Abstract—In this research, designing of an UAV autopilot system,

including, navigation, guidance and control subsystems, will be

discussed. This control subsystem consists of a longitudinal

controller, that compensates the height difference between

aircraft altitude and desired trajectory, and a lateral controller,

that instantaneously adjusts aircraft to the desired flight path.

We used fuzzy and classic methods for autopilot design.

Desired flight path and UAV position are respectively, as input

and output of navigation subsystem. The UAV position’s

deviation as input to guide subsystem is entered, and the height

and required heading angle, in order to track the desired flight

path, are produced as output. Finally, required control surface

deflections, for UAV guidance to the specified trajectory, are

produced by the control subsystem.

Simulation results show that these controllers are capable to

appropriately guide this UAV to the specified path. However,

fuzzy controller can perform slightly better in some uncertainties

in comparison with the classic controller, but in terms of speed of

response is a bit slow.

Index Terms—Autopilot system, Navigation, Guidance,

classical control, fuzzy control

1. INTRODUCTION

Accomplishment of some particular missions, in small or

impassable places is the main motivation for the creation of

unmanned aerial vehicles (UAVs). This kind of performances

also includes high level of risks.

According to some significant data, Australia had major

investments in this area as far as it had 198% growth in aircraft

industries, in recent decades [1].

Between the first kinds of unmanned aerial vehicles, Rayn

Model 154, Tu-21 and D-121 can be noted. Using the Tu-21

recorded some excellent results in Vietnam War and this

industry has entered in a new phase. In the last forty years

researches and developments has been done, has led the

development of this industry. New users of the UAVs,

especially in non-military areas, can be another important

reason for this progress [1].

Figure 1 shows the information, Teal group have been

published, about the progress of drone manufactures during the

years 2010 to 2020. As can be seen, the maximum amounts of

investments are related to USA [2].

Figure 1 :World UAV Production Forecast by Region (Value, $ Millions)

UAVs need to have some particular capabilities like doing

high risk maneuver, for specific missions, in impassable

locations. Therefore, designing of strong and stable autopilot

against disturbances, as the brain of UAV, is so important in

order to gain high capabilities in some special maneuvers.

In UAVs, Autopilot systems guide the aircraft to a specified

direction. These systems are responsible for guiding the UAVs

in absence of human pilot. Most people think autopilot systems

are designed only for aircraft while boats, ships, ... can also

have such as autopilot systems.

Autopilot systems accomplish the control and guidance

Comparison the Performance of a Fully Autonomous

Autopilot System using Fuzzy and Classical Control

Masoud Shakeri

Department of Electrical Engineering, Malek Ashtar University of Technology, Tehran, Iran (shakerim64@gmail.com)

Maryam Razzaghi

Department of Electrical Engineering, Qazvin Islamic Azad University , Qazvin, Iran

Seyyed Nabi Allah Bani Hashemi

Department of Electrical Engineering, Malek Ashtar University of Technology, Tehran, Iran

Mohammad Ali Shahi Ashtiani

Assistant Professor Department of Electrical Engineering, Malek Ashtar University of Technology, Tehran, Iran

process with three subsystems such as navigation, guidance

and control blocks.

In this paper all navigation, guidance and control subsystems

will be outlined. In control subsystem, one controller for

longitudinal motion and two controllers for lateral motion will

be designed. Fuzzy and classical control method will be

applied for control subsystems and their performances will be

compared.

Intelligent controls using neural networks and fuzzy logic in

several applications such as auto pilot [3], process control [4]

and robotics [5] have been studied. In recent years, control law design based on fuzzy logic had

significant progress in industrial applications, especially in

cases with uncertainties presence, in wide range of conditions

[6]. In [7] the fuzzy-neural controller was used for landing

control in a commercial airliner. The controller had been

tested as well, in the some various disturbances. In later works,

genetic algorithm was used in order to find the fuzzy–neural

controller gains [8].

This paper contains the following sections. First, the equations

of motion of an aircraft are studied. Then, navigation and

guidance subsystems will be discussed. Then, fuzzy and

classical methods will be used for control subsystem design.

Finally, simulation results will be presented.

2. EQUATIONS OF MOTION

The equations of motion are obtained with the assumption

of a rigid aircraft. These equations are coupled and nonlinear.

Equations can be linear, with assuming a constant speed,

symmetric flight and low speed disturbances compare with

aircraft flight speed [9].

2 2 2

( cos sin )

cos

1[ cos sin cos sin sin ]

tan sin tan cos

cos sin

( cos sin )sec

sin

T

T

T

T

w u

V

u v wV

p q r

q r

r q

h V

V u v w

(1)

The between velocity in body and inertial Coordinate can be

showed in matrix below. The aircraft position can be

calculated with integration of this matrix that cos( )C and

sin( )S [10].

