Jtam.dvi


JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

49, 1, pp. 175-186, Warsaw 2011

PILOT SUBJECTIVE DECISIONS IN AIRCRAFT ACTIVE

CONTROL SYSTEM

Jozsef Rohacs

Budapest University of Technology and Economics, Budapest, Hungary

e-mail: jrohacs@rht.bme.hu

Valery A. Kasyanov

Kiev Aviation University, Kiev, Ukraine

The aircraft conventional control systems including pilot-operators in
loop are called as active endogenous systems, because the pilots react
actively to real situations evaluated by them and their solutions origin
from their minds, from the nervous system. The pilots must make de-
cisions in situations characterised by lack of information, human robust
behaviour and their individual capabilities. So, decisions born from re-
actions of pilot are an effect of subjective analysis.
This paper investigates the aircraft landing. The subjective factor is the
ratio of required and available time to decision on the go around. The
decision depends on the available information and psycho-physiological
condition of operator pilots and can be determined with the use of the-
ory of statistical hypotheses. This paper introduces a modified Lorenz
attractor for the modelling of the endogenous dynamics of the given
active system.

Keywords:active control system, endogenous system, subjectiveanalysis

1. Introduction

The central deterministic element of the aircraft conventional control systems
is the subject that is an operator-pilot. Such systems are called as active
endogenous systems (Kasyanov, 2007). The pilots make a decision on control
depending on their situation awareness, knowledge, practice and skills. The
pilots must make decisions in situations characterised by lack of information,
human robust behaviour and their individual capabilities. So, the decisions
origin from analysis of pilot-subjects or subjective analysis.



176 J. Rohacs, V.A. Kasyanov

Aircraft control can be characterised with the use of subjective analysis
together with the aircraft motion models. The general model of solving the
control problems includespassive (information, energy-like aircraft control sys-
tem in its physical form) and active (physical, intellectual, psychophysiology,
etc. behaviour of subjects) resources.Thedecisionmaking is the right choosing
of the required results giving the best (effectively, safety, etc.) solutions.

This paper investigates the aircraft landing. The applied equations of mo-
tion describe the motion of aircraft in the vertical plane only. The boundary
constraints are defined for velocity, trajectory angle and altitude. The subjec-
tive factor is the ratio of required and available time for making a decision on
the go-around.The decision depends on the available information and psycho-
physiological condition of the operator pilots and can be determined with the
use of theory of statistical hypotheses. This paper proposes amodified Lorenz
attractor for the modelling of the endogenous dynamics of the given active
system.

2. Aircraft motion as the situation process

Safety of active systems is determined by risks initiated by subjects who are
the central elements of the given systems. For example, the flight safety is the
probability of that the flight will be realised without an accident.
The aircraft are moving in three dimensional space depending on the air-

craft aerodynamic characteristics, flight dynamics, environmental stochastic
disturbances (wind, air turbulence) and applied control. The pilots make a
decision on the control after evaluation of the flight situation awareness. Prin-
cipally, theymust define the problem and after that theymust choose a solu-
tion from their resources. There is a reason why the human controlled active
systems are endogenous. Resources are methods, technologies, etc. that can
be applied for solving the problems. There are passive (finance, materials,
information, energy-like aircraft control system in its physical form) and acti-
ve (physical, intellectual, psycho-physiological, etc. behaviors, possibilities of
subjects) resources. The passive resources are the resources of the system (air
transportation system as, ATM, services provided, etc.), while the active re-
sources belong to the pilot itself. The decision making is the right choosing of
the required results giving the best (effectively, safety, etc.) solutions.

