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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