16.400/453J

Human Factors Engineering

Manual Control II

1

Pitch attitude Actual pitch error 8eattitude 8

Desired pitch attitude 8c

Digital flightcontrol computer

Cockpit inceptor

Fly-by-wire

Actuator Sensed aircraft

motion Control effector

Pilot Input 16.400/453

Image by MIT OpenCourseWare.

2

The Basic Pilot/Plant Feedback Loop16.400/453

Display -

+ What you want

Where you are

Pilot Airplane/ Plant

Sensor Disturbance

Input

• Modeling the system • Human modeling is notoriously problematic

• Save for manual control, tracking tasks • Implications for supervisory control systems

3

Modeling & Design 16.400/453

• Models help us design the “system” to promote the best performance – System = human + computer – Performance depends...

• Stability – Bounded output for bounded input

• Maneuverability • Pilot skill

• Two human models – Crossover – Optimal control

4

Modeling the Human Pilot 16.400/453

Commanded Displayed System er noisenoise

YYHH YP

input ror output

•One dimensional compensatory tracking example •Significant assumption of linearity

• A “correct” assumption with noise input because humans perform most linearly with random inputs

• Or valid under stationary tracking with highly trained operators

•Operator/pilot describing function • Not a true transfer function due to linear approximation

5

noiseControl input

YH YP

System response to a control input16.400/453

• Attitude command

• Attitude-rate command K

s

ssKdstKt

)()()()()()(

• Attitude-acceleration command s

K

s

ssKsstKt

)()()()()()(

• Time delays 2

2

)()()()()()(

s

K

s

ssKsstKt

)(se s

• Lag ks

k

k = 1 (unity gain)6

Pilot/Plant Feedback Loop I 16.400/453

Where δp

Yp(s) )(se

θc θ - -

+ +

)(1 s

δ1

δe θe

What you want

you are

Negative feedback system (reduces error)

7

Pilot/Plant Feedback Loop II 16.400/453

)()(1

)(

1 ss

s

e

e

Gs Where you are δp+ θe

Yp(s) θθc -Whatyou want

8

Open loop transfer function

Closed loop transfer function

)()(1)()(

)(sGsY

sGsYs

p

p

c

Input

Output

1 sec 100 msec

+10 φc 0

-10

-90o

-180o

Crossover frequency

log frequency

1Hz 4Hz 10Hz

Phas

e la

g Am

plitu

de r

atio

(dB

)

Optimal Performance & the Bode Plot 16.400/453

• Bode plot helps us see output/input ratios for signal amplitude and phase shift

• 1st order system (s) Kes

(s) s

– -20db drop for each frequency decade increase

– Pure integrator causes 90◦phase shift

– Time delay dominates at high freqs 9

Image by MIT OpenCourseWare.

0

0

-90o

-180o

Amplitude ratio

Phase leg

Zero order First order Second order

Systems Order & the Bode Plot16.400/453

Image by MIT OpenCourseWare.

• Each order adds a 90◦ phase lag & -20db/decade • Time delay exacerbates errors • Integrator: rate of change of control movement is

proportional to error 10

Bode Plot Elements 16.400/453

Open Loop TF Closed Loop TF

11

60

40

20

0

-20

-40

Am

plitu

de R

atio

(db

)

0

-90

-180

-270

-360

-450

-540

-630

-720

Frequency (radians/s)

Phas

e Shi

ft (

deg)

1 10 100

{ Phase Margin = 79 deg

1 100

φc

}10

Gain Margin = 18db

1 1

Frequency (radians/s)

Frequency (radians/s)

Am

plitu

de R

atio

(db

)

0

-40

1 10 100

-20

Am

plitu

de R

atio

(db

)

0

-360

1 10 100

-90

-180

-270

-3dB

Image by MIT OpenCourseWare. Image by MIT OpenCourseWare.

12

Crossover Frequency Concerns16.40 0/453

• The range of frequencies over which the systems responds satisfactorily – We want to maximize, why?

• Open loop crossover frequency determines the bandwidth of the response of closed loop system

• For stability, OL gain must go through 0 dB before phase shift= -180 – Nyquist stability criterion

• Human pilot dynamics ultimately place upper limit on attainable OLTF ωc – Time delay adds phase lag – .1-.25 s is typical

60

40

20

0

-20

-40

}1 10

Am

plitu

de R

atio

(db

)Frequency (radians/s)

Am

plitu

de R

atio

(db

)

0

-40

1 10 100

-20

100

Gain Margin = 18db

Image by MIT OpenCourseWare.

