Motion Control: Generating Intelligent Commands for Mechatronic Devices
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Transcript of Motion Control: Generating Intelligent Commands for Mechatronic Devices
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Motion Control: Generating Intelligent Commands for Mechatronic Devices
Kelvin PengJanuary 31st 2013
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What is Control?
PhysicalPlant
ControlEffort Response
Getting the System to do What you Want
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How to Control?
PhysicalPlant
ReferenceControlEffort Response
-+FeedbackController
Pros:• Eliminates errors• Disturbance rejection
Cons:• Stability?• Sensors
Controls 101: Add a Feedback Loop!
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Let’s go back to simple control
PhysicalPlant
ControlEffort Response
PhysicalPlant
ControlEffort ResponseCommand
Generator
DesiredPerformance
Today’s topic: How to design the command generator for
oscillatory plants
Pros:• Simple, no sensors• Stable (if plant is stable)• Accurate model not needed
Cons:• No disturbance
rejection• Increase rise time
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Bridge Crane Vibration Problem
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Bridge Crane Vibration Problem(and solution)
Trolley
Cable
Payload
g
x
0
1
2
3
4
5
6
7
8
0 5 10 15
Trolley
Payload
Pos
itio
n
Time
Button On
0
1
2
3
4
5
6
7
8
0 5 10 15
Trolley
Payload
Pos
itio
n
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
Pos
itio
n
Time
A1
A2
t1 t2
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Solving for the two impulses
V , e tn C , 2 S , 2
n
iid
ti teAC i
1
cos,
S , Aieti sin d ti
i1
n
Vibration Amplitude(after n impulses)
1iANormalization
niAi ,...,1 0 Positive Impulses
t1 0Time Optimality
-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
Positio
nTime
A1
A2
t1 t2
We want this to be zero, i.e. V=0
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0 Aieti cos d ti
i1
n
A1et1 cos d t1 A2e
t2 cos d t2
0 Aieti sin d ti
i1
n
A1et1 sin d t1 A2e
t2 sin d t2
0 A1 A2et2 cos d t2
0 A2et2 sin d t2
t2 nd
nTd
2, n 1, 2,...
Solving for the two ImpulsesA1
A2
t1 t2
0 A1 1 A1 e
1 2
A1 e
1 2
1 e
1 2
t2 Td2
Aiti
11K
K1K
0 0.5Td
21
eK
V , e tn C , 2 S , 2
121 AA
3 equations, 3 unknowns
Zero-Vibration (ZV) input shaper
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Input Shaping Arbitrary Commands
• Slight increase in rise time• ΣAi = 1 so that shaped and initial commands have same steady state
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Bridge Crane Vibration Problem
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Typical Responses
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Implementing a Digital Input ShaperUnshaped Command
Shaped Command
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Shaper Robustness
Insensitivity – the width of a sensitivity curve where vibration remains under Vtol , the tolerable level of vibration
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Increasing Shaper Robustness
Insensitivity – the width of a sensitivity curve where vibration remains under Vtol , the tolerable level of vibration
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Increasing Shaper RobustnessExtra Insensitive (EI) Shaper
Insensitivity – the width of a sensitivity curve where vibration remains under Vtol , the tolerable level of vibration
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Increasing Shaper Robustness Like a Boss
Tradeoff: More impulses are needed, and therefore slower rise time.
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Multi-Mode Input Shaping
Design a shaper for each mode, then convolve to get a shaper that eliminates both modes
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ZV Shaper for 1 Hz
ZV Shaper for 2 Hz
X
ZV Shaper for 1 Hz and 2 Hz
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Multi-Mode Specified Insensitivity (SI) Shaper
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Shaping for Double-Pendulum Payloads
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Shapers with Negative Impulses
Unity MagnitudeUMZV shaper
Negative shapers:• Faster• But less robust• May excite un-
modeled higher modes
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Special Case: Negative Shapers for On-Off Actuators
0 0
*Initial Command Input Shaper
0
Shaped Command
D
D+
Not On/Off
UMZV Shaper: On-Off
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On-Off Thrusters: Flexible Satellites(Tokyo Institute of Technology)
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On-Off Thrusters: Flexible Satellites(Tokyo Institute of Technology)
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Input ShapingWith Feedback Control
PlantController
Sensors
CommandGenerator
Input Shaper *
Cascaded set of 2nd order systems
Collapse the feedback loop
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0
1
2
3
4
0 10 20 30 40 50
Bridge Position
Hook Position
Posi
tion
(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
Posi
tion
(in
)
Time (sec)
Disturbance During Motion
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Input Shaping Inside the Feedback Loop:Hand-Motion Crane Control
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RF Hand-Motion Crane Control
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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
Tim
e (s
ec)
Operator Number
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Human Operator Learning
0
50
100
150
200
250
300
0 2 4 6 8 10
Unshaped
Shaped
Com
plet
ion
Tim
e (s
ec)
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
Com
plet
ion
Tim
e (s
ec)
Trial Number
0
50
100
150
200
250
300
1 2 3 4 5 6 7 8 9
Com
plet
ion
Tim
e (s
ec)
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
Payload
Trolley
PLC Drives
AC-AC
Tower CraneMotor
Camera
Limits
PCInternet
Atlanta
JAPAN
Anywhere
Encoder
PC
*
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ME6404 Class Contest
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Other Applications• Many types of cranes
• Milling machines
• Coordinate measuring machines
• Disk drives
• Long reach robots
• Spacecraftx
y
z
Touch- Trigger Probe
Measured Part
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Multi-Hoist Cranes
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Multi-Axis Input Shaping
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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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Experimental Results
-0.02
-0.01
0
0.01
0.02
10 11 12 13 14 15
UnshapedShaped
Y P
osit
ion
(mm
)
X Position (mm)
Stage Tracking Error
-0.02
-0.01
0
0.01
0.02
10 11 12 13 14 15
UnshapedShaped
Y P
osit
ion
(mm
)X Position (mm)
36 m
15 m
Part Surface
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xy
z
Touch- Trigger Probe
Measured Part
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
Def
lect
ion
(L
aser
-En
cod
er)
(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
Uns
hape
d R
espo
nse
(in
) Shaped Response (
in)
Time (sec)
Shaped
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Painting Robot
.
Com
pres
sed
Air
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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GRYPHON Mine Detecting Robot
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GRYPHON Mine Detecting Robot
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• Every control method has strengths and weaknesses (Feedback is not a magic cure-all)
•The command issued to a system has a significant influence on its response
•Input shaping
Is excellent for applications with problematic vibrations
Is easy to implement
Conclusions
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Thank you
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PhysicalPlant
FeedbackController
CommandGenerator
FeedforwardController
ControlEffort
Reference
Reference
ResponseDesired
Performance
Before we go on…A General Control System