Motion Control: Generating Intelligent
Comands for Mechatronic Devices
Kelvin Peng
Feburary 7th 2012
What is Control?
Getting the System to do What you Want
Control
Effort
Physical
Plant
Response
How to Control?
Add a Feedback Loop
Reference
+-

Feedback
Controller
Pros:
•Eliminates errors
•Disturbance rejection
Control
Effort
Physical
Plant
Cons:
•Stability?
•Sensors
Response
Let’s go back to simple control
Control
Effort
Physical
Plant
Response
Desired
Control
Performance Command Effort Physical Response
Generator
Pros:
•Simple, no sensors
•Stable (if plant is stable)
•Accurate model not needed
Plant
Cons:
•No disturbance
rejection
•Increase rise time
Today’s topic:
How to design the command generator
Before we go on…
A General Control System
Reference
Desired
Performance
Command
Generator
Reference
Feedforward
Controller

Feedback
Controller

Control
Effort
Physical
Plant
Response
Bridge Crane Vibration Problem
Bridge Crane Vibration Problem
(and solution)
8
Trolley
7
Payload
6
Position
x
Trolley
Button On
5
4
3
2
1
0
0
Cable

Payload
Time
10
15
8
Trolley
7
Payload
6
Position
g
5
Button On
5
4
3
2
1
0
0
5
Time
10
15
Why is Vibration Cancelled?
0.6
A1 Response
A2 Response
Total Response
A1
A2
Position
0.4
0.2
0
-0.2
-0.4
0
0.5
1
1.5
Time
2
2.5
3
Derivation for a Simple Case
Constraints
Vibration Amplitude
(At the end of n impulses)
V  ,   e tn
C ,    S , 
2
n
C ,    Ai e ti cos  d ti 
i1
n
S ,    Ai et i sin d ti 
i1
Normalization
 A 1
i
Positive Impulses
Ai  0
Time Optimality
t1  0
i 1,...,n
2
Simple Derivation
(V=0, 2 impulses)
V  ,   e tn
C ,    S , 
2
2
n
0   Ai eti cos d t i   A1e t1 cos d t1   A2e t2 cos d t 2 
i 1
n
0   Ai eti sin  d t i   A1et1 sin  d t1   A2e t2 sin  d t 2 
i 1
0  A1  A2 e t2 cos  d t 2 
0  A2 e t2 sin d t 2 
A1  A2  1
t2 
n
d
3 equations,
3 unknowns
e
A1 


  

 1 2 



1 e

nTd
,
2
T
t2  d
2
0  A1  1  A1 e
n  1, 2,...


  

 1 2 



Ai   1
  
1 K
ti  
 0
Ke


  


2 

 1  
K 
1  K 
0.5Td 



  

 1  2 



Input Shaping Arbitrary Commands
From previous
example:
Zero-Vibration (ZV)
shaper
•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 Shaper
Unshaped
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 Robustness
Extra 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 and 2 Hz
Vibration Percentage
Vibration Percentage
ZV Shaper for
2 Hz
ZV (1Hz)
0
1
2
3
4
5
Frequency (Hz)
6
7
8
6
7
8
X
120
100
80
60
40
20
0
Vibration Percentage
ZV Shaper for
1 Hz
120
100
80
60
40
20
0
120
100
80
60
40
20
0
ZV (2 Hz)
0
1
2
3
4
5
Frequency (Hz)
ZV(1Hz)*ZV(2Hz)
0
1
2
3
4
5
Frequency (Hz)
6
7
8
Multi-Mode Specified Insensitivity (SI) Shaper
Shaping for Double-Pendulum Payloads
Shapers with Negative Impulses
Unshaped
Command
a)
0
b)
0
Unity
Magnitude
UMZV shaper
c)
0
d)
0
Input
Shaper
*
*
*
*
D1
0
0
D2
Shaped
Command
D1
0
0
D2
D3
0
D3
0
0
D4
0
D4
Negative shapers:
•Faster
•But less robust
•May excite unmodeled higher
modes
Special Case: Negative Shapers for
On-Off Actuators
*
0
D
Initial Command
0
UMZV Shaper:
On-Off

