A Hovering Control Strategy for a TailSitter VTOL UAV that Increases Stability Against Large Disturbance
Abstract
The application range of UAVs (unmanned aerial vehicles) is expanding along with performance upgrades. Vertical takeoff and landing (VTOL) aircraft has the merits of both fixedwing and rotarywing aircraft. Tailsitting is the simplest way for the VTOL maneuver since it does not need extra actuators. However, conventional hovering control for a tailsitter UAV is not robust enough against large disturbance such as a blast of wind, a bird strike, and so on. It is experimentally observed that the conventional quaternion feedback hovering control often fails to keep stability when the control compensates large attitude errors. This paper proposes a novel hovering control strategy for a tailsitter VTOL UAV that increases stability against large disturbance. In order to verify the proposed hovering control strategy, simulations and experiments on hovering of the UAV are performed giving large attitude errors. The results show that the proposed control strategy successfully compensates initial large attitude errors keeping stability, while the conventional quaternion feedback controller fails.
A Hovering Control Strategy for a TailSitter VTOL UAV that
Increases Stability Against Large Disturbance
Takaaki Matsumoto
∗1
, Koichi Kita
∗2
, Ren Suzuki
∗1
, Atsushi Oosedo
∗1
,
Kenta Go
∗1
, Yuta Hoshino
∗1
, Atsushi Konno
∗1
and Masaru Uchiyama
∗1
∗1
Department of Aerospace Engineering, Tohoku University.
Aobayama 6601, Sendai, Miyagi, 9808579, Japan
∗2
Fuji Heavy Industries Ltd., 1111
Yonan, Utsunomiya, Tochigi, 3208564, Japan
{takaaki, konno, uchiyama}@space.mech.tohoku.ac.jp, KitaK@uae.subarufhi.co.jp
Abstract— The application range of UAVs (unmanned aerial
vehicles) is expanding along with performance upgrades. Ver
tical takeoff and landing (VTOL) aircraft has the merits of
both ﬁxedwing and rotarywing aircraft. Tailsitting is the
simplest way for the VTOL maneuver since it does not need
extra actuators. However, conventional hovering control for
a tailsitter UAV is not robust enough against large distur
bance such as a blast of wind, a bird strike, and so on. It
is experimentally observed that the conventional quaternion
feedback hovering control often fails to keep stability when the
control compensates large attitude errors. This paper proposes
a novel hovering control strategy for a tailsitter VTOL UAV
that increases stability against large disturbance. In order to
verify the proposed hovering control strategy, simulations and
experiments on hovering of the UAV are performed giving large
attitude errors. The results show that the proposed control
strategy successfully compensates initial large attitude errors
keeping stability, while the conventional quaternion feedback
controller fails.
I. INTRODUCTION
VTOL UAVs make missions possible which are normally
impossible to accomplish using either ﬁxedwing or rotary
wing UAVs alone; for example, search and rescue operations
covering a broad area located at the rooftop of a building.
There are several ways to perform VTOL maneuvers such as
tiltingrotor, tiltingwing, thrustvectoring and tailsitting etc.
The simplest way is tailsitting since it does not need extra
actuators for the VTOL maneuver. A simple mechanism is
preferable for UAVs, because weight saving is crucial for the
VTOL maneuver and has the advantage of cost saving. Tail
sitter VTOL aircraft switches between level ﬂight mode and
hover mode by changing the pitch attitude of the fuselage
by 90 ° as shown in Fig. 1.
US Air Force Research Lab and AeroVironment Inc.
have developed “SkyTote” which is equipped with a coaxial
contrarotating propeller [1]. The Defense Advanced Re
search Projects Agency (DARPA) and Aurora Flight Sciences
have developed “GoldenEye” which is equipped with a
ducted fan. It uses ﬁns outside the duct during level ﬂight
and ﬁns in the duct during hovering [2]. Stone developed “T
Wing” which has a canard wing and tandem rotors [3],[4].
Kubo and Suzuki proposed a twinfuselage plane [5]. Green
and Oh developed a micro air vehicle [6], and added two
Transition to LandingTransition from Takeoff
Hovering
Fig. 1. Takeoff and landing of the tailsitter VTOL aircraft.
wingtip rotors which generate a rotational force countering
the motor torque to their MAV [7].