X C C S S C C S C S C S S u

Y C S S S S C C C S S S C v

Z S S C C C w

(2)

In equation (2), u, v and w are respectively, the forward,

lateral and downward velocity in the body coordinate system

and the units are in feet, seconds and radians.

3. PROPOSED STRATEGY FOR AUTOPILOT DESIGN

Figure 2 shows a simple pattern of autopilot system. As can

be seen, it includes navigation, guidance and control

subsystems.

Figure 2: General view of aircraft landing

To adjust the UAV to a predetermined trajectory,

controllers have to generate appropriate commands for

aerodynamic control surfaces such as aileron, rudder and

elevator [11]

General performance of autopilot system:

1. Navigation subsystems, determine UAV position,

instantaneously, then produce some required data for

guidance subsystems.

2. Guidance subsystems receive reference flight path from

ground stations and other such important information

like linear and angular position of UAV then provide

required longitudinal and lateral angle for control

subsystems.

3. Control subsystems prepare the required commands for

the control surfaces, in order to guide the aircraft to the

specified trajectories.

3.1. NAVIGATION SUBSYSTEM

Navigation subsystems, obtain the information due to UAVs

position from avionic sensors (GPS) in geodetic and NED

coordinate system. Therefore, with some essential conversions,

the data are transferred to ECEF or flat axes. Finally, the

required information will be sent to the guidance subsystem.

In Figure 3, the geographical location of a point, relative to

the earth, in NED and ECEF coordinate systems has been

shown [ ].

Figure 3: UAV position in NED and ECEF coordinate systems

As can be seen, UAV position is specified in geodetic

coordinate such as longitude (λ), latitude (φ) and altitude (h)

that can be converted to (x,y,z) in ECEF or flat axes.

In avionic systems, especially in navigation and guidance

subsystems, usually flat earth coordinate data is applied.

Therefore, first geodetic and NED coordinate data have to be

converted to UAV flat earth position then required processes

have to be imposed to these kinds of data. Equations below

show some of useful calculations for data conversion between

axes [ ].

To convert geodetic latitude and longitude to the North and

East coordinates, the estimation uses the radius of curvature in

the prime vertical (RN) and the radius of curvature in the

meridian (RM) that are defined by the following relationships:

2

20

2 20

(1 (2 ))

2(1 (2 ) )

(1 (2 ) )N

M N

f fR R

f f sin

Re

f f sinR

(3)

Where R 6378137me is the equatorial radius of the earth

and f 0.0033 is earth flattening factor.

0

0

0

1

1

1

1cos

,tan ( )

,tan ( )

M

N

NR

ER

dd d

dd d

(4)

Where Small changes in the North (dN) and East (dE)

positions are approximated from small changes in the in

latitude and longitude.

Finally, UAV position in flat earth coordinate can be

demonstrate with the equations below.

cos sin

sin cosflat

x N

y E

(5)

Where ψ is the angle in degrees clockwise between the x-axis

and north. The flat Earth z-axis value is the negative altitude

minus the reference height (href) [14].

( )ref

z h h (6)

3.2. GUIDANCE SUBSYSTEM

Commands generations, in order to adjust UAVs to the desired

trajectory, are the main duties of guidance systems.

Figure 4 shows a general block diagram of a guidance system.

As can be seen, desired path, from ground station and

navigation data are this block inputs. Then, after some

calculations, desired altitude and heading angle will be

produced for control subsystem.

Figure 4: An overview of guidance system

Figure 5 represents UAV flight path from position (i-1) to

(i). It is observed that for getting to this flight path, height has

to increase as far as z or UAV Pitch angle has to rise to Theta

in XY_Z plane while for lateral motion in X_Y plane, UAV

Heading angle has to change as far as Psi.

Figure 5: UAV flight path between two points.

Because of the UAV limited rotation, command angles have to

divide to smaller size then send to control subsystem in several

times to rotate up along the desired flight route. Therefore,

amount of the command angle according to equation (7) is

calculated:

1

wp UAV

wp UAV

wp UAV

-1 Ywp X

2 2

1

-1 Zwp d

X X (i) X (i-1)

Y Y (i) Y (i-1)

Z Z (i) Z (i-1)

= tan ( )

d = x +y

= tan ( )

(7)

That wp is different heading angle between positions (i-1)

and (i). e is required heading angle in order to reach to the

next desired point can be computed by equation below.

UAV wpe (8)

Figure 6: required heading angle for reaching to desired point

For obtaining the required pitch angle, wp can be

calculated as difference pitch angle between positions (i-1) and

(i). Therefore, required pitch angle can also be computed from

equation (9).

UAV wpe (9)

However, for exact altitude control of UAV, it is better to

obtain the difference between UAV altitude and desired

one. Hence, the command altitude can be counted by equation

below.

