Ci a ion: Dalwadi, N.; Deb, D.;
Ozana, S. Ro o Failu e
Compensa ion in a Biplane
Quad o o Based on Vi ual
De lec ion. D ones 2022,6, 176.
h ps://doi.o g/10.3390/
d ones6070176
Academic Edi o s: Mehdi
Ghommem, Jawha Ghommam,
B ahim B ahmi and Quanmin Zhu
Recei ed: 15 June 2022
Accep ed: 11 July 2022
Published: 17 July 2022
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d ones
A icle
Ro o Failu e Compensa ion in a Biplane Quad o o Based on
Vi ual De lec ion
Nihal Dalwadi 1,† , Dipanka Deb 1,*,† and S epan Ozana 2,†
1Depa men o Elec ical Enginee ing, Ins i u e o In as uc u e Technology Resea ch and Managemen
(IITRAM), Ahmedabad 380026, India; [email p o ec ed]
2Depa men o Cybe ne ics and Biomedical Enginee ing, Facul y o Elec ical Enginee ing and Compu e
Science, VSB-Technical Uni e si y o Os a a, 17. lis opadu 2172/15, 708 00 Os a a-Po uba, Czech Republic;
[email p o ec ed]
*Co espondence: dipanka [email p o ec ed]
† These au ho s con ibu ed equally o his wo k.
Abs ac :
A biplane quad o o is a hyb id ype o UAV ha has wide applica ions such as payload
pickup and deli e y, su eillance, e c. This simula ion s udy mainly ocuses on handling he o al
o o ailu e, and o ha , we p opose a con ol a chi ec u e ha does no only handle o o ailu e
bu is also able o na iga e he biplane quad o o o a sa e place o landing. In his s uc u e, a e
he de ec ion o o al o o ailu e, he biplane quad o o will imi a e ealloca ing con ol signals
and hen pe o m he ansi ion maneu e and swi ch o he ixed-wing mode; con ol signals a e
also ealloca ed. A syn he ic je ac ua o (SJA) is used as he edundancy ha gene a es he desi ed
i ual de lec ion o con ol he pi ch angle, while o he s a es a e aken ca e o by he h ee o o s.
The SJA has pa ame ic nonlinea i y, and o handle i , an in e se adap i e compensa ion scheme
is applied and a closed-loop s abili y analysis is pe o med based on he Lyapuno me hod o he
pi ch subsys em. The e ec i eness o he p oposed con ol s uc u e is alida ed using nume ical
simula ion ca ied ou in he MATLAB Simulink.
Keywo ds:
biplane quad o o ; o al o o ailu e; syn he ic je ac ua o ; adap i e in e se compensa ion
scheme; adap i e backs epping con ol design
1. In oduc ion
Nowadays, Unmanned Ae ial Vehicles (UAVs) play a key ole in all sec o s ha
a ec human li e di ec ly and indi ec ly. UAVs a e used in a ic moni o ing [
1
], p ecision
ag icul u e (PA) [
2
], humani a ian elie [
3
], ba hyme ic mapping [
4
,
5
], payload deli e y [
6
].
Among hese, payload deli e y by a UAV has become common because i sa es ime as
well as ene gy; in gene al, con en ional quad o o UAVs a e used o payload deli e y.
A biplane quad o o is mo e sui able o he payload deli e y han a o a y-wing UAV
because i is a hyb id- ype UAV ha can ly like bo h o a y-wing and ixed-wing UAVs.
Many esea che s ha e wo ked o de eloped a design and con ol me hodology o hyb id
quad o o . P oo -o -concep o a iable pi ch biplane quad o o o he payload deli e y
is de eloped and demons a ed by [
7
]. A mo phing wingle is de eloped o he biplane
quad o o wi h enhanced e iciency in [
8
]. The e a e many linea and nonlinea con ol
schemes ha ha e been de eloped o con ol hyb id UAVs, such as PID [
9
], LQR [
10
], and
SMC [
11
–
13
]. Dalwadi e al. [
14
] de eloped a backs epping con olle o he ajec o y
acking and nonlinea dis u bance obse e -based backs epping con olle s o handle
wind gus s in he quad o o mode o a ail-si e quad o o , while a hyb id con olle based
on wo di e en nonlinea con ol me hods was designed o he ajec o y acking o
biplane quad o o s [15].
UAVs a e highly nonlinea and coupled sys ems ha become mo e complex and
uns able du ing o o ailu e. The e ha e been many con ol s uc u es de eloped o handle
D ones 2022,6, 176. h ps://doi.o g/10.3390/d ones6070176 h ps://www.mdpi.com/jou nal/d ones
D ones 2022,6, 176 2 o 20
o o ailu e du ing ligh . In es iga ion and con olling s a egies o he one o mo e o o