However, those tailsitter UAVs have some complex equip
ments such as a coaxial contrarotating propeller [1], a ducted
fan and ﬁns [2], sidebyside rotors [4],[5], and wingtip rotors
[7] for the tailsitting VTOL maneuver.
Only few attempts have been made to develop tailsitter
UAVs without any extra equipment so far. However, since
these simple tailsitter UAVs have no extra equipment for
countering the motor torque, robust stationary hovering is
more difﬁcult than other robots with complex equipments.
Large disturbances in hovering such as strong wind or bird
impact are major problems to overcome.
Frank et al. have succeeded in the indoor ﬂight experiment
using a commercially available R/C acrobatic airplane and
the motion capture system [8]. However, since the ﬂight
experiments were performed in a room, there was no dis
turbance such as strong wind which is a major problem to
overcome [8]. Knoebel et al. proposed a new airframe design
[9]. They are working on ﬂight tests using a commercially
available single propeller R/C model which represents the
“XFY1”. However, hovering performance with large distur
bance were not reported in [9]. Johnson et al. have developed
“GTEdge” which is a large scale R/C airplane weighting
about 15 kg and studied the tailsitter maneuver [10],[11].
They have succeeded transition ﬂight and hovering; however,
the robustness of hovering control was not discussed.
This paper is intended to propose a novel control strategy
for robust hovering when large attitude errors are generated
by some disturbances. Simulations and experiments on hov
ering control of the UAV are performed giving large attitude
2010 IEEE International Conference on Robotics and Automation
Anchorage Convention District
May 38, 2010, Anchorage, Alaska, USA
9781424450404/10/$26.00 ©2010 IEEE 54
Fig. 2. TailSitter UAV.
errors to verify the robustness against the errors. The results
show that the proposed strategy successfully compensates the
large errors, while the conventional control strategy failed to
stabilize the UAV. The UAV used in this paper is equipped
with all necessary sensors and computers on the fuselage
[12].
II. SYSTEM CONFIGURATION
An overview of the tailsitter VTOL UAV is shown in
Fig. 2. The main wingspan is 1.0 m, and the weight is
0.75 kg. The main and tail wings are parts of commercially
available R/C airplane (Hyperion Co., Sniper 3D), and other
parts such as the body are newly developed. The motor and
propeller, of which the static thrust amounts to 120 % of the
fuselage weight at a continuous maximum motor load are
selected.
The UAV is equipped with the following processors and
sensors.
• A microcomputer board (Alpha Project Co., STK7125)
that has an SH2 microcomputer made by Renesass
Technology Co. The microcomputer calculates control
input based on each sensor data, and sends pulsewidth
modulated (PWM) signals to servo motors to control
surfaces (aileron, elevator, and rudder) and the thrust
motor.
• An attitude sensor module (Microstrain Co., 3DM
GX1). This module provides the attitude, azimuth,
threeaxis angular velocity and acceleration. The sen
sor’s datasheet gives its attitude angle accuracy as ±2 °.
• An ultrasonic sensor to detect altitude when the air
craft’s distance from the ground is less than 6 m.
• An atmospheric pressure sensor to detect altitude when
aircraft distance from the ground is more than 6 m.
• A global positioning system (GPS) receiver module
(Garmin Co., GPS 185Hz). The GPS module obtains
absolute position on the earth and absolute velocity of
the three axes.
• A microSD card module to record ﬂight data and other
information for postexperiment analysis.
• A R/C receiver to control aircraft by a human in emer
gency. The main computer receives commands from
an R/C transmitter, but these are not used in control
calculation.
A conﬁguration diagram of the electronic system is shown
in Fig. 3.
Pressure Altitude
Sensor
MicroSD Card Module
R/C Transmitter
Microcomputer
GPS Module
Ultrasonic Sensor
Attitude Sensor
Module
Thrust Motor
Motor Controller
Aileron Servo
Elevator Servo
Rudder Servo
Ground
Aerial Robot
R/C Receiver
Fig. 3. Onboard electronics system.
Z
Y
X
Aileron
Rudder
Elevator
Fig. 4. Aircraft body coordinates and control surfaces.
III. HOVERING CONTROL
A. Quaternion Feedback Control
The earth ﬁxed coordinate system deﬁnes X axis as true
north, Y axis as east, and Z axis as perpendicular downward.
The fuselage ﬁxed coordinate system is deﬁned as shown
in Fig. 4 as a principal axis of inertia. The attitude of
the fuselage is expressed with respect to the earth ﬁxed
coordinate system.
