
44
:If 1 fail or signal is used
signal is used
TRx 1
TRx 1
TRx 2
TRx 3
Plant 1
Rx 2 3
Proposed Scheme (selection of the signal)
TRx 2
TRx 3
plant 2
plant 3
Rx 1 3
Rx 1 2 -
-
Select the most
similar signal
=
45
:If 1and3 fail signal is used
TRx 1
TRx 1
TRx 2
TRx 3
Rx 2 3
Plant 1
Proposed Scheme (selection of the signal)
TRx 2
TRx 3
plant 2
plant 3
Rx 1 3
Rx 1 2
= 46
:If 1and2 fail
TRx 1
TRx 1
TRx 2
TRx 3
Rx 2 3
Plant 1
signal is used
TRx 2
TRx 3
plant 2
plant 3
Rx 1 3
Rx 1 2
Proposed Scheme (selection of the signal)
=
47
:If all fail
TRx 1
TRx 1
TRx 2
TRx 3
Rx 2 3
Plant 1
TRx 2
TRx 3
plant 2
plant 3
Rx 1 3
Rx 1 2
Proposed Scheme (selection of the signal)
= 48
Proposed Transmission Scheme (input)
Controller 1
TRx 1
Main controller
Controller 2
TRx 2
Controller 3
TRx 3
The state information of each controller is available to every other controller.
TRx 1
TRx 2
TRx 3
49
e.g. Feedback loop No.1
Controller 1
TRx 1
Main controller
controller 2
TRx 2
controller 3
TRx 3
TRx 1
TRx 2
TRx 3
Proposed Scheme (selection of the signal)
50
:If 1 success
Main controller
Controller 1
TRx 1
controller 2
TRx 2
controller 3
TRx 3
TRx 1
TRx 2
TRx 3
Proposed Scheme (selection of the signal)
=
51
or -
-
signal is used
signal is used
Main controller
Select the most
similar signal
Controller 1
TRx 1
controller 2
TRx 2
controller 3
TRx 3
TRx 1
TRx 2
TRx 3
Proposed Scheme (selection of the signal)
= 52
:If 1and3 fail signal is used
Main controller
Controller 1
TRx 1
controller 2
TRx 2
controller 3
TRx 3
TRx 1
TRx 2
TRx 3
Proposed Scheme (selection of the signal)
=
53
:If 1and2 fail signal is used
Main controller
Controller 1
TRx 1
controller 2
TRx 2
controller 3
TRx 3
TRx 1
TRx 2
TRx 3
Proposed Scheme (selection of the signal)
= 54
:If all fail
Main controller
Controller 1
TRx 1
controller 2
TRx 2
controller 3
TRx 3
TRx 1
TRx 2
TRx 3
Proposed Scheme (selection of the signal)
=
55
Simulation
Pendulum angle( ) Arm angle( ) Arm angle( )
0 [rad] 0 [rad] 0 [rad]
Period of arm motion (T) 10 [s] Precision level 10-3[rad]
Falling down range of pendulum /6[rad]
Every 5 seconds, the desired values are flipped.
Packet loss :Random
Desired value
The motion of plants 1and3 is equal
Plant 1 Plant 2 Plant 3 Top view
2. Synchronization performance :The difference among arm angles
1. Control performance :The rate at which the pendulum collapses
56
Simulation
Pendulum angle( ) Arm angle( ) Arm angle( )
0 [rad] 0 [rad] 0 [rad]
Period of arm motion (T) 10 [s] Precision level 10-3[rad]
Falling down range of pendulum /6[rad]
Every 5 seconds, the desired values are flipped.
Desired value
The motion of plants 1and3 is equal
Plant 1 Plant 2 Plant 3 Top view
2. Synchronization performance :The difference among arm angles
1. Control performance :The rate at which the pendulum collapses
Packet loss :Random
57
Rotary Inverted Pendulum
Failure:Reuse the last received value
:Success :Failure
:Success
Success:Input the transmitted signal
:Failure
Controller TRx Plant TRx
In wireless channels, packet errors may occur.
Plant
:Control information (torque) :State information
58
Pendulum Angle
Low packet loss (p=0.01)
Transmission Success Transmission Failure
:Packet transmission rate (20Hz)
Plant Controller
The pendulum can maintain its upright position.
Pen
dulu
m a
ngle
[ra
d]
Time [s]
59
High packet loss (p=0.2)
Time [s]
The pendulum falls down.
