16.400/453J
Human Factors Engineering
Manual Control II
Pilot Input
16.400/453
Actual pitch
attitude 8
Pitch attitude
error 8e
Digital flight
control computer
Desired pitch
attitude 8c
Cockpit inceptor
Fly-by-wire
Sensed aircraft
motion
Actuator
Control effector
Image by MIT OpenCourseWare.
2
The Basic Pilot/Plant Feedback Loop
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+
What
you
want
-
Display
Pilot
Sensor
• Modeling the system
Airplane/
Plant
Disturbance
Input
• Human modeling is notoriously problematic
• Save for manual control, tracking tasks
• Implications for supervisory control systems
3
Where
you are
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
16.400/453
Modeling the Human Pilot
Commanded Displayed
input
error
noise
noise
System
output
Control
input
YHH
Y
Y
YPP
• 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
System response to a control input
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• Attitude command
 ( s)
K
 (t )  K (t )  (s)  Kd (s)
 ( s)
• Attitude-rate command
 ( s) K


 (t )  K (t ) s (s)  K (s)
 ( s) s
• Attitude-acceleration command
(t )  K (t ) s 2 (s)  K (s)  ( s)  K
2
 ( s) s
• Time delays
s
• Lag
e  (s)
k
sk
k = 1 (unity gain)
6
Pilot/Plant Feedback Loop I
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θ
+ e
θc
What
Yp(s)
δp
+
δe
-
you
want

(s )
e
δ1
Negative feedback system (reduces error)
7
1
(s)

Where
you are
θ
Pilot/Plant Feedback Loop II
16.400/453
θc
+
What
you want

G
s
(
s
)
θe
δp
e
Yp(s)

1
1  ( s) ( s)
e

Y p ( s )G ( s )

(s) 
c
1  Y p ( s )G ( s )
Where you are θ
Open loop transfer function
Closed loop transfer function
8
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
1 sec
Input
Amplitude ratio (dB)
Output
Phase lag
 (s) Ke s

s
 (s)
– -20db drop for each
frequency decade increase
– Pure integrator causes 90◦
phase shift
– Time delay dominates at
high freqs
100 msec
φc
+10
0
-10
Crossover
frequency
1Hz
4Hz
10Hz
log frequency
-90o
-180o
9
Image by MIT OpenCourseWare.
Systems Order & the Bode Plot
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Zero order
Amplitude
ratio
First order
Second order
0
0
Phase
o
leg -90
-180o
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
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Closed Loop TF
Open Loop TF
0
Amplitude Ratio (db)
Amplitude Ratio (db)
60
40
φc
20
0
1
Gain Margin = 18db
10
-20
}
100
-40
-90
-180
-270
10
100
-3dB
-20
-40
1
10
Frequency (radians/s)
100
Amplitude Ratio (db)
Phase Shift (deg)
0
1
{
Phase Margin = 79 deg
-360
-450
-540
-630
0
1
10
100
-90
-180
-270
-360
-720
Frequency (radians/s)
Image by MIT OpenCourseWare.
Frequency (radians/s)
11
Image by MIT OpenCourseWare.
Crossover Frequency Concerns
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• 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
Amplitude Ratio (db)
– We want to maximize, why?
60
40
Gain Margin = 18db
20
0
1
10
-20
}
100
-40
0
Amplitude Ratio (db)
• The range of frequencies over
which the systems responds
satisfactorily
1
10
100
-20
-40
Frequency (radians/s)
Image by MIT OpenCourseWare.
Stable vs. Unstable
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60
Amplitude Ratio (db)
Amplitude Ratio (db)
60
40
20
0
Gain Margin = 18 db
1
10
-20
}
100
40
20
0
-270
100
1
10
Frequency (radians/s)
100
0
1
10
100
-90
{
Phase Shift (deg)
Phase Shift (deg)
-180
10
-20
Frequency (radians/s)
-90
1
-40
-40
0
Gain Margin = -2 db
Phase Margin = 79 deg
-360
-450
-540
-630
-720
-180
-270
-360
Phase Margin = -25 deg
-450
-540
-630
-720
Frequency (radians/s)
Frequency (radians/s)
Image by MIT OpenCourseWare.
13
Operator Characteristics
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• What can we say about
this system in terms of the
OLTF?
0th order system
Gain
1
-20
-40
0
Phase Shift (deg)
• Gain
• Time delay
• Lag or integrator
0
10
100
-20db/decade
drop – only at
high freqs
10
1
100
1
0.63
0
{
Amplitude Ratio (db)
20
Ti
-90
-180
Continuous roll of w/
freq = time delay
-270
Images by MIT OpenCourseWare.
Frequency (radians/s)
14
Images by MIT OpenCourseWare.
 Ke jw 
YH ( j )  