ailu es in a hexacop e while in he ho e s a e is p esen ed in [
16
] and NTSMC (Non-
singula Te minal Sliding Mode Con ol) o o al o o ailu e in quad o o is p esen ed [
17
].
AFTCS is de eloped and implemen ed in ha dwa e by Saied e al. [
18
] o an oc ocop e
UAV. Howe e , a deep neu al ne wo k-based aul de ec ion algo i hm is de eloped o he
oc ocop e [
19
]. The c ash p obabili y densi y (CPD) is e alua ed based on he New on’s
laws, as well as Galileo’s ee all o di e en ypes o UAVs using MATLAB simula ion
ca ied ou in MATLAB in [
20
].To handle o o ailu e in he quad-plane, a no el I-ASMC
is p oposed in [
21
]. Fo pa ial as well as o al o o ailu e in quad o o UAVs, a obus ,
linea pa ame e - a ying obse e is designed, and i s e ec i eness is alida ed using
nume ical expe imen s in [
22
]. The aul eco e able measu e o a nonlinea sys em like a
UAV is p esen ed [
23
], which is cus omized o ensu e an adequa e edundancy le el o
he achie emen o FTC, and a guide o inc ease he edundancy le el while he FTC is
de eloped [
24
] o econ igu e he us sys em based on he op imal con ol du ing he
ailu e in he mul i- o o UAVs. A comple e ac i e FTC sys em o quad o o UAVs has
been de eloped [
25
], while he BSMC app oach and i e a i e lea ning algo i hm-based FTC
a e de eloped in [
26
]. A me a-lea ning-based scheme is de eloped o imp o e he ajec o y
acking pe o mance o UAVs in he p esence o he ailu e in he sys em and ex e nal
dis u bance [
27
], and a model- ee deep ein o cemen lea ning scheme is applied o a
quad o o wi h signal o o ailu e in [
28
]. A hie a chical FTC is designed o a hexacop e ,
whe e an adap i e sliding mode con olle is used o no mal ope a ion, and a sliding-
mode-based con olle is used o o o ailu e [
29
]. ]. To handle he pa ial o o ailu e and
wind gus ac ing on he biplane quad o o wi h a slung load, a nonlinea dis u bance-based
backs epping con ol app oach is de eloped in [30].
Resea che s ha e shown mo e in e es in small ac i e low de ices in he las ew
decades because hey subs an ially a ec he low ield and can modi y o ces and momen-
um ac oss he li ing su ace. The main bene i o a syn he ic je is i s ze o ne mass lux
ha emo es he need o plumbing and, when applied o a base low, causes unique e ec s
no possible wi h s eady o pulsed suc ion o blowing. Syn he ic je s con ain o ex pai s
ha p o ide mo e luid han con inuous je columns [
31
]. The ad an ages o SJAs a e hei
low cos , simple s uc u e, easy ope a ion, compac ness, and lowe ene gy consump ion.
P ima ily, ou usage o SJAs as he speci ic choice among he a ious a ailable ac i e
de ices is because o he a ailabili y o ma hema ical SJA models a low angles o a ack,
which a e needed o closed-loop con ol alida ion, as well as he success ul expe imen al
implemen a ion o SJAs wi h his model in o he ligh egimes. The p esen applica ion
is a low angle o a ack ligh , so SJAs wi h a known model a e a ac i e. I is no ou
con en ion ha o he ac i e low con ol de ices would no wo k in such an applica ion. We
a emp o p o ide an on-demand li o ce (when o o ailu e akes place) ha is enough
o land he ehicle sa ely. SJAs can change he low sepa a ion pa e n and po en ially
eplace o hodox con ol su aces such as laps. An SJA p oduces a luid low o ze o mass
o e an en i e cycle. S ill, he momen um is non-ze o beyond a nozzle on he o he side o
he piezo-elec ically d i en diag am, which imposes an oscilla ing p essu e g adien [
32
].
Many simula ions and expe imen s ha e been conduc ed o s udy he SJA’s e ec on
he li ing su ace. Tang e al. [
33
] p oposed and alida ed a je c ea ion c i e ion o SJAs,
while Zong e al. [
34
] p esen ed a no el analy ical mode o he PSJA (Plasma Syn- he ic Je
Ac ua o ) in which he ine ia o he h oa gas and hea ans e e ec a e bo h conside ed.
Based on his model, whole cycle cha ac e is ics can be p edic ed. A no el mul i-me e -
scale hyb id SJA is p oposed o enhance he pe o mance o a con en ional SJA in ac i e
