Biomechatronics - Lecture 12. Artificial motor control part 2

BiomechatronicsDelft University of Technology

Course 2006-2007(Wb 2432)

Frans van der Helm

Lecture 13Artificial motion control

Contents• Introduction• Definitions from control engineering

– dynamical systems– stability– Phase-margin and gain margin

• Model of human controller– stability analyis– limitations and adaptation

• Supervisory control situations– supervisor over automated control loops

The human as controller

• Marine vessels• Vehicles• Airplanes• ….

Humancontroller vehicle

+

-

Closed-loop systeem

Visualsystem

��

Block diagram of a control loop

controller system+ -

sensor

controlorgan

disturbancereal

valuedesiredvalue

H1(ωωωω) H3(ωωωω)+ -

H4(ωωωω)

H2(ωωωω)

N(ωωωω)Y(ωωωω)U(ωωωω)

Block diagram of a control loop


H4(ωωωω)

H2(ωωωω)

N(ωωωω)Y(ωωωω)U(ωωωω)

YH H HH H H H

UH H H H

N=+

++

1 2 3

1 2 3 4 1 2 3 411

1

Examples in biomechatronics

humancontroller

Limb +prosthesis+ -

tactileinterface

muscles

disturbance

jointangle

setpointforce

skinstimulation

Examples in biomechatronics

humancontroller

Handprosthesis+ -

visualsystem

electro-motor

disturbancehand

openingsetpoint

EMG force

Stability of a control loop� ��

�� !

� ��"ω#�$��%�

��"ω#�� &� ��"ω#�� $�

� '� $�(� ��

)��"ω# �� "ω# *�( �+,�

� - �(� ��

)�� "ω# ��(�+,� ��"ω# .��

-1.5 -1 -0.5 0 0.5 1 1.5-2.5

-2

-1.5

-1

-0.5

0

0.5

Re (Hr)

Im (H

r)

-1

Gain-margin

Gain = 1

Phase-margin

'� $�(� ��/�� (� ��

0�1�$��

Cross-overfrequency

ωωωω = ωωωωc

frequency (rad)

'� $�(� ��

10^0 10^1 10^2 10^3 10^-2

10^-1

10^0 = 1

10^1

10^2

10^3

2��(��

gain

10^-1 10^0 10^1 10^2 -315

-270

-225

-180

-135

-90

-45

0

2��(��

frequency (rad)

phas

e (d

egre

es)

'� $�(� ��

ωωωω�Cross-over frequency

10^0 10^1 10^2 10^3 10^-2

10^-1

10^0 = 1

10^1

10^2

10^3

frequency (rad)

gain

10^-1 10^0 10^1 10^2 -315

-270

-225

-180

-135

-90

-45

0

frequency (rad)

phas

e (d

egre

es)

- �(� ��

2��(�� 2��(��

- �(� ��

Input- & output signals� )��"�#��$�"ω�#� 3��"�#��$��"ω��4�ϕ#� - �� $��ϕϕϕϕ

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1.5

-1

-0.5

0

0.5

1

1.5

�

ϕϕϕϕ

Stability of a control loop


H4(ωωωω)

H2(ωωωω)

N(ωωωω)Y(ωωωω)U(ωωωω) E(ωωωω)

0 1 2 3 4 5-3

-2

-1

0

1

2

3

time (sec)

ampl

itude

'� $�( �� (�+,�

� - �� .��

� $� ��

� - ��

� ��5��$� ��

� - �� *��

� ��$� ��

Stability of a control loop


H4(ωωωω)

H2(ωωωω)

N(ωωωω)Y(ωωωω)U(ωωωω) E(ωωωω)

Phase shift = -180 degreesgain = 0.75

Positive gain margin

0 1 2 3 4 5-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Model human controller

human plant+ -

U(ωωωω) Y(ωωωω)E(ωωωω)Control

interface

sensor

human system+

-

U(ωωωω) Y(ωωωω)E(ωωωω)

display

Model human controller 1

human system+

-


Hm (ωωωω) Hs(ωωωω)+

-

U(ωωωω) Y(ωωωω)E(ωωωω)N(ωωωω)