60 60

40

-40

}1 10 100

Gain Margin = 18 db

1

Gain Margin = -2 db

10 100

Phas

e Shi

ft (

deg)

Am

plitu

de R

atio

(db

)

Phas

e Shi

ft (

deg)

Am

plitu

de R

atio

(db

)

40

20

0

-20

20

0

-20

-40

Frequency (radians/s) Frequency (radians/s)

1 101 10 100

-720

{ Phase Margin = 79 deg

00 -90-90

-720

Phase Margin = -25 deg

-180 -180

-270 -270

-360 -360

-450 -450

-540 -540

-630-630

Frequency (radians/s) Frequency (radians/s)

100

Stable vs. Unstable 16.400/453

Image by MIT OpenCourseWare. 13

1 0.63

{0

Ti

Operator Characteristics 16.400/453

0th order system • What can we say about

14

1 10 100

20

0

-20

-40

Am

plitu

de R

atio

(db

)

1 10 0

-90

-180

-270

Phas

e Shi

ft (

deg)

Frequency (radians/s)

Continuous roll of w/ freq = time delay

-20db/decade drop – only at high freqs

Gain

100

this system in terms of the OLTF?

• Gain • Time delay

• Lag or integrator

1)(

jT

KejY

I

jw

H

Images by MIT OpenCourseWare.

j

KejY

jw

H )(Images by MIT OpenCourseWare.

e delay

One operator, three systems…16.400/453

1 10 100

40

20

0

-20

-40

Am

plitu

de R

atio

(db

)

1 10 100

90

0

-90

-180

Phas

e Shi

ft (

deg)

Frequency (radians/s)

1 10 100

40

20

0

-20

-40

Am

plitu

de R

atio

(db

)

1 10 100 0

-90

-180

Phas

e Shi

ft (

deg)

Frequency (radians/s)

1 10 100

20

0

-20

-40

Am

plitu

de R

atio

(db

)

1 10 100 0

-90

-180

-270

Phas

e Shi

ft (

deg)

Frequency (radians/s)

So which system in better?

Yp=4/jw Yp=4/(jw)2Yp=5

Image by MIT OpenCourseWare.

0th order 1st order 2nd order Gain Gain Gain

TTimime delaye delay Integrator

TTimime de delelayay 15

TTimime delayLead at high freqs

YH is dynamic & adaptive 16.400/453

YHYP

Position (0-order) Lag + Time delay

Gain + Time delay

Lead + Time delay

Velocity (1st-order)

Acceleration (2nd-order)

Plant Human Human + Plant

Image by MIT OpenCourseWare.

16

17

Crossover Model 16.400/453

• McRuer, et al. • Human and plant modeled as a

team • YHYP looks like a gain, a time

delay, and an integrator (first order system) in the region of ωc

• Want (relatively) high gain sothat errors can be fixed quicklybut must be below 0db prior tophase lag of -180

jceY ( j)Y ( j) H P j

0.01 0.1 1.0 10 100

60

40

20

0

-20

-40

-60

φc

|YpYc(jφ)|dB

0.01 0.1 1.0 10 100

0

-90

-180

-270

-360

deg

φ rad/sec

YpYc(jφ)

Image by MIT OpenCourseWare.

Crossover Model, II 16.400/453

Human Operator Limitations Model Strategic Parameters

1 )1(

1(

jT

jTK

jT

e

I

L

N

j

YH j )

Numerator Information processing delay

time: perception/cognition Denominator

Action: Neuromuscular lag (< .2s)

Assumptions: Linearity & perfect attention

Plant dependent: •0th order: YH is a apx.

integrator/low pass filter •1st order: YH = pure gain

•2nd order: YH is a differentiator

Zero order First order 0.1 1.0 10.0 0.1 1.0 10.0

10.01.00.1

Controlled element alone

Contribution of

pilot

φc

4040

2020

dBdB

00

-20-20

0o0o

-90o-90o

-180o-180o

-270o-270o

Frequency (radians/sec)

φc

0.1 1.0 10.0

Phas

e an

gle

Gai

n

40

20

0

-20

0o

dB

0.1 1.0

Second order 10.0

-90o

-180o

-270o

0.1 1.0 10.0

φc

Measured data Transfer function predicted by the expanded crossover model

System transfer function φc Crossover frequency Transfer function predicted by the

crossover model

Crossover Model Results16.400/453

19Image by MIT OpenCourseWare.

McRuer et. al (1967)

Handling Qualities Rating Scale

Adequacy for selected task Aircraft

characteristics Demands on the pilot in selected

task or required operation* Pilot rating

or required operation*

Is it satisfactory without improvement ?

YES

Deficiencies warrant NO improvement

Is adequate performance attainable

with a tolerable pilot workload ?