low con ol o a supe sonic ai c a [
35
]. MacKunis e al. [
36
] p oposed a obus nonlinea
acking con ol me hod o an ai c a equipped wi h an SJA.
Du igneau e al. [37]
p e-
sen ed a nume ic simula ion o he con ol o he ae odynamic s all angle using a syn he ic
je ac ua o wi h au oma ic op imiza ion o he con ol pa ame e s and low physiognomies;
he impac o he pa icula con ol pa ame e s we e examined. An adap i e in e se com-
D ones 2022,6, 176 3 o 20
pensa ion scheme is de eloped in [
38
] o con olling he SJA’s ae odynamic low on a
dynamic ai c a sys em.
A no el echnique o con olling nex -gene a ion ai -c a s by using SJA is p oposed
in [
39
] whe e ai c a dynamics con olled by a s a e eedback con olle and adap i e
laws ensu e closed-loop s abili y and asymp o ic acking. In con as , a neu al ne wo k-
based adap i e compensa ion s uc u e elimina es he e ec o ambiguous, highly complex,
and dynamic SJA nonlinea i ies [
40
]. T anscossi e al. [
41
] p esen ed a nume ic as well
as he heo e ical concep o he Coanda e ec ha can be used o ae onau ical na al
p opulsion and indus ial applica ions. The impac o he geome ic pa ame e s like
heigh , diame e s o he ca i y as well as he o i ice, shape, and edge con igu a ion o he
o i ice on he pe o mance o he SJA is discussed in [
42
]. SJA-based nume ical simula ion
is ca ied ou o imp o e he ae odynamics e iciency o he lying wing ai c a [
43
].
Jabbal e al. [44]
de eloped an SJA a ay ha dwa e o enhance high li sys em e iciency in
a wind unnel model which consis s o he design, manu ac u e, and bench es o he SJA
a ay.
Li e al. [45]
p oposed a no el AFC (Ac i e Flow Con ol) me hod o an ai c a ha
does no ha e any de lec ing su ace bu SJAs a e used o ge con ol o e oll-pi ch-yaw
angle when a s all occu s.
Pos e al. [
46
] ha e documen ed he con ol o leading-edge low sepa a ion using
plasma ac ua o s while ai c a a els abo e s all angle. Nume ical in es iga ion o sub-
sonic low sepa a ion a ound an ai oil (NACA0012) wi h lowe AoA (6
◦
) is in es iga ed
in [
47
] unde (i) uncon olled baseline case, (ii) con olled case wi h passi e o ex make ,
and (ii) con olled case wi h ac i e o ex make . Lee e al. [
48
] pe o med 2-D lami-
na and 3-D implici la ge eddy simula ions o p edic he sepa a ion poin and ea u es
o a sepa a ion bubble o NACA 0012 ai oil accu a ely a Reynolds numbe s 1
×
10
4
,
3
×
10
4
, and 5
×
10
4
and di e en AoA Table 1using Reynolds-a e aged Na ie –S okes
wi h Baldwin-Lomax u bulence model 2-D RANS(BL).
Table 1. Sepa a ion poin (xs/c) a di e en AoA and Reynolds Numbe s (Re) [48].
AoA◦Re = 1 ×104Re = 3 ×104Re = 5 ×104
0 0.869 0.979 0.869
1.5 0.713 0.832 0.781
3 0.582 0.713 0.770
4.5 0.461 0.575 0.674
6 0.340 0.429 0.556
7.5 0.198 0.209 0.409
9.0 0.082 0.056 0.115
NACA 0012 Ai oil 3-D suc ion low con ol in es iga ion is pe o med in [
49
] o
unde s and he ae odynamic ea u es o a ec angula wing. A DNS (Di ec Nume ic
Simula ion) is ca ied ou o s udy he low o e NACA 0012 ai oil a 5
◦
–15
◦
AoA and
adequa e Reynolds numbe s o
Re =
50
×
10
3
and 1
×
10
6
[
50
]. In con as , a nume ical
s udy is ca ied ou o lea n he low o e NACA 0012 ai oil o unde s and in equen li
cha ac e is ics a low Reynolds numbe s [
51
]. Cas elli e al. [
52
] pe o med a 2D nume ical
simula ion o in es iga e he abili y o he
γ−θ
ansi ion model o o ecas he lamina o
u bulen ansi ion and subsequen ic ion d ag o e a NACA 0012 ai oil o a Reynolds
numbe o 3.6k. Mejia e al. [
53
] p esen ed a compu a ional s udy o he NACA 4415 wi h
SJA o low AoA whe e SJA was placed close o he ailing edge and p o ided ho ough
in o ma ion abou he adjus men o ai oil ae odynamic p ope ies. Wei e al. [
54
] applied
an ac ua o o con ol he oll angle a high AoA o NACA 0015 ai oil wi h 0.3 m cho d and
3 m span ae o oil, and 19 plasma ac ua o s placed a he uppe su ace. A he same ime,
o he same ae o oil and con ol objec i e, [
55
], SJAs a e placed a 12% o he cho d wi h 45
◦
D ones 2022,6, 176 4 o 20
