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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are needed to see this picture.

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