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