The subjects (like pilots) develop their available active resource during
learning and practice (developing their competences). However, the ability of
choosing and using the right resources depend on the information support,



Pilot subjective decisions in aircraft... 177

time available for decision making, real knowledge, way of thinking and skills
of the subjects. Such decisions are results of the subjective analysis (Berger,
1985; Kasyanov, 2007).
There is not enough information about the physical, systematic, intellectu-

al, psychophysiology, etc. characteristics of the subjective analysis about the
way of thinking and decision making of subjects-operators like pilots. Only
limited information is available about the time effects, possible damping of
non-linear oscillations, long term memory, etc. making the decision system
chaotic.
In our case, safety of personal planes can be characterized with the use of

subjective analysis together with the aircraft motion models.
At first (Fig.1a), the pilot as a subject Σ must identify and understand

the problem (situation) Si, then from the set of accessible or possible devices,
methods and factors, Sp must choose the disposable resources R

disp, available
for possible solution of the identified problem, and finally must decide and
apply the required resources Rreq. As it has beenmentioned, the pilot utilizes
the passive and active resources (Kasyanov, 2007). The active resources are
defined by pilot’s decision which and how will the passive resources be used

Rreqa = f(R
req
p ) (2.1)

Often, instead of function (2.1) between the resources, the velocity of trans-
ferring the passive resources into the active ones is used

vreqa = fv(v
req
a )v

req
a (2.2)

where

vreqa =
dRreqa
dt

vreqp =
dRreqp

dt
(2.3)

and in simple cases

fv =
∂Rreqa
∂R
req
p

(2.4)

It is clear that the operational processes can be given by a series of si-
tuations: pilot identifies the situation Si makes a decision and applies the
control Rreqa , which transits the aircraft into the next situation Sj randomly
(the situation Sj is one of the sets of possible situations). This is a repeating
process (see Fig.1b), in which the transition from one situation into another
depends on (i) the evaluation (identification) of the given situation, (ii) ava-
ilable resources, (iii) appropriate decision of the pilot, (iv) correct application
of the active resources, (v) limitation of the resources and (vi) the affecting
disturbances.



178 J. Rohacs, V.A. Kasyanov

Fig. 1. Aircraft operation as the active endogenous system; (a) pilot decision –
action process, (b) siyuation chain process

The situation chain process can be given by the following mathematical
representation (Berger, 1985; Kasyanov, 2007)

c(t) :
(

x0, t0,ω(tf ∈ [t0, t0+ τ]);R
disp(t0),R

req(t0), . . .
)

(2.5)

or in a more general approach

c(t) :
(

P : σ0(t0)→σj(tf ∈ [t0, t0+ τ])∈Sf ⊂Sa,R
disp(t0),R

req(t0), . . .
)

(2.6)
where x0 is the vector of parameters at the initial state (actually starting)
state at t0 time; σ is the state of the system at the given time; τ is the
available time that is enough for transition of the state vector into a set of ω
not later than [t0, t0+τ]; P are the problems how to transit the system from
the initial state intoanother oneof thepossible state Sf ⊂Sa not later than τ.
During a flight, one flight situation is followed by another. So the flight

as the aircraft operational process in a continuous state space and time can
be approximated by a stochastic process of flight situations in a continuously
time and discrete state space (Rohacs and Németh, 1997; Rohacs and Simon,
1989). This means that the flight is a typical situation chain process.

3. Aircraft landing

Asan example, the aircraft landingprocess asmotion of aircraft in the vertical
plane is investigated. There is no side wind, no lateral motion. With the use
of the trajectory reference system (when the x axis shows the wind direction,
the axis z is perpendicular to x in the local vertical plane, and the centre of
system is put into the centre of gravity of the aircraft) motion of the aircraft
canbedefinedbymotion of its centre of gravity and rotation around the centre
of gravity (Kasyanov, 2004)



Pilot subjective decisions in aircraft... 179

m
dV

dt
=T(V,z,t)−W sinθ−D(V,z,t) mV

dθ

dt
=L(V,z,t)−W cosθ

(3.1)

Iy
dq

dt
=M(α,q,V,z,t)

The thrust T , lift L, drag D and aerodynamicmoment M are clearly depen-
ding on time because of the applied control. The altitude z also has influence
on them through the ground effect. Themass m and, of course, then the we-
ight W of the aircraft are assumed as constant. The aircraft velocity V and
pitch rate q describe theaircraftmotion,while theflightpathangle (ordescent
angle) θ depicts the aircraft position. The angle of attack α is a difference
between the pitch attitude ϑ and the flight path angle