Because the tailsitter maneuver covers a wide range of
attitudes, quaternion expression which theoretically has no
singularity is used as a method of describing the attitude.
Quaternion expresses the attitude by a three dimensional unit
vector r and its rotation angle
ζ
, as follows:
q =
cos(
ζ
/2)
rsin(
ζ
/2)
=[q
0
q
1
q
2
q
3
]
T
. (1)
Quaternion feedback is generally used for UAVs. In con
trolling the attitude of the UAV, following three quaternions
are deﬁned: q
r
that shows the desired reference attitude, q
c
that shows the current attitude, and q
e
that shows the error
or deviation between q
r
and q
c
. The q
e
is shown as follows
55
Propeller
Downwash
Center of Gravity
Control Surface
mg
mg
mg tanθ
≈ mgθ
T
θ
Fig. 5. Operating principle for hovering.
by using q
c
and q
r
[13]:
q
e
=
q
r0
q
r1
q
r2
q
r3
−q
r1
q
r0
q
r3
−q
r2
−q
r2
−q
r3
q
r0
q
r1
−q
r3
q
r2
−q
r1
q
r0
q
c
, (2)
where q
r
=[q
r0
q
r1
q
r2
q
r3
]
T
. The vector part of q
e
(q
e1
,q
e2
,q
e3
) calculated by (2) shows amount of error about
each axis in the body coordinates.
Each three axes are controlled by a PID controller. The
control command is sent to control surfaces corresponding
to each axis as follows:
δ
i
= −2(K
P
q
ei
+ K
I
q
ei
dt + K
D
˙q
ei
), (3)
where
δ
1
,
δ
2
and
δ
3
are the aileron angle, elevator angle
and rudder angle, respectively. The PID gains are provided
by the ultimate sensitivity method, and tuned by trial and
error. The attitude is operated by blowing a slip stream of
the propeller to each control surface as shown in Fig. 5.
B. Resolved TiltTwist Angle Feedback Control
Quaternion feedback works well when attitude errors are
not very large. However, when the rolling error is large, the
quaternion feedback control presented in the previous section
may fail to stabilize the UAV.
For example, let (
αβγ
) = (0 90 0) ° in a reference attitude
and let (
αβγ
)=(180800)° be the current attitude, where
α
,
β
, and
γ
are ZYX Euler angles (yaw, pitch, and roll,
respectively). In this case, the error quaternion is calculated
as [0 − 0.57 0 − 0.34]
T
. This error quaternion derives no
error around the Y axis of the aircraft body coordinates.
Therefore, the pitch error (error around Y axis) is not
compensated in the beginning of the quaternion feedback
control.
We propose a novel hovering control strategy based on an
analogy of inverted pendulum to achieve robustness against
large attitude errors. The proposed hovering control strategy
is named Resolved tilttwist angle control. In this control,
attitude error is resolved into the tilt and twist angles. The tilt
angle is composed of two angles of orthogonal axes. Fig. 6
shows the concept of the control. The resolved tilttwist angle
control is composed of the following four steps.
X
C
X
N
v
X
N
θ
twist
θ
tilt
X
N
Y
N
(a) Step 1. Tilt
(Current Attitude)
(c) Reference Attitude(b) Step 2. Twist
Fig. 6. Concept of the resolved tilttwist angle control.
Step 1 Derive pitch and yaw errors based on an analogy
of inverted pendulum
The ﬁrst step derives the pitch and yaw errors.
Current attitude
O
C
R and reference attitude
O
N
R of the
UAV are deﬁned as follows:
O
C
R ≡ [e
x
C
e
y
C
e
z
C
], (4)
O
N
R ≡ [e
x
N
e
y
N
e
z
N
], (5)
where e
jC
and e
jN
( j = x,y,z) are the unit vectors
along j axis of the body coordinate frame with
respect to the world coordinate frame at current
attitude and reference attitude, respectively.
Considering the UAV as an inverted pendulum, its er
ror angles can be calculated. The attitude of inverted
pendulum is deﬁned as follows,
R
E
=
O
N
R
TO
C
R =
r
11
E
r
12
E
r
13
E
r
21
E
r
22
E
r
23
E
r
31
E
r
32
E
r
33
E
. (6)
The X axis elements of R
E
gives pitch and yaw errors
as follows,
θ
Y
= atan2(r
31
E
,r
11
E
), (7)
θ
Z
= atan2(r
21
E
,r
11
E
), (8)
where atan2(y, x) is a function that calculates
tan
−1
(y/x).