 TI j  1
 Ke jw 
YH ( j )  

j



One operator, three systems…
16.400/453
40
0
1
10
100
-20
0
1
10
100
-20
Yp=4/(jw)2
20
0
1
10
100
-20
-40
10
100
0
-90
-180
-270
Frequency (radians/s)
1
10
90
-90
-180
100
Phase Shift (deg)
1
Phase Shift (deg)
Phase Shift (deg)
Yp=4/jw
20
-40
-40
0
40
Amplitude Ratio (db)
Yp=5
Amplitude Ratio (db)
Amplitude Ratio (db)
20
0
1
10
100
-90
-180
Frequency (radians/s)
Frequency (radians/s)
So which system in better?
0th order
Gain
Tim
imee delay
Integrator
1st order
Gain
Tim
imee del
delay
ay
15
Image by MIT OpenCourseWare.
2nd order
Gain
Tim
imee delay
Lead at high freqs
YH is dynamic & adaptive
16.400/453
Plant
Human
Position (0-order)
Lag + Time delay
Velocity (1st-order)
Gain + Time delay
Acceleration (2nd-order)
Lead + Time delay
Human + Plant
Image by MIT OpenCourseWare.
16
YHYP
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 so
that errors can be fixed quickly
but must be below 0db prior to
phase lag of -180
j
c e
YH ( j )YP ( j ) 
j
60
40
|YpYc(jφ)|dB
20
0
-20
φc
-40
-60
0.01
0.1
1.0
10
100
0
-90
-180
YpYc(jφ)
deg
-270
φ rad/sec
-360
0.01
0.1
1.0
10
100
Image by MIT OpenCourseWare.
Crossover Model, II
16.400/453
Human Operator Limitations
Model Strategic Parameters
 e
 K(TL j 1) 
YH
( j
)
 


TN j 1 TI j 1 
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
Crossover Model Results
16.400/453
Zero order
40
0.1
First order
1.0
10.0
40
Gain
Second order
1.0
10.0
40
20
20
φc
dB
0
Controlled
element
alone
Contribution
of
pilot
φc
0
0
-20
0o
0o
-90o
-90o
-90o
-180o
-180o
-180o
-270o
0.1
1.0
10.0
10.0
1.0
dB
-20
-270o
0.1
20
φc
dB
0o
-20
Phase angle
0.1
-270o
0.1
1.0
10.0
0.1
1.0
10.0
Frequency (radians/sec)
Measured data
Transfer function predicted by the
expanded crossover model
System transfer function
Transfer function predicted by the
crossover model
19
φc
Crossover frequency
Image by MIT OpenCourseWare.
McRuer et. al (1967)
Subjective Pilot Feedback
16.400/453
• Pilots like gain
• Don’t like to
have to generate lead
• Bottom line –
2nd order and
higher systems
are poorly rated
(and for good
reason)
Handling Qualities Rating Scale
Adequacy for selected task
or required operation*
YES
Is it satisfactory
without improvement ?
Deficiencies warrant
improvement
NO
Aircraft
characteristics
NO
Deficiencies require
improvement
YES
Is it controllable ?
Improvement
mandatory
NO
Pilot
rating
Excellent
Highly desirable
Pilot compensation not a factor for
desired performance
1
Good
Negligible deficiencies
Pilot compensation not a factor for
desired performance
2
Fair-some mildly
unpleasant deficiencies
Minimal pilot compensation required for
desired performance
3
Minor but annoying
deficiencies
Desired performance requires moderate
pilot compensation
4
moderately objection
-able deficiencies
Adequate performance requires considerable
pilot compensation
5
Very objectionable but
tolerable deficiencies
Adequate performance requires extensive
pilot compensation
6
Major deficiencies
Adequate performance not attainable with
maximum tolerable pilot compensation.
Controllability not in question.
7
Major deficiencies
Considerable pilot compensation is
required for control.
8
Major deficiencies
Intense pilot compensation is
required to retain control.
9
Major deficiencies
Control will be lost during some portion of
required operation.
YES
Is adequate
performance attainable
with a tolerable
pilot workload ?
Demands on the pilot in selected
task or required operation*
10
Pilot decision
Image by MIT OpenCourseWare.
20
Optimal Control Model
16.400/453
• Crossover model limitations
– Model & parameters are based on empirical data (essentially black box the
human)
Human operator
Observation
noise
Command
+
Display
Delay
Kalman
filter
Predictor
Internal
model
Motor
noice
x(t)
Optimal
gain
matrix
+
Goals: minimize
J = (u2 τ+ e2) dt
"cost functional"
Output
– Cannot account for operator
strategies, which are often dynamic
System
Control
Disturbance
Image by MIT OpenCourseWare.
21
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
Human Structural Model
16.400/453
PILOT
+
C
E
-
Ke
e-δ0s
Vehicle
EM +
-
Us
Vestibular feedback
YNM
�F
YFS
-
UM
�
YC
M
YPF
Proprioceptive
feedback
sKm
Visual feedback
Image by MIT OpenCourseWare.
Hess, 1997
23
Multi-axis Control
16.400/453
• Cross-coupled
& hierarchical
tasks
• Lower order
variables must
be controlled
to regulate
higher order
variables
• Cognitive
workload &
design
interventions
�
(a)
�
τ
Steering wheel
angle
�
(b)
Aileron position
(rate of roll)
τ
Heading
τ
Bank angle
Lateral position
�
0
τ
Heading
τ
Lateral
deviation
(c)
Rubber plane
angle
τ
Pitch rate
τ
Pitch angle
τ
Depth
Image by MIT OpenCourseWare.
Inner Loop
24
Outer Loop
Multi-Axis Systems
16.400/453
DRIVER
Previewed road
curvature
1/R
i
Internal
noise
n
KpR
Kpx
Driving
lane
angle
θi
Lead
Kpxxe + θe
+ +
+
+
Kpθ
+
Time
delay
δ
Steering
wheel angle
�sw
Disturbances
+
+
Ks
Tire
angle
+
�
Steering
linkage
Heading
angle
error
θe
+
Curvature
of car
path
1/R
1/L
Wheel
base
V _dt
Car
heading
angle
θc
V _dt
Car
lateral
position
xc
Speed and path geometry
-
V _dt
Lateral
Position
error
xe
+
Driving lane
lateral position
xi
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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16.400 / 16.453 Human Factors Engineering
Fall 2011
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