angle and 150 Hz ope a ion equency. Ac i e low sepa a ion con ol using SJA ins alled
nea he loca ion o he maximum hickness o he ai oil is p oposed and implemen ed
o he s all con ol o he NACA 0012 ai oil in a wind unnel es [
56
], and he ou come
shows 11% imp o emen in li coe icien and 4
◦
s all angle inc ease. Li e al. p oposed a
no el AFC echnology using an SJA o oll mo ion o mo phing ai c a a high AoA [57].
Tang e al. [
58
] s udied he e ec i eness o he SJA a ays ha a e placed a 23 % and 43 %
o he cho d om he leading edge o a low-speed wing mode (used in small UAVs) and
obse ed he delay and gene a e he high-momen um low nea he ou e egion.
Mon aze e al. [
59
] discussed he op imiza ion o he SJA in he con ol low a ound
he NACA 0015 a a 15
◦
s all angle and 16
◦
(pos -s all angle) o maximize he pe o mance o
he ai oil. Jee e al. [
60
] in es iga ed low con ol using he SJAs on pi ching and plunging
ai oil LQR, and a neu al ne wo k-based adap i e con olle is joined o he CFD model,
including he model o SJAs. Luca e al. [
61
] p oposed a lumped elemen ma hema ical
model o he SJA. Based on i , analy ical and nume ical in es iga ions ha e been done o
ge mo e in o ma ion abou he equency esponse o he SJA. SJA can be used o bo h
luid ypes: (i) wa e and (ii) ai . In [
62
] unde wa e h us ec o ing me hod based on
he double SJA is s udied and alida ed using he nume ical me hod. Ca uana e al. [
63
]
desc ibed he physics o he plasma SJA wi h nume ical and expe imen al s udies based on
he desc ip ion o he PSJA de ice wi h and wi hou low and he abili y o PSJA ac ua o s
o educe he sepa a ed low egion on a decele a ing amp as well as on a NACA 0015
ai oil. A neu al ne wo k-based adap i e in e se compensa ion scheme is de eloped in [
64
]
o cancella ion o he e ec o unce ain ies in he SJA. An SMC (sliding mode con ol)
scheme is used o achie e asymp o ic SJA-based LCO supp ession and supp ession o
bo h pi ching and plunging mo emen s o a class o so-called dual pa allel unde ac ua ed
sys ems in which a single scala con ol signal concu en ly dis u bs bo h s a es [65].
In his pape , we p opose a con ol s uc u e o he biplane quad o o o deal wi h
o al o o ailu e whe e SJA is used as he edundancy, and sugges he SJA loca ion should
be a e he sepa a ion poin and close o he ailing edge (2% o 15% o cho d leng h).
We assume ha o o ailu e can happen a any ime and in any mode o he biplane
quad o o du ing he ligh , and such a mechanical a angemen is de eloped o educe
he uns eady low a ound he wing gene a ed by he o o s. To compensa e o non-
linea i ies in he SJA, an adap i e in e se compensa ion scheme is applied and an adap i e
backs epping-based con olle is designed o he pi ching momen s du ing ixed-wing
mode, and ha is p o ided by SJA. Lyapuno -based closed-loop s abili y analysis is p o en.
Simula ion is ca ied ou using MATLAB and he esul s show he e ec i eness o he
p oposed con ol s uc u e.
2. Biplane Dynamics and Ro o Failu e
Du ing he ake-o , landing, and ho e ing s a e, he biplane quad o o ’s beha io
is same as ha o a con en ional quad o o , whe e no su icien ae odynamics o ces a e
gene a ed, and du ing ixed-wing mode, i ac s like ixed-wing UAVs. An anima ed pic u e
o a biplane quad o o UAV wi h all h ee modes is shown in Figu e 1.
Biplane quad o o dynamics a e p esen ed in [66] as
¨
x=Fax
m−g sθ+ −qw (1)
¨
y=Fay
m−g sφcθ+pw − u (2)
¨
z=Faz −T
m−g cφcθ+qu −p (3)
¨
φ= (b1 +b2p)q+b3(La+L ) + b4(Na+N )(4)
¨
θ=b5p −b6(p2− 2) + b7(Ma+M )(5)
¨
ψ= (b8p−b2 )q+b4(La+L ) + b9(Na+N )(6)
D ones 2022,6, 176 5 o 20
whe e
c(·) = cos(·)
and
s(·) = sin(·)
, linea accele a ion is
[¨
x¨
y¨
z]
, and eloci y is
[u w]
,
while
[¨
φ¨
θ¨
ψ]
is angula accele a ion and angula eloci y
[p q ]
.
m
is he mass and
T
is he h us . The momen s a e
[L M N ]
, he ae odynamic o ces a e
[Fax Fay Faz]
a e
ae odynamic o ces, and ae odynamic momen s
[LaMaNa]
ac on he biplane quad o o .
Ine ial e ms a e de ined as cons an bi:








