Motion Control: Generating Intelligent Comands for Mechatronic Devices
Kelvin PengFeburary 7th 2012
What is Control?
PhysicalPlant
ControlEffort Response
Getting the System to do What you Want
How to Control?Add a Feedback Loop
PhysicalPlant
ReferenceControlEffort Response
-+FeedbackController
Pros:• Eliminates errors• Disturbance rejection
Cons:• Stability?• Sensors
Let’s go back to simple controlPhysical
PlantControlEffort Response
PhysicalPlant
ControlEffort ResponseCommand
Generator
DesiredPerformance
Today’s topic: How to design the command generator
Pros:• Simple, no sensors• Stable (if plant is stable)• Accurate model not needed
Cons:• No disturbance
rejection• Increase rise time
PhysicalPlant
FeedbackController
CommandGenerator
FeedforwardController
ControlEffort
Reference
Reference
ResponseDesired
Performance
Before we go on…A General Control System
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
TrolleyPayload
Posit
ion
Time
Button On
0
1
2
3
4
5
6
7
8
0 5 10 15
TrolleyPayload
Posit
ion
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
Posi
tion
Time
A1
A2
Derivation for a Simple Case
V , e tn C , 2 S , 2
C , Aieti cos dti
i1
n
S , Aieti sin d ti
i1
n
Constraints
Vibration Amplitude (At the end of n impulses)
1iANormalization
Ai 0 i 1,...,nPositive Impulses
t1 0Time Optimality
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,...
Simple Derivation(V=0, 2 impulses)
A1 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
K e
1 2
V , e tn C , 2 S , 2
121 AA
3 equations, 3 unknowns
Input Shaping Arbitrary Commands
• Slight increase in rise time• ΣAi = 1 so that shaped and initial commands
have same steady state
From previous example: Zero-Vibration (ZV) shaper
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 Number0
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 OverviewScreen Interface
Payload
Trolley
PLC DrivesAC-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
• 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
ositi
on (m
m)
X Position (mm)
Stage Tracking Error
-0.02
-0.01
0
0.01
0.02
10 11 12 13 14 15
UnshapedShaped
Y P
ositi
on (m
m)
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 DeflectionUnshaped Deflection
Def
lect
ion
(Las
er-E
ncod
er) (
m)
Time(sec)
Pre-Hit Region
Coordinate Measuring Machine (CMM) Deflection
Disk Drive Head TesterCapacitance Gage
Piezo Actuator
x stagey 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
XY
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
Can dramatically reduce system vibrationIs easy to implement
Conclusions
Thank you