Is it controllable ?

Pilot decision

YES

NO Deficiencies require improvement

YES

Improvement NO mandatory

Excellent Pilot compensation not a factor for Highly desirable desired performance 1

Good Negligible deficiencies

Pilot compensation not a factor for desired performance 2

Fair-some mildly unpleasant deficiencies

Minor but annoying deficiencies

moderately objection -able deficiencies

Very objectionable but tolerable deficiencies

Major deficiencies

Major deficiencies

Major deficiencies

Major deficiencies

Minimal pilot compensation required for desired performance

Desired performance requires moderate pilot compensation

Adequate performance requires considerable pilot compensation Adequate performance requires extensive pilot compensation

Adequate performance not attainable with maximum tolerable pilot compensation. Controllability not in question.

Considerable pilot compensation is required for control. Intense pilot compensation is required to retain control.

Control will be lost during some portion of required operation.

7

8

9

10

3

4

5

6

Subjective Pilot Feedback16.400/453

• Pilots like ga in • Don’t like to

have to generate lead

• Bottom line – 2nd order and higher syste ms are poorly rat ed(and for goo d reason) Image by MIT OpenCourseWare.

20

Internalmodel

Human operator

Observation Motor noise noice

Kalman Command

+ filter x(t) Optimal

Delay Predictor gainDisplay + matrix

Goals: minimize J = (u2τ+ e2) dt "cost functional"

Output System Control

Disturbance

Optimal Control Model16.400/453

• Crossover model limitations– Model &

parameters are based on empirical data (essentially black box thehuman)

– Cannot account for operator Image by MIT OpenCourseWare.strategies, which are often

dynamic21

Optimal Control Model,, II 16.400/453

• Cost functional: J=∫(Au2+Be2) dt

• u = control effort • e = control precision • A & B are adjustable weights • Cost benefit analysis by operator, e.g., smooth control vs. small

error • Two additional distinct operator states

• Prediction • Estimation (Kalman filtering)

• Pros & Cons • Incorporates imperfect attention • Several parameters that must be adjusted to fit the data • PREDICTIVE MODEL BUILDING WARNING!!!

22

PILOT

C

Visual feedback

Vestibular feedback sKm

YPF

YFSYNMKe YCe -δ0s + +

- - -

Proprioceptive feedback

Vehicle E EM �F �

M

Us UM

Human Structural Model 16.400/453

Image by MIT OpenCourseWare.

Hess, 1997 23

(a) �

�

Steering wheel Headingτ

Lateral position τ

angle

Aileron position (rate of roll)

(b)

τ Bank angle

�

τ

0

Heading τ

�

Lateral deviation

(c)

Rubber plane τ

Pitch rate τ

Pitch angle τ

Depth angle

Multi-axis Control 16.400/453

• Cross-coupled & hierarchic al tasks

• Lower order variables m ust be controlle d to regulate higher ordervariables

• Cognitive workload & designintervention s

Image by MIT OpenCourseWare.

Inner Loop Outer Loop24

DRIVER

1/Ri

Curvature Car Car of car heading lateral

V _dt V _dt1/L

path angle position 1/R+ θc xc

Wheel Speed and path geometry base

Lateral Position

error xe

Driving lane lateral position

xi

V _dt

Driving lane angle

θi

Heading angle error

θe

Kpx

Kpxxe + θe Lead

Kpθ

Time delay

δ Ks

KpR

Disturbances

Tire angle

�

Steering wheel angle

�sw Internal noise

n

Previewed road curvature

Steering linkage

+

+

+ +

+

+

+

+ +

-

-

Multi-Axis Systems 16.400/453

Image by MIT OpenCourseWare.

25

References 16.400/453

• McRuer, D. T., Krendel, E. S., & Reisener, W. (1965). Human pilot dynamics in compensatory systems (Wright-Patterson Air Force Base Technical Report, AFFDL-TR-65-15). NASA.

• A Review of Quasi-linear Pilot Models, Duane T. McRuer and Henry R. Jex, IEEE Transactions on Human Factors in Electronics HFE-3 (1967): 231-249.

• McRuer, D. T., & Krendel, E. S. (1974). Mathematical models of human pilot behavior (NASA Technical Report. AGARD-AG-188).

• Hess, R.A.: Uni¯ed Theory for Aircraft Handling Qualities and adverse Aircraft-Pilot Coupling, Journal of Guidance, Control and Dynamics, Vol. 20 No 6, 1997, pp. 1141-1148

• An optimal control model of human response Part 1: Theory and validation DL Kleinman, S. Baron and WH Levison: Automation 6 (1970): 357-368.

26

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