6�7��

� �� $��8$�� 5��8��

� ��$�$��$

� �� $��$�� $��5�(�� 5��

��"ωωωω# ��"ωωωω#��$"ωωωω# ��9:ωωωω

3�� $��5�� 5��"ωωωω# ��9:ωωωω

10^0 10^1 10^2 10^3 10^-2

10^-1

10^1

10^2

10^3

2��(��

frequency (rad)

gain

10^-1 10^0 10^1 10^2

2��(��

frequency (rad)

phas

e (d

egre

es)

-90

Slope -110^0

3�� $��5�� 5��"ωωωω# ��9:ωωωω

-1.5 -1 -0.5 0 0.5 1 1.5-2.5

-2

-1.5

-1

-0.5

0

0.5

Re (Hr)

Im (H

r)

-1 0�1�$��

�8 �$$� ��

10^0 10^1 10^2 10^3 10^-2

10^-1

10^1

10^2

10^3

gain

phas

e (d

egre

es)

;� �$��(��

frequency(rad)10^-1 10^0 10^1 10^2

frequency (rad)

��"ωωωω#��9:ωωωω+

-

U(ωωωω) Y(ωωωω)E(ωωωω)H

YU

j

jj

uy( )( )( )

ωωω

ω

ωω

= =+

=+

1

11

11

Low frequencies: transfer =1Input is followed accurately

High frequencies: transfer almost 0Input is followed badly

0

-90

1

;� �$��(��

10^0 10^1 10^2 10^3 10^-2

10^-1

10^1

10^2

10^3

frequency (rad)

gain

10^-1 10^0 10^1 10^2

frequency (rad)

phas

e (d

egre

es)

��"ωωωω#��9:ωωωω+

-

U(ωωωω) Y(ωωωω)E(ωωωω)H

EU

j

jj

ue( )( )( )

ωωω

ω

ωω

= =+

=+

1

11 1

1

0

-90

Low frequencies: error almost 0Input is followed accurately

High frequencies: error = inputInput is followed badly

Model human controller 2

6�7��

� �� $�� %� �� $��5�(

� �� 5��"ωωωω# ��"ωωωω#��$"ωωωω# ��9:ωωωω� 2��$��<

≈≈≈≈

human system+

-



-


Limitations & adaptability human controller

� =�� $�

> �� $��$$��

> )�� $�� $�$�� 8��

> �� $ ��

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�� $��

� ��

> �� 8� ��$�$�� $�

> �� $��5�� $��

"��5��$�$��$��#

Cross-over model


-


vjmm e

jjj

KH ωτ

ωτωτωτω −

+++= .

11

.11

)(32

1

� �� $

?��8��1��$�"ωωωω .� �� 9$�≈ ,�@��#�

ejmm e

jj

KH ωτ

ωτωτω −

++= .

11

)(2

1

Cross-over model

For frequencies around ωωωω = ωωωωc human tries to:

• Loop gain is then equal to 1• Loop gain function approximates integrator• ωωωωc roughly between 2 & 6 rad/s (≈ 0.3 & 1 Hz)• τe equal to 200 till 300 ms

ejcmm e

jHH ωτ

ωωωω −=)().( s


-


10^0 10^1 10^2 10^3 10^-2

10^-1

1

10^1

10^2

10^3

2��(��

frequency (rad)

gain

10^-1 10^0 10^1 10^2

-540

-450

-360

-270

-180

-90

2��(��

frequency (rad)

phas

e (d

egre

es)

Hr(ω)= Hm(ω).Hs(ω)= ωc / j(ω) . e-jωτe

-630

0

ωωωωc = 3 rad/s

'� $�(� ��

Hr(ω)= Hm(ω).Hs(ω)= ωc / j(ω) . e-jωτe

-1.5 -1 0 0.5 1 1.5-2.5

-2

-1.5

-1

-0.5

0

0.5

Re (Hr)

Im (H

r)

-1

Gain = 1

ωωωω = ωωωωc

Phase-margin

-0.5

�� $��

�� $� ��


-


ejmm e

jj

KH ωτ

ωτωτω −

++= .

11

)(2

1

ejcmm e

jHH ωτ

ωωωω −=)().( s

Examples of adaptation

•

•

•

•

H Hj

e Hj H

em sc j

mc

s

j( ). ( ) . ( ) .( )

.ω ωωω

ωωω ω

ωτ ωτ= → =− −1

H Kjj

em mj e( ) . .ω

ωτωτ

ωτ=++

−11

1

2

HKj

Kjj j

jK K

ss

mc

s

c

s( ) . .ω

ωωτωτ

ωω

ωτ τ

ω= →

++

= → = =11

1

22 1 m0, 0, K =

H K Kjj j K K

s s mc

s

c

s( ) . .

