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