b1
b2
b3
b4
b8
b9








=1
IxIz−I2
xz








(Iy−Iz)Iz−I2
xz
(Ix−Iy+Iz)Ixz
Iz
Ixz
(Ix−Iy)Ix+I2
xz
Ix








,

b5
b6
b7
=1
Iy

(Iz−Ix)
Ixz
1
. (7)
Ro o ailu e can happen a any ime du ing he ligh . Figu e 2shows he low
diag am o he p oposed scheme. When ailu e is de ec ed in quad o o mode ( ake-o o
ho e ing s a e), i will immedia ely ealloca e he con ol signals o a poin wi h no con ol
o e he yaw angle, and hen pe o m he ansi ion and swi ched o ixed-wing mode.
The syn he ic je s a e ac ua ed, and g adually educe he al i ude while na iga ing o he
sa e zone. The same p ocedu e ollows when he ailu e occu s in he ansi ion mode
and in ixed-wing mode when o o ailu e happen, in which case, only he syn he ic je is
ac ua ed. The main ad an age o his con ol s uc u e is ha he e no need o comp omise
con ol o e any o i s s a es.
Figu e 1. Anima ed pic u e o biplane quad o o .
Figu e 2. P oposed con ol scheme.

D ones 2022,6, 176 6 o 20
Anima ed pic u e o low sepa a ion du ing ixed-wing mode and low AoA is shown
in Figu e 3, whe e i can be obse ed ha low sepa a ion s a s om he ailing edge a
low AoA.
Figu e 3. Flow Sepa a ion du ing he Low AoA.
The con ol alloca ion block p o ides sui able con ol signals o he ac ua o based on
he con ol signals gene a ed by he con olle . The e a e wo ypes o p opulsion sys em
used in he biplane quad o o , (i) a iable pi ch, and (ii) a con en ional BLDC mo o -based
p opulsion sys em. In his pape , we used a con en ional BLDC-mo o -based p opulsion
sys em whe e h us and momen s a e achie ed using he RPM changes in he espec i e
ac ua o s. Con ol alloca ion o he biplane quad o o wi hou o o ailu e is




T
L
M
N




=



knknknkn
knln−knln−knlnknln
knlnknln−knln−knln
−dndn−dndn








Ω2
1
Ω2
2
Ω2
3
Ω2
4




, (8)
whe e
[T L M N ]
a e he h us and momen s gene a ed by he ou o o s,
kn
,
dn
a e he
mo o pa ame e s, and
ln
is he dis ance be ween CoM and he espec i e mo o o biplane
quad o o , and
Ωi
is he RPM o he
i h
mo o . Based on Equa ion (8), he RPM o he each
o o can be calcula ed as




Ω2
1
Ω2
2
Ω2
3
Ω2
4




=



knknknkn
knln−knln−knlnknln
knlnknln−knln−knln
−dndn−dndn




−1



T
L
M
N




. (9)
The p oposed con ol s uc u e is designed only o single- o o ailu e. So, le us
assume ha among ou o o s, o o 1 ails. So, Equa ion (8) will become




T
L
M
N




=



knknkn
−knln−knlnknln
knln−knln−knln
dn−dndn





Ω2
2
Ω2
3
Ω2
4

, (10)
and he RPM calcula ion is


Ω2
2
Ω2
3
Ω2
4

=



knknkn
−knln−knlnknln
knln−knln−knln
dn−dndn




−1



T
L
M
N




, (11)
I is no possible o sol e Equa ion (11), so one s a e has o comp omise, and he
equa ion becomes


