Generating Intelligent Commands to Control Mechatronic Devices William Singhose.
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Transcript of Generating Intelligent Commands to Control Mechatronic Devices William Singhose.
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Generating Intelligent Commands to Control Mechatronic Devices
William Singhose
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What is Control?
PhysicalPlant
ControlEffort Response
Getting the System to do What you Want
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Add a Feedback Loop
PhysicalPlant
FeedbackControllerΣReference Control
Effort Response
-+Response
PhysicalPlant
FeedbackControllerΣ
Reference ControlEffort Response
-+ResponsePhysical
PlantΣReference
ControlEffort Response
-+FeedbackController
Response
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Simple Control Systems
PhysicalPlant
ControlEffort Response
PhysicalPlant
ControlEffort ResponseCommand
Generator
DesiredPerformance
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PhysicalPlant
FeedbackController
CommandGenerator
FeedforwardController
ΣΣ
ControlEffort
Reference
Reference
ResponseDesired
Performance
General Control System
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Landmine Detecting Robot
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Bridge Crane
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Bridge Crane Problem(and solution)
θ
T r o l l e y
C a b l e
P a y l o a d
g
x
0
1
2
3
4
5
6
7
8
0 5 10 15
Trolley
Payload
Position
Time
Button On
0
1
2
3
4
5
6
7
8
0 5 10 15
Trolley
Payload
Position
Time
Button On
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Why is Vibration Cancelled?
-0.4
-0.2
0
0.2
0.4
0.6
0 0.5 1 1.5 2 2.5 3
A1 ResponseA2 ResponseTotal Response
Position
Time
A1
A2
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Simple Derivation
V ω,ζ( ) =e−ζωtn C ω,ζ( )[ ]2
+ Sω,ζ( )[ ]2
C ω,ζ( ) = Aieζωti cosωdti( )
i=1
n
∑
S ω,ζ( ) = Aieζωti sinωdti( )
i=1
n
∑
Constraints
VibrationAmplitude
Ai =1∑Normalization
Ai >0 i =1,...,nPositive Impulses
t1 =0Time Optimality
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0 = Aieζωti cosωdti( )
i=1
n
∑ =A1eζωt1 cosωdt1( )+A2e
ζωt2 cosωdt2( )
0 = Aieζωti sinωdti( )
i=1
n
∑ =A1eζωt1sinωdt1( )+A2e
ζωt2 sinωdt2( )
0=A1 +A2eζωt2 cosωdt2( )
0=A2eζωt2 sinωdt2( )
ωdt2 =nπ, n=1,2,...
t2 =nπωd
=nTd2
, n=1,2,...
Simple Derivation(V=0, 2 impulses)
A1A2
t1 t2
0=A1 − 1−A1( )e
ζπ
1−ζ2
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
A1 =e
ζπ
1−ζ2
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
1+e
ζπ
1−ζ2
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
t2 =Td2
Aiti
⎡
⎣ ⎢
⎤
⎦ ⎥ =
11+K
K1+K
0 0.5Td
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
K =e
−ζπ
1−ζ2
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
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Input Shaping Arbitrary Commands
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Typical Responses
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10-Ton Industrial Bridge Crane
• 6mx5mx40m
• Interfaces: Pendent, Joystick, Touchscreen, Wireless
• Overhead Camera
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0
1
2
3
4
0 10 20 30 40 50
Bridge Position
Hook Position
Position (in)
Time (sec)
Input Shaping and Feedback Control:Experimental Data
Disturbance at End
0
1
2
3
4
0 5 10 15 20 25 30 35
Bridge Position
Payload Position
Position (in)
Time (sec)
Disturbance During Motion
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Concurrent DesignWith Feedback Control
PlantController
Sensors
ΣCommandGenerator
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Current Design of PD Feedback And Command Shaping
0
0.5
1
0 0.2 0.4 0.6 0.8 1
PD
PD+Shaping
5% Settling Time, s
Damping Ratio (ζ)
0.39
0.15
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Human Operator Studies
LongShort
End
Start
0
50
100
150
200
250
1 2 3 4 5 6 7 8 9 10 11 12 13
ShapedUnshaped
Time (sec)
Operator Number
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Human Operator Learning
0
50
100
150
200
250
300
0 2 4 6 8 10
Unshaped
Shaped
Completion Time (sec)
Trial Number
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Human Operator Learning
0
50
100
150
200
250
300
1 2 3 4 5 6 7 8 9
Completion Time (sec)
Trial Number
0
50
100
150
200
250
300
1 2 3 4 5 6 7 8 9
Completion Time (sec)
Trial Number
Unshaped Shaped
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Portable Tower Crane
• 2mx2mx340o
• Interfaces: Pendent, GUI, Internet GUI
• Overhead Camera
• Used by Researchers and Students in Atlanta, Japan, Korea
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Tower Crane: System Overview
Screen Interface
P a y lo a d
Tr o ll e y
P L C D r iv e s
A C - A C
T o w e r C r a n eM o to r
C a m e r a
L i m i t s
P CIn t e r n e t
A t la n t a
J A P A N
A n yw h e r e
E n c o d e r
P C
*
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Other Applications• Many types of cranes