Input Shaper
c)
0
0

D+
Shaped Com mand
Not On/Off
*
0
D3
0
D3
On-Off Thrusters: Flexible Satellites
(Tokyo Institute of Technology)
On-Off Thrusters: Flexible Satellites
(Tokyo Institute of Technology)
Input Shaping
With Feedback Control
Collapse the
feedback loop
Input
Shaper *
Cascaded set of 2nd
order systems
Input Shaping and Feedback Control:
Experimental Data
Disturbance During Motion
4
4
3
3
2
Bridge Position
1
Hook Position
0
0
10
20
30
Time (sec)
40
50
Position (in)
Position (in)
Disturbance at End
2
Bridge Position
1
Payload Position
0
0
5
10
15
20
Time (sec)
25
30
35
Input Shaping Inside the Feedback Loop:
Hand-Motion Crane Control
RF Hand-Motion Crane Control
Human Operator Studies
Long
Short
Shaped
Unshaped
250
200
Time (sec)
End
Start
150
100
50
0
1
2
3
4
5
6
7
8
9 10 11 12 13
Operator Number
Human Operator Learning
Completion Time (sec)
300
Unshaped
Shaped
250
200
150
100
50
0
0
2
4
6
Trial Number
8
10
Human Operator Learning
300
Completion Time (sec)
Completion Time (sec)
300
250
250
200
200
150
150
100
100
50
0
1
2
3
4
5
6
Trial Number
Unshaped
7
8
9
50
0
1
2
3
4
5
6
Trial Number
Shaped
7
8
9
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
JAPAN
Motor
PLC
Tower Crane
Drives Encoder
AC-AC
Camera
Trolley
Limits
*
Payload
PC
Internet
Anywhere
Atlanta
PC
ME6404 Class Contest
Other Applications
•Many types of cranes
•Milling machines
•Coordinate measuring machines
•Disk drives
z
•Long reach robots
y
x
•Spacecraft
Meas ured
P art
TouchTrigger
P robe
Application of Command Shaping
to Micro Mills
• Scale of Micro Meters
(10-6m)
• High Spindle Speeds
(120 kRPM)
Experimental Results
Unshaped
Shaped
0.02
Y Position (mm)
Y Position (mm)
0.02
0.01
0
-0.01
36 m
15 m
0.01
0
-0.01
-0.02
-0.02
10
Unshaped
Shaped
11
12
13
14
15
X Position (mm)
Stage Tracking Error
10
11
12
13
14
X Position (mm)
Part Surface
15
Coordinate Measuring Machines
z
y
x
Meas ured
P art
TouchTrigger
P robe
Deflection (Laser-Encoder) ( m)
Coordinate Measuring Machine
(CMM) Deflection
Shaped Deflection
Unshaped Deflection
60
40
Pre-Hit Region
20
0.0
-20
-40
-60
0.40
0.60
0.80
Time(sec)
1.00
1.20
Disk Drive Head Tester
Capacitance Gage
Drive Head Holder
Piezo Actuator
x stage
250
200
200
150
150
100
100
50
Unshape d
Shape d
50
0
-50
0
-50
0
0.01
0.02
0.03
0.04
Time (se c)
0.05
0.06
-100
Shaped Response ( in)
Unshaped Response ( in)
y stage
Painting Robot
Direction
of Travel
Recording
Surface
Simulat ed Response
(Scaled Down)
Desired Response
Air
Brush
Desired Response
Compressed Air
Direct ion
of T ravel
X
Y
Simulat ed Response
(Scaled Down)
Desired Response
Desired Response
GRYPHON Mine Detecting Robot
GRYPHON Mine Detecting Robot
Conclusions
• 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 vibration
Is easy to implement
Thank you