Plant Controller
Pendulum Angle
Pen
dulu
m a
ngle
[ra
d]
The pendulum is considered to fall down when its angle goes over /6 or below - /6 rad
Packet errors occur before the pendulum can restore its upright position.
Transmission Success Transmission Failure
:Packet transmission rate (20Hz)
60
Pendulum Angle
High packet loss (p=0.2)
Plant Controller
Pen
dulu
m a
ngle
[ra
d]
Time [s]
If packet transmission rate is high, the pendulum can maintain its upright position.
Transmission Success Transmission Failure
:Packet transmission rate (50Hz)
61
Transmission Rate / Loss Rate
Plant
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”
in 1
00s
Controller TRx Plant TRx
62
Transmission Rate vs Loss Rate Each point :At least one of the pendulums falls down in a simulation of 1000 runs of 1000[s]
0.1
0.15
0.2
0.25
0.3
Pac
ket
loss
rat
e
0.05
Packet period [s] 0.1 0.02 0.04 0.06 0.08 0.12 0
(25Hz) (10Hz)
The proposed scheme is especially effective when packet transmission rates are low.
Proposed
Independent
63
Simulation
Pendulum angle( ) Arm angle( ) Arm angle( )
0 [rad] 0 [rad] 0 [rad]
Period of arm motion (T) 10 [s] Precision level 10-3[rad]
Falling down range of pendulum /6[rad]
Every 5 seconds, the desired values are flipped.
Desired value
The motion of plants 1and3 is equal
Plant 1 Plant 2 Plant 3 Top view
2. Synchronization performance :The difference among arm angles
1. Control performance :The rate at which the pendulum collapses
Packet loss :Random
64
Arm Angle (no packet loss)
Time [s]
Arm
ang
le [
rad]
Desired value 1 Output 1
Desired value 2 Output 2
Time [s]
Every 5 seconds, the desired values are flipped.
65
Arm Angle (Independent) A
rm a
ngle
[ra
d]
Arm
ang
le [
rad]
Arm
ang
le [
rad]
Time(s)
Output 1( )
Output 2( ) Output 3( )
Packet loss rate :0.05
66
Arm Angle (Proposed)
Arm
ang
le [
rad]
Arm
ang
le [
rad]
Arm
ang
le [
rad]
Time(s)
Output 1( )
Output 2( ) Output 3( )
Packet loss rate :0.05
67
Synchronization Error of Arm Angle
Arm
ang
le [
rad]
Time [s] Time [s]
Synchronization error: The difference between the two arm angles
Sync
hron
izat
ion
erro
r of
arm
ang
le [
rad]
Output 1
Output 2
68
Synchronization Error of Arm Angle Independent Proposed
Synchronization error between output 1 and output 2
The proposed scheme reduces the synchronization error.
Time [s]
Sync
hron
izat
ion
erro
r of
arm
ang
le [
rad]
Sync
hron
izat
ion
erro
r of
arm
ang
le [
rad]
Time [s]
69
Distribution of Worst Synchronization Error The distribution of worst synchronization errors in a simulation run of 1000[s] (number of trials :1000)
600
400
200
0 ~0.05 ~0.1 ~0.15 ~0.2 ~0.25 ~0.3 ~0.35
Num
ber
of t
imes
Synchronization error range [rad]
Proposed Independent
Average and variance of the synchronization error of the proposed scheme are smaller than independent scheme.
~0.4 ~0.45
Packet loss rate :0.05
~0.45 ~0.5 ~0.55 ~0.6 over
70
Synchronization Error for Packet Transmission Rate
Proposed
Independent
Packet transmission rate [Hz]
Ave
rage
of
wor
st
sync
hron
izat
ion
erro
r
[rad
]
20 30 40 10
10-1
10-2
10-3
1
The average of worst synchronization errors in a simulation run of 1000[s] (number of trials :1000)
Packet loss rate :0.05
The proposed scheme reduces the synchronization error for whole packet transmission rate.
71
Synchronization Error for Packet Loss Rate
Proposed
Independent
Packet loss rate 0 0.05 0.1 0.075
10-1
10-2
Packet transmission rate :20Hz
0.025
The average of worst synchronization errors in a simulation run of 1000[s] (number of trials :1000)
10-3
Ave
rage
of
wor
st
sync
hron
izat
ion
erro
r
[rad
]
The proposed scheme reduces the synchronization error for whole packet loss rate.
72
Conclusions
The control performance of each machine is improved.
The synchronization performance of machines is improved.