( )UAVwphe Z Z (10)

3.3. CONTROL SUBSYSTEM

Selecting an appropriate configuration and choosing the best

variables as inputs or outputs are the most important steps in

order to attain the best performance in controller design.

Figure 7 shows a general block diagram of an aircraft

controller subsystem. As can be seen, he and e are

controller input variables that will be generated by guidance

subsystem.

Longitudinal controller has to compensate the altitude

difference ( he ) with proper elevator commands. Lateral

controller also has to adjust the aircraft to the desired flight

path with producing appropriate aileron and rudder deflection

for heading compensation (e ).

Figure 7: general block diagram of controller subsystem

3.3.1. CLASSICAL CONTROLLER DESIGN

Classical controls are the simplest methods for designing an

aircraft controller by using linear equations of the plant. For

linearization, a series of simplifying assumptions are regarded

to obtain relatively simple mathematical relation. This

simplification leads to a great difference rather than the actual

conditions. Therefore, their usages are not applicable for all

real conditions. However, the classic controllers are used in

most industrial systems because of their speed and simplicity

[15].

Longitudinal Controller Design: Figure 13 shows a general

block diagram of aircraft longitudinal controller. As can be

seen, eh (difference values of aircraft altitude compared to the

desired value) has to be compensated by generating required

elevator deflection [11].

Figure 8: general block diagram of longitudinal controller

That , , qFCG G k can be calculated by Ziegler-Nichols

method like equation below.

2 0.40.001

2.4 10( )

1.21

C

F

q

SG

S

SG

S

k

(11)

Lateral-Directional Controller Design: Lateral motion will

be controlled by aileron deflection and rudder deflection can

control directional motion.

In order to adjust aircraft to the main trajectory, by lateral

controller, the required heading angle first has to be converted

to bank angle afterwards be compensated by aileron deflection,

Figure 9.

Figure 9: Required structure for lateral controller

Figure 10 shows the internal loop of lateral controller. This

block can completely control the aircraft roll angle in order to

compensate required heading angle.

Figure 10: Internal loop of lateral controller

In order to decrease aircraft side slip, directional controllers

are required, Figure 11. As can be seen, aircraft side slip can

be compensated by rudder deflection.

Figure 11: Required structure for directional controller

As can be seen, one filter, washout circuit, is used to drive

input signal to zero by the magnitude of time constant, τ. The

amount of directional controller parameters is expressed in

equation below.

4 , 0.25rk (12)

3.3.2. FUZZY CONTROLLER DESIGN

Fuzzy logic was first introduced by Lotfi Zadeh in the 60s.

Later, he continued with fuzzy sets described by linguistic

variables [16]. Fuzzy logic procedures are quite different from

classical logic [17]. These differences cause the fuzzy

controllers are used to control complex systems with

uncertainty conditions.

Membership functions and rule bases can be set by some

numerical methods such as neural networks [18], genetic

algorithm [19], Kalman filter [20] or numerical optimization

techniques [21].

Figure 12 shows an example of input and output defined

membership functions. The triangular membership functions,

defined for all variables, are completely symmetrical.

Figure 12 : An example of the membership functions

Interpretation of some of the linguistic variables for input

and output are defined as:

PM = Positive Medium PL = Positive Large

PS = Positive Short ZE = Zero

Longitudinal Controller Design: Figure 13 shows a general

block diagram of aircraft longitudinal controller. Input

variables in the first controller are eh and h (difference

values of aircraft altitude compared to the desired value and

descent rate) and ref (suitable pitch angle for desired

trajectory) is produced as its output. Then, the second

controller gets values of q and e

as its input, and produces

the required elevator deflection [11].

Figure 13: general block diagram of longitudinal controller

Table 1 and Table 2 show defined fuzzy rules for fuzzy

controller. These controller outputs equal to the proper pitch

angle. In this research, the fuzzy logic membership functions

and its associated rule base are determined heuristically. The

crisp FLC outputs are also determined by the centroid method.

Table 1: Fuzzy rules for the first controller.

PLPSZENS NLeh

.

h

NLNLNLNS ZE NL

NLNLNS ZE PSNS

NLNS ZE PSPLZE

NS ZEPSPL PL PS

ZEPSPLPL PL PL

Table 2: Fuzzy rules for the second controller.

PLPSZENS NLeθ

q

ZEPSPLPL PL PL

NSZEPSPL PLPS

NLNSZEPS PLZE

NLNLNSZE PSNS

NLNLNLNS ZENL

Lateral-Directional Controller Design: Lateral motion will

be controlled by aileron deflection and rudder deflection can

control directional motion.

In order to adjust aircraft to the main trajectory, the required

heading angle first has to be converted to bank angle

afterwards be compensated by aileron deflection, Figure 14.