.ω

ωτωτ

ωω

τ τω τ

= →++

= → =11

11

22 1 m

2>> 1, 0, K =

( )( )

HK

jK

jj j

jK K

ss

mc

s

c

s( ) . .

.ω

ω

ωτωτ

ωω

ωτ τ

ωτ

= →++

= → =2

1

2

211

2 1 m1

0, >> 1, K =

( )( )

HK

jK

jj j

jK

ss

mc

s( ) . .ω

ω

ωτωτ

ωω

ω= →

++

= →3

1

2

311

not controllable

10^0 10^1 10^2 10^3 10^-2

10^-1

1

10^1

10^2

10^3

gain

10^-1 10^0 10^1 10^2 -1400

-1200

-1000

-800

-600

-400

-200

0

frequency (rad)

phas

e (d

egre

es)

;� �$��(��

e + j

e = e

j + 1

e j =

UY

)(He

e

e

e

j-c

j-c

j-c

j-c

uy τω

τω

τω

τω

ωωω

ωω

ωω

ωω=ω

)()(

ωωωωc = 3 rad/s

10^0 10^1 10^2 10^3 10^-2

10^-1

1

10^1

10^2

10^3

10^-1 10^0 10^1 10^2 -20

0

20

40

60

80

100

frequency (rad)

phas

e (d

egre

es)

;� �$��(��

e + j

j =

e j

+ 1

1 =

)U()E(

= )(He

e

j-cj-c

ue τωτω ωω

ω

ωωω

ωω

ωωωωc = 3 rad/s

gain

10^-1 10^0 10^1 10^2 10^3 10^-2

10^-1

10^0

10^1

10^2

10^3

frequency (rad)

gain

10^-1 10^0 10^1 10^2 -40

-20

0

20

40

60

80

100

frequency (rad)

phas

e (d

egre

es)

ωωωωc = 1 rad/sωωωωc = 3 rad/sωωωωc = 5 rad/s

ωωωω� /�ττττ� �� /�$��

A�� 8��

/��$�$��ωωωω� /�ττττ�

Higher bandwidth� More effort � higher ωωωωc and lower ττττe

Higher order system� More difficult � lower ωωωωc and higher ττττe

Demonstration

Conclusions

• Humans can adapt to the system to be controlled:– Km, τ1 and τ2: Adaptation parameters– ωc: Determines bandwidth of controlled system

• Still some limitations apply: – Only zero, first order and second order systems can be

controlled!!– Human controller properties known for systems with visual

and vestibulary feedback, not for tactile feedback, etc.

• Design of biomechatronic systems:– Be aware that humans must be able to control the system

Supervisory control situations

• System with automated control loops– FES system with artificial sensors, controller and stimulator– Above-knee prosthesis with automatic knee locking

• Humans should be in control of whole system– Monitoring:

• Feedback of result• Feedback of performance controller

– Actions:• Setpoint generation for controller• Overruling of controller

Manual control

human plant+ -

U(ωωωω) Y(ωωωω)E(ωωωω)Control

interface

sensor

display

Supervisory control

Automaticcontrol

loop

goal display

performance

Control actions

overrule

human

Setpoint

sensor

plantController

Actuator

Model Rasmussen

Skill-based

Rule-based

Knowledge-based

Model Rasmussen• Knowledge-based behaviour:

– Difficult tasks– performance based on reasoning– Requires much attention: High mental loading– Examples: control room, FES walking?

• Rule-based behaviour:– Tasks with intermediate difficulty– Performance based on applying standard rules– Examples: Control of helping robots

• Skill-based behaviour:– Easy tasks, incorporated in normal behaviour– Performance based on well-trained skills– Requires little mental effort– Examples: Body-powered prosthesis, Bladder control,

Cochlear implants

Model Rasmussen

• Decrease mental load: From knowledge-based behaviour to skill-based behaviour

• Humans generate internal model of system• ‘Ecological’ interface displays system output

resembling internal model• ‘Ecological’ interfaces allow for an intuitive control

Biomechatronics - Lecture 12. Artificial motor control part 2

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