T
L
M 
=

knknkn
−knln−knlnknln
knln−knln−knln


Ω2
2
Ω2
3
Ω2
4

. (12)
D ones 2022,6, 176 7 o 20
Con ol alloca ion o he quad o o mode and ansi ion mode is gi en in
Equa ion (12)
,
whe e no con ol o e he yaw angle is comp omised.
3. Ma hema ical Mode o he SJA
A biplane is able o swi ch i s mode a e pe o ming he ansi ion maneu e .
A biplane quad o o is mos ly used o payload deli e y and, du ing i s whole mission, he
biplane quad o o always lies wi h low AoA. We p oposed a SJA-based edundancy o a
biplane quad o o when signal o al o o ailu e occu s. SJAs a e connec ed a he ailing
edge o he wings, because he biplane quad o o is designed o ly wi h low AoA, and
low sepa a ion s a s om he ailing edge while AoA is low. So, SJA should p e e ably
be placed a he ailing edge o wings o ea ach he sepa a ed low. To al o o ailu e
can occu a any ime o ins ance. To handle his o o ailu e, he biplane will ollow some
maneu e s based on hose a which mode aul occu ed. When ailu e occu s du ing he
quad o o mode, he i s s ep is o ealloca e i s con ol signals in such a way ha he e is
no con ol o e he yaw angle. A e wa ds, he biplane quad o o will pe o m a ansi ion
maneu e o swi ch he quad o o mode o ixed-wing mode, and hen SJAs a e ac i a ed o
con ol pi ch momen s while olling and yawing momen s a e con olled by he emaining
h ee o o s. When ailu e occu s in he ansi ion mode, i will swi ch o ixed-wing mode,
and hen SJAs a e ac i a ed. When o al o o ailu e occu s in ixed-wing mode, he SJAs
a e ac i a ed wi h no need o pe o m he ansi ion.
Nex , we will discuss he ma hema ical model o he SJA o he low AoA. As explained
ea lie , he biplane quad o o is designed o a el a a low angle o a ack du ing ixed-
wing mode. Resea che s ha e al eady de eloped a pa ame ic model o he SJA [
38
,
39
] o
he low AoA, and i is mo e sui able o he biplane quad o o because i lies wi h low
AoA. I is de i ed based on wind- unnel es ing, in which pick- o-pick ol age, ai -s eam
low, equency, and cho d leng h a e conside ed. Pa ame e alues may be changed o
biplane quad o o , bu he s uc u e o he model emains he same. So, his simula ion
s udy is ca ied ou wi hin he SJA low angle o a ack model ha is gi en in [
67
]. Now, le
us conside he inpu ol age as
( )
and he equi alen i ual de lec ion as
Ua( ) = Cl( )
,
exp essed by a non-linea i y in SJA as N(·):
λs( ) = ClS( ) = N( S( )) = N(A2
( )), (13)
whe e
SJA( ) = A2
( )
,
A
is inpu peak- o-peak ol age. Fo mo e simpli ica ions, some
assump ions a e needed:
• The ac ua o non-linea i y’s N(·)ou pu is no measu able.
• Pa ame e s o he ac ua o non-linea i y N(·)a e unknown.
• Je momen um does no a y du ing he en i e pe iod o he diaph agm mo ion.
• The ai -s eam densi y and con ol o low along he wid h a e cons an .
The SJ is ac ua ed such a way ha he con ol signal gene a es a o able changes in he
i ual shape o he ae o oil. Fo unknown pa ame e s
psi
,
i=
1,
. . .
, 4 wi h ce ain physical
meaning, he SJA model a low AoA is gi en as
Cls( ) = ps1−ps2ps3V∞
cCµs
, (14)
whe e
is he equency in inpu ol age,
c
is he wing cho d, and
V∞
is he ee-s eam
eloci y a ound SJA. Cµsis he momen um coe icien o he ac ua o , and i is gi en as
Cµs( ) = ps4A2
( )
V∞
. (15)
D ones 2022,6, 176 8 o 20
4. Con ol A chi ec u e
To handle he o al o o ailu e in an unde ac ua ed sys em is a complex ask. While e-
con igu ing he con ol alloca ion du ing he o o ailu e, con ol o e one pa ame e mus
be comp omised, and gene ally, his pa ame e in he o a y wing UAVs is he yaw angle.
I can be obse ed ha he biplane quad o o dynamics oll and he yaw angle a e coupled.
He e, we conside e ha he o o ails du ing he ho e ing s a e. So, a e he de ec ing
he ailu e, he biplane quad o o is commanded o pe o m he ansi ion maneu e and
swi ch o ixed-wing mode, and hen i will ly wi h low eloci y and na iga e o a sa e
place o land. The con ol a chi ec u e low diag am is shown in Figu e 4.
Figu e 4. Con ol a chi ec u e low diag am.
Ro o ailu e can happen in any mode o a biplane quad o o . So, i o o ailu e
happens in he quad o o mode o ansi ion mode, he biplane will i s ealloca e con ol
