Generating Intelligent Commands to Control Mechatronic Devices
William Singhose
What is Control?
PhysicalPlant
ControlEffort Response
Getting the System to do What you Want
Add a Feedback Loop
PhysicalPlant
FeedbackControllerΣReference Control
Effort Response
-+Response
PhysicalPlant
FeedbackControllerΣ
Reference ControlEffort Response
-+ResponsePhysical
PlantΣReference
ControlEffort Response
-+FeedbackController
Response
Simple Control Systems
PhysicalPlant
ControlEffort Response
PhysicalPlant
ControlEffort ResponseCommand
Generator
DesiredPerformance
PhysicalPlant
FeedbackController
CommandGenerator
FeedforwardController
ΣΣ
ControlEffort
Reference
Reference
ResponseDesired
Performance
General Control System
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
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
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
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
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
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
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
Concurrent DesignWith Feedback Control
PlantController
Sensors
ΣCommandGenerator
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
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
Human Operator Learning
0
50
100
150
200
250
300
0 2 4 6 8 10
Unshaped
Shaped
Completion Time (sec)
Trial Number
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
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
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
*
Other Applications• Many types of cranes
• Disk drives
• Long reach robots
• Coordinate measuring machines
• Milling machines
• Spacecraft
xy
z
Touch-TriggerProbe
MeasuredPart
• 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 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
xy
z
Touch-TriggerProbe
MeasuredPart
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
Deflection (Laser-Encoder) (
μ )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
Unshaped Response (
μ)in
(Shaped Response
μ)in
( )Time sec
Shaped
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
Space Robot
Spacecraft Control
umbilical secondary gimbalprimary gimbal
reaction wheels
umbilical secondary gimbalprimary gimbal
reaction wheels
MACE Space Shuttle Endeavor, 1995
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)
Input Shaping with On-Off Actuators
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
Flexible Satellites(Tokyo Institute of Technology)
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
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
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
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
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?
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
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)
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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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)
• 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