θ
Y
and
θ
Z
deﬁne the tilt angle of inverted
pendulum
θ
tilt
as follows:
θ
tilt
=
θ
2
Y
+
θ
2
Z
. (9)
Step 2 Derive roll error
The second step derives the roll error. The rotation
of
θ
tilt
is given by Rodrigues’ rotation formula as
follows,
R
v
=
E + ˆv sin
θ
tilt
+ ˆv
2
(1 − cos
θ
tilt
), for R
E
= E
(10a)
E, for R
E
= E (10b)
where E is a 3 × 3 identity matrix, v is the rotation
axis vector given by the normalized cross product of
e
x
C
and e
x
N
as follows,
v =
e
x
C
× e
x
N
e
x
C
× e
x
N

≡ [v
x
v
y
v
z
]
T
. (11)
56
The hat operator transforms a vector v into a skew
symmetric matrix as follows,
ˆv =
0 −v
z
v
y
v
z
0 −v
x
−v
y
v
x
0
. (12)
The UAV attitude after compensating
θ
tilt
(see the
Fig. 6(b)), is given using R
v
as follows:
R
P
= R
v
O
C
R ≡ [e
x
P
e
y
P
e
z
P
], (13)
where e
jP
( j = x,y, z) are the unit vectors along j
axis of the body coordinate frame after compensating
θ
tilt
with respect to the world coordinate frame. The
absolute roll error is deﬁned as follows,
θ
twist
= cos
−1
e
z
P
· e
z
N
e
z
P
e
z
N

. (14)
Since aircraft roll angle range is −180 ° ∼ 180 °, the
sign of the roll error must be identiﬁed. In order to
identify the sign of the roll error
θ
X
,
θ
sign
is deﬁned
as follows:
θ
sign
= cos
−1
e
y
P
· e
z
N
e
y
P
e
z
N

. (15)
Using
θ
sign
, the roll error
θ
X
of the UAV is identiﬁed
as follows:
θ
X
=
θ
twist
, for
θ
sign
≤
π
2
(16a)
−
θ
twist
. for
θ
sign
>
π
2
(16b)
Step 3 Projection of pitch and yaw errors onto the rolling
body coordinate frame
In order to simultaneously compensate pitch, yaw,
and roll errors, the pitch and yaw errors must be
projected onto the body coordinate frame which is
rolling with respect to the world coordinate frame.
Errors around each axis in the aircraft body coordi
nates are given as follows:
d
1
d
2
d
3
=
10 0
0 cos
θ
X
−sin
θ
X
0 sin
θ
X
cos
θ
X
θ
X
θ
Y
θ
Z
. (17)
Step 4 Feedback control for each control surface
Control command is sent to control surfaces based
on individual axes as follows:
δ
i
= −(K
P
d
i
+ K
I
d
i
dt + K
D
˙
d
i
), (18)
where
δ
1
,
δ
2
and
δ
3
are the aileron angle, elevator
angle and rudder angle, respectively. d
1
∼ d
3
are cal
culated by (17). PID gains are same as the quaternion
PID feedback gains.
C. Altitude Control
The altitude controller is independently designed. The
desired propeller reference rotation speed is calculated from
the reference and current altitudes. Altitude control is gener
ally possible without propeller rotation speed feedback, but
control performance is deteriorated by changes in battery
conditions and motor load due to disturbance. Therefore, a
feedback control of propeller rotation speed is introduced in
altitude control system to enhance robustness against these
changes. Control gains of the altitude control system were
determined through simulation.
IV. SIMULATION
A. Mathematical Model
To evaluate the hovering algorithms, a twodimensional
tailsitter UAV simulator was developed. The translational
mathematical model of the UAV in the aircraft body coordi
nates is represented as follows,
m
˙
U + QW
= L sin
α
− Dcos
α
− mgsin
θ
+ T − D
P
, (19)
m
˙
W − QU
= −L cos
α
− Dsin
α
+ mgcos
θ
, (20)
where U and W are velocities along the X and Z axes in the
aircraft body coordinates, L and D are lift and drag forces,
α
is the attack angle,
θ
is the pitch angle, m is the fuselage
mass, g is the gravitational acceleration, T is the thrust force,
D
P
is the propeller drag force, and Q is the angular velocity
of the Y axis around the aircraft body coordinates.