α=ϑ−θ (3.2)

The pitch rate and the changes in altitude can be determined very simply

q=
dϑ

dt

dH

dt
=V sinθ (3.3)

According to flight operationalmanuals and airworthiness requirements, there
are limitations on the velocity, descent angle and decision altitude

V ∈ [V ∗min,V
∗

max] θ∈ [θ
∗

min,θ
∗

max] H ­H
∗

Dmin (3.4)

A simple assumption can be applied: during the approach, pilots should deci-
de whether to land or to make a go-around. For this decision they need time,
which is the sum of (i) the time to understand and evaluate the given situ-
ation σk, (ii) the time for decisionmaking and (iii) the time to react (covering
also the reaction timeof the aircraft for the applieddecision) (Kasyanov, 2007)

treq = treque (σk)+ t
req
dec
(Sa)+ t

req
react(σk,Sa) (3.5)

Here σk defines all possible situations (e.g. σ1 might be the situation of
landing at the first approach without any problems, σ2 could be related to
the situation when the undercarriage system could not be opened, σ3 might
stand for a landing on the fuselage, σ5 for go-around, or σ5 for a successful
landing after the second approach).

Sa is the chosen solution from the set of possible solutions. It is clear that
all solutions have a limiting drawback, such as extra cost or extra fuel.



180 J. Rohacs, V.A. Kasyanov

4. Subjective factor in aircraft landing control

The subjective factor of pilots can be assumedby the ratio of the required and
disposable resources (Kasyanov, 2007)

rk =
Rreq(σk)

Rdisp(σk)
=
treq(σk)

tdisp(σk)
(4.1)

By making use of this factor, an endogenous index can be defined as

εk(σk)=
rk

1−rk
=

τreq(σk)

τdisp(σk)− τ
req(σk)

(4.2)

Naturally, we can assume that the pilots are able to evaluate the consequ-
ences of their decisions, namely they can evaluate the risk of the applied so-
lutions. Such an evaluation can be defined as the subjective probability of
situations P(σk), the canonic distribution of which as a distribution of the
canonic assemble of preferences is assumed to hold the following form

p(σk)=
P−a(σk)e

−bεk(σk)

∑2
q=1P

−a(σq)e
−bεk(σq)

(4.3)

where p(σk) describes the distribution of the best alternatives from anegative
point of view.
The time-depending coefficients α and β should be chosen in a way to

model the endogenous dynamics, i.e. the subjective psycho-physiological per-
sonalities of pilots. The qualities of the pilots depend on different factors inc-
luding ”periodical” unfixity that increases while getting closer to the decision
time (altitude) of go-around.
Formula (4.3) has special features when

tk =
treq(σk)

tdisp(σk)
→ 0

the preferences are determined by the subjective probability, P(σk) only, and
in the case tk → 1, the preferences turn to zero. Expression (4.3) comes from
solution of the functional

Φp =−
N
∑

k=1

p(σk)lnp(σk)−β
N
∑

k=1

p(σk)εk(σk)+

(4.4)

−α

N
∑

k=1

p(σk)lnP(σk)+γ
N
∑

k=1

p(σk)



Pilot subjective decisions in aircraft... 181

A special feature of this functional is that the structure of the efficiency func-
tion includes the logarithm of the subjective probability

ηp =−
N
∑

k=1

[α lnP(σk)+βε(σk)]p(σk) (4.5)

The complexity of decisionmaking could be characterised byuncertainties and
the hereupon unfixedness of the pilots that are increasing while getting closer
to theminimum decision altitude H∗Dmin. Tomake decisions, the pilots must
overcome their ”entropic barrier” Hp. The rate of unfixity can bedefinedwith
a norm of entropy

Hp =
Hp

lnN
(4.6)

Figure 2 showsa simplifieddecisionmaking situation at an approach about
the go-around (Kasyanov, 2004, 2007). At (t0,x0), Sa : (σ1,σ2) indicates
the set of alternative situations with the distribution of preferences p(σ1)
and p(σ2) (where σ1 indicates the landing and σ2 defines the go-around).

