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Motion Control: Generating Intelligent Commands for Mechatronic Devices. Kelvin Peng January 31 st 2013. What is Control?. Getting the System to do What you Want. How to Control ?. Controls 101: Add a Feedback Loop!. Pros: Eliminates errors Disturbance rejection. Cons: Stability? - PowerPoint PPT Presentation
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Motion Control: Generating Intelligent Commands for Mechatronic Devices
Kelvin PengJanuary 31st 2013
What is Control?
PhysicalPlant
ControlEffort Response
Getting the System to do What you Want
How to Control?
PhysicalPlant
ReferenceControlEffort Response
-+FeedbackController
Pros:• Eliminates errors• Disturbance rejection
Cons:• Stability?• Sensors
Controls 101: Add a Feedback Loop!
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
Bridge Crane Vibration Problem
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
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
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
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
Input Shaping Arbitrary Commands
• Slight increase in rise time• ΣAi = 1 so that shaped and initial commands have same steady state
Bridge Crane Vibration Problem
Typical Responses
Implementing a Digital Input ShaperUnshaped Command
Shaped Command
Shaper Robustness
Insensitivity – the width of a sensitivity curve where vibration remains under Vtol , the tolerable level of vibration
Increasing Shaper Robustness
Insensitivity – the width of a sensitivity curve where vibration remains under Vtol , the tolerable level of vibration
Increasing Shaper RobustnessExtra Insensitive (EI) Shaper
Insensitivity – the width of a sensitivity curve where vibration remains under Vtol , the tolerable level of vibration
Increasing Shaper Robustness Like a Boss
Tradeoff: More impulses are needed, and therefore slower rise time.
Multi-Mode Input Shaping
Design a shaper for each mode, then convolve to get a shaper that eliminates both modes
ZV Shaper for 1 Hz
ZV Shaper for 2 Hz
X
ZV Shaper for 1 Hz and 2 Hz
Multi-Mode Specified Insensitivity (SI) Shaper
Shaping for Double-Pendulum Payloads
Shapers with Negative Impulses
Unity MagnitudeUMZV shaper
Negative shapers:• Faster• But less robust• May excite un-
modeled higher modes
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
On-Off Thrusters: Flexible Satellites(Tokyo Institute of Technology)
On-Off Thrusters: Flexible Satellites(Tokyo Institute of Technology)
Input ShapingWith Feedback Control
PlantController
Sensors
CommandGenerator
Input Shaper *
Cascaded set of 2nd order systems
Collapse the feedback loop
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
Input Shaping Inside the Feedback Loop:Hand-Motion Crane Control
RF Hand-Motion Crane Control
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
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
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
Portable Tower Crane
• 2mx2mx340o
• Interfaces: Pendent, GUI, Internet GUI
• Overhead Camera
• Used by Researchers and Students in Atlanta, Japan, Korea
Tower Crane: System Overview
Screen Interface
Payload
Trolley
PLC Drives
AC-AC
Tower CraneMotor
Camera
Limits
PCInternet
Atlanta
JAPAN
Anywhere
Encoder
PC
*
ME6404 Class Contest
Other Applications• Many types of cranes
• Milling machines
• Coordinate measuring machines
• Disk drives
• Long reach robots
• Spacecraftx
y
z
Touch- Trigger Probe
Measured Part
Multi-Hoist Cranes
Multi-Axis Input Shaping
• Scale of Micro Meters (10-6m)
• High Spindle Speeds (120 kRPM)
Application of Command Shapingto Micro Mills
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
xy
z
Touch- Trigger Probe
Measured Part
Coordinate Measuring Machines
-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
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
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
GRYPHON Mine Detecting Robot
GRYPHON Mine Detecting Robot
• 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
Thank you
PhysicalPlant
FeedbackController
CommandGenerator
FeedforwardController
ControlEffort
Reference
Reference
ResponseDesired
Performance
Before we go on…A General Control System