The rotational mathematical model of the UAV is repre
sented as follows,
I
xx
˙
P + C
p
P = M
a
+ M
p
, (21)
I
yy
˙
Q +C
q
Q = M
t
+ M
e
, (22)
where P and Q are angular velocities around the X and Y
axes of the aircraft body coordinates, I
xx
and I
yy
are inertia
around the X and Y axes of the aircraft body coordinates, C
p
and C
q
are viscous resistance coefﬁcients, M
a
and M
p
are the
aileron and propeller rolling momentum around the X axis
of the aircraft body coordinates, M
t
and M
e
are fuselage
and elevator pitching momentums around the Y axis of the
aircraft body coordinates.
To identify aerodynamic forces (L,D,D
p
,M
a
,M
p
,M
t
,M
e
),
experiments including wind tunnel test are performed with
scale model of the UAV. Coefﬁcients of main wing aerody
namic forces (C
L
,C
D
,C
M
t
) are measured in all attack angle
range (−180 ° ∼ 180 °). Inherent parameters of the propeller
are measured through wind tunnel test. The momentum the
ory is used for its aerodynamic force calculation. Electrical
and mechanical time constants of the DC motor are identiﬁed
by experiment.
B. Simulation Results
A typical hovering simulation result of quaternion feed
back is shown in Fig. 7. The initial attitude is (
αβγ
)=
(0 0 90) ° and the reference attitude is (
αβγ
)=(1700
80) ° , where
α
,
β
, and
γ
are ZXY Euler angles. The error
angle around Z axis decreased rapidly. However, note that
the error angle around Y axis increased in the early stage
57
01234
−180
−150
−120
−90
−60
−30
0
30
60
90
120
150
Time [s]
ZXY Euler angle [°]
Z result
Z reference
Y result
Y reference
Fig. 7. Quaternion feedback control simulation.
01234
−180
−150
−120
−90
−60
−30
0
30
60
90
120
150
Time [s]
ZXY Euler angle [°]
Z result
Z reference
Y result
Y reference
Fig. 8. Resolved tilttwist angle control simulation.
0
1
2
3
4
5
6
7
8
0 20 40 60 80 100 120 140 160 180
Time [s]
Yaw [°]
Resolved tilttwist angle feedback control
Quaternion feedback control
Fig. 9. Simulated recovery time comparison resolved tilttwist angle control
with quaternion feedback control.
of simulation. This error increase causes a long horizontal
movement.
Fig. 8 is the result of simulation on a resolved tilttwist
angle control hovering. Same conditions are given in both
simulations. The deceleration in error angle around Z axis is
slightly slower than quaternion feedback. Nevertheless, the
error angle around Y axis deceleration is very fast. As a
result, with short horizontal movement, stable hovering is
realized.
Fig. 9 shows a comparison of recovery times of both the
strategies. In quaternion feedback control, when the error
angle around Z axis surpasses approx 70 °, the recovering
time increased exponentially. On the other hand, in resolved
tilttwist angle control, the rate of increase of recovering
time is linear. Therefore, resolved tilttwist angle control has
superior stability against the large error angle around Z axis.
Furthermore, the error angle around Y axis was converged
very quickly in resolved tilttwist angle feedback in all
error angle ranges around Z axis. However, in quaternion
feedback, the larger the error angle around Z axis exists, the
longer the error angle around Y axis converge time is needed.
01234
−180
−150
−120
−90
−60
−30
0
30
60
90
120
150
Time [s]
ZXY Euler angle [°]
Z result
Z reference
Y result
Y reference
X result
X reference
Fig. 12. Quaternion feedback control experiment.
01234
−180
−150
−120
−90
−60
−30
0
30
60
90
120
150
Time [s]
ZXY Euler angle [°]
Z result
Z reference
Y result
Y reference
X result
X reference
Fig. 13. Resolved tilttwist angle control experiment.
V. EXPERIMENTAL RESULTS
A. Hovering with Quaternion Feedback Control
Fig. 10 shows snapshots of one of the hovering experi
ments with quaternion feedback control. In this experiment,
the reference and initial attitudes are about the same as
simulation. The result of the experiment is shown in Fig. 12.