signals in which he e is no con ol o e he yaw angle, and hen immedia ely pe o m
he ansi ion and swi ch o ixed-wing mode. Du ing ixed-wing mode, a syn he ic je is
ac ua ed and i ual de lec ion is gene a ed o con ol he pi ching momen s o he biplane
quad o o . The biplane quad o o ’s al i ude g adually declines, and i na iga es o a sa e
zone and al i ude. When he biplane quad o o eaches he sa e zone and al i ude, i is
commanded o swi ch in o quad o o mode and hen ealloca e he con ol signals, a e
which i will land wi hou damage. The block diag am o he p oposed con ol a chi ec u e
o handle he biplane quad o o in ixed-wing mode is shown in Figu e 5.
Figu e 5. P oposed Con ol A chi ec u e.
The biplane quad o o wing is enhanced wi h SJA as a edundancy. In ixed-wing
mode, he al i ude, oll, and yaw angles a e con olled by he h ee o o s, and he pi ch
angle is con olled using he i ual de lec ion gene a ed by he SJA. The con ol signal
gene a ed using he BSC con olle is con e ed o he desi ed i ual de lec ion and hen
D ones 2022,6, 176 9 o 20
gi en o he in e se adap i e unc ion block, and i will gene a e he desi ed ol age,
which is gi en o he SJA mode block. Then, i ual de lec ion is gene a ed. Again, i will
con e based on he momen and he biplane dynamics. In ixed-wing mode, he e a e
wo ypes o o ces ac ing on he biplane quad o o . (i) Fo ce gene a ed by h ee o o s, and
(ii) ae odynamic
o ce and momen s gene a ed by he de lec ing su ace. The o ce and
momen s gene a ed by he de lec ing su ace a e
F=AρV2sin δ
2,M=2FL (16)
whe e
F
is he o ce gene a ed and
M
is he momen gene a ed by he su ace.
L
is he
dis ance om cen e o g a i y,
A
is he a ea o he wing,
ρ
is he ai densi y,
δ
is he angle
o he de lec ing su ace, and
V
is he ehicle eloci y. We use he simpli ied e sion o he
o ce and momen s equa ion because he objec i e is o demons a e he e ec i eness o
he SJA on he biplane quad o o om a con ol pe spec i e.
5. Con olle Design
Nex , we design an in e se adap i e unc ion o he SJA o compensa e o pa ame ic
unce ain y. As shown in Figu e 6, we combine he blocks o BSC wi h calcula ion o he
desi ed de lec ing angle and he angle o momen s and pi ch dynamics.
Figu e 6. Block diag am o con olle design o pi ch angle acking.
In ou p e ious wo k [
6
], backs epping con olle -based con ol laws a e designed o
he biplane quad o o in quad o o mode as
L =1
b3−eφ−kpep+¨
φd−kφ˙
eφ−b1 q −b2pq −b4N , (17)
M =1
b7¨
θd−eθ−kqeq−kθ˙
eθ+b6p2− 2−b5p , (18)
N =1
b9¨
ψd−eψ−k e −kψ˙
eψ−(b8p−b2 )q−b4L , (19)
T=m
cφcθ(ez+ewkw−¨
zd+kz˙
ez+g), (20)
ux=m
T(ex+kueu−¨
xd+kx˙
ex), (21)
uy=m
Tey+k e −¨
yd+ky˙
ey. (22)
D ones 2022,6, 176 16 o 20
0 10 20 30 40 50 60 70 80 90
2
4
ea
0 10 20 30 40 50 60 70 80 90
10
15
eb
0 10 20 30 40 50 60 70 80 90
Time (seconds)
-10
0
10
e
Figu e 17. Pa ame e E o s.
When he biplane quad o o is na iga ed o he sa e zone, as well as he desi ed
al i ude, which is 4 m, i will pe o m he ansi ion and swi ch o he quad o o mode, and
ealloca e he con ol signal such a way ha he yaw angle is in ee all. Now, he posi ion
and al i ude du ing he quad o o mode B a e shown in Figu es 18 and 19. Du ing he
ansi ion om ixed-wing o quad o o mode, an e o is gene a ed in he al i ude, and i
is e ec i ely acked by he backs epping con olle while holding x-yposi ion cons an .
0 0.5 1 1.5 2 2.5 3 3.5 4
968
969
X axis (m)
0 0.5 1 1.5 2 2.5 3 3.5 4
-2
-1
0
Y Axis (m)
0 0.5 1 1.5 2 2.5 3 3.5 4
Time (seconds)
0
2
4
Z Axis (m)
Figu e 18. Posi ion and al i ude acking du ing quad o o mode B.
The e is a e y small e o gene a ed du ing he landing in he yaw angle because i is
no con olled. The oll and pi ch angle a e e ec i ely con olled.
0 0.5 1 1.5 2 2.5 3 3.5 4
-1
0
1
Roll (deg)
Desi ed oll angle Ac ual oll angle
0 0.5 1 1.5 2 2.5 3 3.5 4
-1
0
1
Pi ch (deg)
Desi ed pi ch angle Ac ual pi ch angle
0 0.5 1 1.5 2 2.5 3 3.5 4
Time (seconds)
-0.01
0
0.01
0.02
Yaw (deg)
Desi ed yaw angle Ac ual yaw angle
Figu e 19. A i ude acking du ing quad o o mode B.
The h us and momen s du ing he landing a e shown in Figu e 20, and he RPM o
mo o 2 and mo o 4 a e shown in Figu e 21.