Fig. 2. Final phase of aircraft approach

The preferences are oscillating because of the exogenous fluctuation (while
the decision altitude is getting closer) and the endogenous processes (depen-
ding on the uncertainties in the situation awareness and unfixedness of the
pilots). If the pilots are able to overcome their entropy barrier up to the com-
mand for go-around (reaching the decision minimum altitude) (t∗,x∗), then
they couldmake a decision. Due to this decision, the set of situations Sa , can
be given by the following

(

Sa : (σ2);p(σ2);T < t
∗;p(σ1)+p(σ2)= 1

)

⇒

⇒

(

Sa1 : (σ2);p(σ2)= 1;p(σ1)= 0
)

∨

(

Sa2 : (σ1);p(σ1)= 1;p(σ2)= 0
)

t­ t∗ (4.7)



182 J. Rohacs, V.A. Kasyanov

If they are not able to overcome their entropy barrier before reaching (t∗,x∗),
the flight situation would becomemore complex, and therefore the possibility
to perform a go-around (case σ2) might be even out of the possible set of
situations.

5. Pilot endogenous dynamics

ProfessorKasyanov introduceda special chaoticmodel (Kasyanov, 2007)based
on themodifiedLorenzattractor (Strogatz andSteven, 1994) for themodelling
of the endogenous dynamics of the described process.

dX

dt
= aY − bZ−hX2+f(t)

dY

dt
=−Y −XZ+ cX−mY 2

(5.1)
dZ

dt
=XY −dZ−nZ2

where a, b, c, d, h,m, n are constants while f takes into account the distur-
bance. In the case of h=m=n=0 and f(t) = 0, the model turns into the
classic form of Lorenz attractor.

In this model, the coordinates of attractors can be defined as X – the
inner endogenous parameter, Y =β and Z =α.

Principally, there are not strong arguments (Kasyanov, 2007) explaining
the use of Lorenz attractor for the modelling of the human way of decision
making (human thinking), but the results of its application are close to real
situations that need further investigation (Dartnell [2]).

Professor Kasyanov has investigated various types of the model, and eva-
luated model parameters (Kasyanov, 2007). For a medium sized aircraft (we-
ight W = 106N; wing area S = 100m2; wing aspect ratio A = 7; thrust
T = 9.4 ·104N; and velocity V =70m/s) with commercial pilots, he recom-
mended to use the following values: a = 8, b = 8, c = 20, d = 43, f = 0.8,
h=0.065, m=0.065, n=0.065.

Subjective probabilities might be chosen as P(σ1) = 0.53, P(σ2) = 0.6
and ε1 =5.5+0.01t, ε2 =5.4+0.04t which take into account the decreasing
difference in the required and available time for a decision.

The results of using the describedmodel are shown in Fig.3.

In this example, thefiguresdemonstrate that pilots are unfixed for aperiod
about 10s, during which their preferences (A,B) are changing by sudden
oscillations, and the entropy H at the beginning is rather high. If the limit



Pilot subjective decisions in aircraft... 183

Fig. 3. Results of using the developedmodel for a medium sized aircraft

for the entropy would be 0.7 (that is still quite high) then decisions could be
made in about 10s. Thismeans that the pilots will not be able to do thatwith
accordance to Fig.2.

If theparameters are set to a=10, b=10, c=35,d=1,f =0,h=0.065,
m = 0.065, n = 0.065 and P(σ1) = 0.53, P(σ2) = 0.6, then (see Fig.4) the
entropy would quickly decrease and the decision could be made in about 3s.
According to the ICAO requirements, the time t= tga−t

∗ (see Fig.2) should
not be less than 3.16s. Therefore, if the situation presented in Fig.2 appears
before (t0,x0), then the right decision could bemade.