In the beginning of experiment, the error angle around Y
axis increased and the UAV lost stability. This result is the
same as the computer simulation. Moreover, the error angle
around Y axis increase and the error angle around Z axis
decrease caused the error angle around X axis. As a result,
the UAV couldn’t continue hovering.
It is notable that quaternion feedback control works well
when errors are not very large. However, in some cases
as shown in Fig. 10, quaternion feedback control causes
problem.
B. Hovering with Resolved TiltTwist Angle Feedback Control
Fig. 11 shows snapshots of one of the hovering experi
ments with resolved tilttwist angle control. The experiment
conditions are largely similar to the quaternion feedback
expriment. The result of the experiment is shown in Fig. 13.
The angles around Y and X kept reference values, respec
tively. The error angle around Z axis decreases smoothly.
This arises from independent calculation steps for tilt and
twist angles in resolved tilttwist angle control.
Additionally, even when a human inﬂicted large distur
bance during hovering the UAV continued stable ﬂight and
errors were converged (Figs. 14 and 15). This robustness will
be effective in order to overcome dynamic disturbance like
a bird strike during hovering. These ﬂights are experimented
indoors, but the strategies brought out same performance in
the open air.
58
Fig. 10. Quaternion feedback control experiment. The UAV couldn’t continue hovering.
Fig. 11. Resolved tilttwist angle control experiment. Since large aileron angle caused drag force, the UAV lost altitude slightly. However, the UAV could
continue hovering stably.
Fig. 14. Human inﬂicted rotational disturbance while hovering with
resolved tilttwist angle control, but the UAV continued hovering stably.
Fig. 15. Human inﬂicted translational disturbance while hovering with
resolved tilttwist angle control, but the UAV continued hovering stably.
VI. CONCLUSIONS
In this paper, we presented a novel hovering control
strategy and applied it to PID controller to realize robust
UAV hovering. The hovering control strategy is based on
the analogy of an inverted pendulum model and composed
of four steps. The twodimensional UAV simulator was de
veloped to evaluate the strategy. The resolved tilttwist angle
control achieves superior stability to quaternion feedback
control when aircraft has large error angle around Z axis
through simulation and experiment.
The application of the resolved tilttwist angle feedback
control for UAVs is not limited in hovering motion. It doesn’t
depend on any aircraft current and reference attitude. We be
lieve it can be extended for many kind of aircraft maneuvers
which dynamically shift attitude with stall condition, not just
normal motion such as level ﬂight.
VII. ACKNOWLEDGMENTS
This work was supported by GrantinAid for Exploratory
Research (No. 21656219), and GrantinAid for JSPS Fel
lows (216015).
R
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 "In recent years, there has been a considerable attention towards the propellerpushing and flappingwing aircrafts which can not only take off vertically, but also fly forward with high speed. A successful example includes V22 aircraft [8] as well as tailsitter designs91011121314151617. The Twing is a VTOL UAV that is capable of both wingborn horizontal flight and propeller born vertical mode flight including hover and descent. "
[Show abstract] [Hide abstract] ABSTRACT: This paper presents a model of an agile tailsitter aircraft, which can operate as a helicopter as well as capable of transition to fixedwing flight. Aerodynamics of the coaxial counterrotating propellers with quad rotors are analysed under the condition that the coaxial is operated at equal rotor torque (power). A finitetime convergent observer based on Lyapunov function is presented to estimate the unknown nonlinear terms in coaxial counterrotating propellers, the uncertainties and external disturbances during mode transition. Furthermore, a simple controller based on the finitetime convergent observer and quaternion method is designed to implement mode transition. "However, PID controller is applicable only for SISO systems, therefore it does not account for the cross coupling effects present in UAVs. For such cases, multiple independent PID controllers are usually utilized in the hybrid UAVs such as in [35], [43], [52], [72], [55], [73], [76], [80], [82], [85]. 2) Linear Quadratic Regulator (LQR) Controller: LQR controllers goal is to find a control input of the form, that minimizes the performance index, ℑ, which is given by "
 "However, PID controller is applicable only for SISO systems, therefore it does not account for the cross coupling effects present in UAVs. For such cases, multiple independent PID controllers are usually utilized in the hybrid UAVs such as in [35], [43], [52], [72], [55], [73], [76], [80], [82], [85]. 2) Linear Quadratic Regulator (LQR) Controller: LQR controllers goal is to find a control input of the form, that minimizes the performance index, ℑ, which is given by "
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