D ones 2022,6, 176 17 o 20
0 0.5 1 1.5 2 2.5 3 3.5 4
200
300
400
T (N)
0 0.5 1 1.5 2 2.5 3 3.5 4
-1
0
1
L (N-m)
0 0.5 1 1.5 2 2.5 3 3.5 4
Time (seconds)
-1
0
1
N (N-m)
Figu e 20. Th us and momen s gene a ed du ing quad o o mode B.
0 0.5 1 1.5 2 2.5 3 3.5 4
Time (seconds)
3000
3500
4000
4500
Speed ( pm)
Mo o 2
Mo o 3
Figu e 21. Ro o speed du ing he quad o o mode B.
I can be obse ed ha he speeds o mo o s 2 and 4 a e made he same o balance he
biplane while mo o 1 has ailed, and o compensa e o ha , he speed o mo o 3 is ze o
du ing landing.
7. Conclusions
In his simula ion s udy, we adop he SJA model de i ed in [
38
] o he low AoA
because, o mos o i s ligh ime, he biplane quad o o lies wi h low AoA. We p opose
a con ol s uc u e o handle he o al o o ailu e and assume ha he o o can ail in
any mode. SJA is used o gene a e i ual de lec ion o con ol he pi ch angle, while oll
and yaw a e con olled by he emaining h ee o o s when he biplane quad o o is in
ixed-wing mode. In his s udy, we also show he adap i e compensa ion scheme o handle
he pa ame ic non-linea i y in he SJA. The ou comes o his simula ion s udy a e,
•
The biplane quad o o is able o pe o m he ansi ion maneu e e en a e he o al
o o ailu e.
•
In ixed-wing mode, a e he ealloca ion o he con ol signals, he desi ed al i ude,
oll, and pi ch angles a e acked.
•
SJA is able o deli e he desi ed i ual de lec ion o con olling he pi ching mo emen .
•
By using he adap i e in e se compensa ion scheme, non-linea i y in he SJA is
e ec i ely compensa ed.
•
Based on he Lyapuno me hod, closed-loop s abili y o he o e all con ol a chi ec u e
is p o en.
Au ho Con ibu ions:
Concep ualiza ion, N.D. and D.D.; me hodology, N.D. and D.D.; so wa e,
N.D.; alida ion, N.D. and D.D.; o mal analysis, N.D. and D.D. and S.O.; w i ing—o iginal d a
p epa a ion, N.D. and D.D.; w i ing— e iew and edi ing, D.D. and S.O.; supe ision, D.D.; unding
acquisi ion, S.O. All au ho s ha e ead and ag eed o he published e sion o he manusc ip .
D ones 2022,6, 176 18 o 20
Funding:
This esea ch was unded by he Eu opean Regional De elopmen Fund in he Resea ch
Cen e o Ad anced Mecha onic Sys ems p ojec , g an numbe CZ.02.1.01/0.0/0.0/16_019/0000867
wi hin he Ope a ional P og amme Resea ch, De elopmen and Educa ion.
Ins i u ional Re iew Boa d S a emen : No applicable
In o med Consen S a emen : No applicable
Da a A ailabili y S a emen : No applicable
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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