• Disk drives
• Long reach robots
• Coordinate measuring machines
• Milling machines
• Spacecraft
xy
z
Touch-TriggerProbe
MeasuredPart
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• Scale of Micro Meters (10-6m)
• High Spindle Speeds (120 kRPM)
Application of Command Shapingto Micro Mills
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QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
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Experimental Results
-0.02
-0.01
0
0.01
0.02
10 11 12 13 14 15
UnshapedShaped
Y Position (mm)
X Position (mm)
Stage Tracking Error
-0.02
-0.01
0
0.01
0.02
10 11 12 13 14 15
UnshapedShaped
Y Position (mm)
X Position (mm)
36 μm
15 μm
Part Surface
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xy
z
Touch-TriggerProbe
MeasuredPart
Coordinate Measuring Machines
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-60
-40
-20
0.0
20
40
60
0.40 0.60 0.80 1.00 1.20
Shaped Deflection
Unshaped Deflection
Deflection (Laser-Encoder) (
μ )m
( )Time sec
- Pre Hit Region
Coordinate Measuring Machine (CMM) Deflection
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Disk Drive Head TesterCapacitance Gage
Piezo Actuator
x stage
y stage
Drive Head Holder
Unshaped
-50
0
50
100
150
200
250
-100
-50
0
50
100
150
200
0 0.01 0.02 0.03 0.04 0.05 0.06
Unshaped Response (
μ)in
(Shaped Response
μ)in
( )Time sec
Shaped
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Painting Robot
.
RecordingSurface
AirBrush
X
Y
Simulated Response(Scaled Down)
Desired Response
Directionof Travel
Simulated Response(Scaled Down)
Desired Response
Directionof Travel
Desired Response
Desired Response
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Space Robot
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Spacecraft Control
umbilical secondary gimbalprimary gimbal
reaction wheels
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umbilical secondary gimbalprimary gimbal
reaction wheels
MACE Space Shuttle Endeavor, 1995
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MACE Space Shuttle Endeavor, 1995
-1.5
-1
-0.5
0
0.5
1
1.5
0 1 2 3 4 5 6 7 8
Unshaped Step
2-Hump EI ShapedGimbal Position (degrees)
Time (sec)
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Input Shaping with On-Off Actuators
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How Can We UseInput Shaping on On/Off Actuators?
0 0 Δ
* Initial Command Input Shaper
0 Δ
Shaped Command
D
+D Δ
Not On/Off
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Flexible Satellites(Tokyo Institute of Technology)
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Time Optimal Control(Special Input Shaper)
0
0.5
1.0
-0.5
-1.0
Shaped Input
12
1
-2 -2Unshaped Input
Input Shaper
0
0.5
1.0
*
Variables: 1) Impulse Times
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Fuel-Efficient Input Shaping
Time-Optimal
Fuel-Efficient
-u max
u max
t1
t2
t3
t4
t5
*1
-2 -2
2
1
t1
t2
t3
t4
t5
umax
-u max
u max
t1
t2
t3
t4
t5
t6
t7
t8
*1
-1 -1
11 1
-1 -1
t1
t2
t3
t5
t4
t6
t7
t8
umax
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Comparison of Maneuver Times
4
6
8
10
12
14
16
18
0 5 10 15 20 25 30 35 40
Time-Optimal ProfilesFuel-Efficient Profiles
Move Duration (sec.)
Slew Distance
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Comparison of Fuel Usage
0
5
10
15
20
0 5 10 15 20 25 30 35 40
Time-Optimal
Fuel Efficient
Fuel Usage (sec.)
Slew Distance
Wasted Fuel
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Transient Deflection with On-Off Shaping
-1
0
1
2
3
4
5
0 2 4 6 8 10 12
Mass CenterDeflection (x 2-x 1)
Response
Time (sec)
m2m1
Too Large?
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Deflection Sampling
-0.5
0
0.5
0 2 4 6 8 10
Percentage Deflection, D(t)/D
max
Time (sec)
Limit the Deflection at Specific Times
Deflection May Exceed Limit Between Deflection Sampling Points
DL
-D L
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Simulation Results(Slew Distance = 5 units)
m2m1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
0 5 10 15
Fuel-Efficient80% Limited60% Limited20% Limited
Deflection, x
2-x
1
Time (sec)
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Slew Duration vs. Deflection Limit(Slew Distance = 5 units)
0
5
10
15
20
25
0.0 0.2 0.4 0.6 0.8 1.0
Slew Duration (sec)
Percentage Deflection
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QuickTime™ and aMotion JPEG OpenDML decompressor
are needed to see this picture.
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Endpoint Deflection
-40
-20
0
20
40
0 1 2 3 4 5 6
Bang-Bang
ZV FE-FE-FE
ZVD FE-FE-FE
Endpoint Deflection (mm)
Time (sec)
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• The Command Used toDrive a Machine is ofFundamental Importance
• Unwanted Motion can beDangerous & Costly
• Oscillation Can Be Reduced Quickly and Easily by Command
Shaping
• Command Shaping is the EASIEST Control Method
Conclusions
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