184 J. Rohacs, V.A. Kasyanov

Fig. 4. Results when the parameters are chosen for well-skilled pilots

From the results of the developedmodel, (after application and analysis of
the describedmethodbyHungarian national projects SafeFly: development of
the innovative safety technologies for a 4-seats composite aircraft andEUFP7
project PPlane: Personal Plane)we can conclude that in the case of a problem
at the final approach, common airliner pilots require about three times more
time to decide than the well-skilled crew.

The developed model can also be applied for small aircraft, controlled
by less-skilled pilots. From Fig.2, the descent velocity of a small aircraft is
calculated to be about 100 km/h for airliner common pilots, and 75km/h for
those less-skilled.

In this case, the airport canbedesignedwitha landingdistance of less than
600m (runway about 250-300m) and a protected zone under the approach (to
overfly the altitude of 100m) of about 1500m.These characteristics enable to
place small airports close/closer to the city center.

These are the preliminary results and draft description. We are going to

make some other calculations and we will make more accurate conclusions.

6. Conclusions

This paper introduced a subjective analysis methodology into investigation of
the real flight situation, flight safety.The subject – thepilot operator generates
his decision on the basis of his subjective situation analysis depending on the
available information and his psycho-physiological condition. The subjective
factor is the time available for the decision of the given task.

The paper concerns the aircraft landing. The subjective decision making
of pilots was modelled by the modified Lorenz attractor that needs further
investigation and explaination, however the practice shows good applicability
of the developed model. The model is well usable for the investigation of



Pilot subjective decisions in aircraft... 185

differences between skills of well- and less-trained pilots. Themodel helped to
define requirements for the aircraft and airport characteristics for the personal
air transportation system.

References

1. Berger J.O., 1985,Statistical Decision Theory and Bayesian Analysis, Sprin-
ger, NewYork, US

2. Dartnell L.,Chaos in the Brain,
http://plus.maths.org/issue35/features/dartnell/2pdf/index.html/op.pdf

3. Kasyanov V.A., 2004, Flight Modeling, National Aviation University, Kiev,
pp.400 [in Russian]

4. KasyanovV.A., 2007SubjectiveAnalysis,NationalAviationUniversity,Kiev,
pp.512 [in Russian]

5. Rohács J.,NémethM., 1997,Effects of aircraft anomalies onflight safety, in:
Aviation Safety, H.M. Soekkha (Edit.), VSP,Utrecht, TheNetherlands,Tokyo,
Japan, 203-211

6. Rohacs J., Simon I., 1989, Repülögépek és helikopterek üzemeltetési
zsebkönyve (The handbook of airplane and helicopter operation), Müszaki
Könyvkiadó, Budapest

7. Strogatz S., 1994,NonlinearDynamics andChaos: withApplications to Phy-
sics, Biology, Chemistry, and Engineering, Perseus Books, Massachusetts, US

Subiektywne decyzje pilota w aktywnym układzie sterowania samolotu

Streszczenie

Konwencjonalneukłady sterowania samolotem,włączającw to rolę pilotów, nazy-
wane są aktywnymi układami endogennymi z racji znaczenia bieżącej oceny sytuacji
i reakcji pilotów wynikających z ich świadomości i cech układu nerwowego. Piloci
muszą podejmować decyzjewwarunkachbrakupełnej informacji o parametrach lotu,
posiadając przy tym swoiste cechy reaktywnych zachowań i własny zestaw wytreno-
wanychnawyków.Wten sposóbanalizawłaściwościmonitorowania samolotu staje się
badaniemukładu zawierającego zmienne subiektywne.Wpracy zbadano problempo-
dejścia do lądowania. Za czynnik subiektywnywzięto stosunek czasuwymaganego do
faktycznie posiadanego przed podjęciem decyzji o możliwej rezygnacji z lądowania.



186 J. Rohacs, V.A. Kasyanov

Decyzja ta zależy od ilości zgromadzonych informacji w danej chwili oraz kondy-
cji psycho-fizjologicznej pilotów i została opisana za pomocą hipotez statystycznych.
Do zamodelowaniadynamiki rozważanegoendogennegoukładu sterowania samolotem
użyto zmodyfikowanego atraktora Lorentza.

Manuscript received June 21, 2010; accepted for print July 30, 2010