Figure 14: Required structure for heading and bank angle conversion

The PID compensator, which has been designed for classical

controller, can be used for fuzzy lateral controller.

Figure 15 and Table 3 show, respectively, the general block

diagram of aircraft lateral controller and defined fuzzy rules

for fuzzy lateral controller. As can be seen, e (difference

between desired and UAV roll angle) and P (roll rate) are

input variables that fuzzy controller can generates aileron

deflection with processing these variables.

Figure 15: An overview of the lateral controller

Table 3: Fuzzy rules for the lateral controller

PLPSZENS NLEφ

P

ZE NSNLNLNL PL

PS ZE NSNLNLPS

PLPS ZE NSNLZE

PLPL PS ZE NS NS

PLPLPLPS ZENL

In this section, directional controller, which has been designed

for classical controller, can be used to diminish aircraft side

slip by proper rudder deflection command.

4. CONCLUSION

The main objectives of this paper are to compare the

performance of the fuzzy and classical controllers in trajectory

tracking. These controllers are used to control UAV in some

maneuvers.

In future work, improving the range of input and output

membership functions, in fuzzy controller and also adaptive

controllers, for improving the response and reliability of these

controllers against sudden and severe wind disturbance will be

considered.

REFERENCES

[1] Report of Aerospace Industry Action, ''Department of Industry

Tourism and Resources" Canberra ITR 2003.

[2] http://www.tealgroup.com„‟ Teal group, World UAV Systems,

Market Profile and Forecast 2011.

[3] J. Juang and K. Cheng, “Wind disturbances encountered during

controlled landings using neural network approaches,” Proc. of the IEEE

Int. Conf. on Control Applications, pp. 835-840, 2001.

[4] L. McLauchlan and M. Mehrubeoglu, “Neural network internal

model process control,” Proc. of SPIE Volume 6961: Intelligent

Computing: Theory and Applications VI, 69610M-1 - 69610M-10,

April 2008.

[5] K. Ishii and K. Yano, “Path planning system for a mobile robot

using self-organizing map,” Proc. of the International Conf. on Info-tech

and Info-net, Beijing, vol. 4, pp. 32-37, 2001.

[6] J.G.Juang, C.Cheng. “Application of Neural Networks to

Disturbances Encountered Landing Control”, IEEE Transactions On

Intelligent Transportation Systems, December 2006.

[7] J. Juang and J. Chio, “Aircraft landing control based on fuzzy

modeling networks,” Proc. of the 2002 IEEE Int. Conf. on Control

Applications, Glasgow, Scotland, U. K., Sept. 18-20, pp.144-149.

[8] J. Juang, K. Chin, and J. Chio, “Intelligent automatic landing system

using fuzzy neural networks and genetic algorithm,” Proc. of the

American Control Conf., Boston, MA, June 30-July 2, 2004.

[9] A.R. Babaei, et al., Classical and fuzzy-genetic autopilot design for

unmanned aerial vehicles, (2009)

[10] C.Nelson, Robert. Flight Stability and Automatic Control. Mc

Graw-Hill Book Company, 1989.

[11] G.Ducard,” Unmanned aircraft design modeling and control ,

Introduction to navigation system”, Lecture notes,2009.

[12] S.Ronnback,”Development of an INS/GPS navigation loop for an

UAV”,Master thesis,2000.

[13] J.Berg,”Development and impelement of guidance, navigation and

control systems for an autonomous air vehicle”, Master thesis, 2009.

[14] Stevens, B. L., and F. L. Lewis. Aircraft Control and Simulation,

2nd ed. New York: John Wiley & Sons, 2003.

[15] S.E. Woodward and D.P. Garg, “A numerical optimization

approach for tuning fuzzy logic controllers,” IEEE Transactions on

Systems, Man and Cybernetics, Part B, vol. 29, no. 4, pp. 565-9, Aug.

1999.

[16] F.Saghafi, S.Pouya, S. M. Khansari Zadeh. “Intelligent Landing of

Autonomous Aerial Vehicles using Fuzzy Logic Control,” IEEEAC,

December 14, 2008.

[17] L. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, pp. 338-

353,1965.

[18] L. Zadeh, “Is there a need for fuzzy logic,” Annual Meeting of the

North American Fuzzy Information Processing Society, 2008. NAFIPS

2008, 19-22 May, 2008, pp. 1 – 3.

[19] D. van Cleave, K.S. Rattan, “Tuning of fuzzy logic controller using

neural network,” Proc. of the IEEE 2000 National Aerospace and

Electronics Conference, 2000. NAECON 2000, 10-12 Oct. 2000 pp.305

– 312.

[20] C. Moraga, M. Sugeno, and E. Trillas, “Optimization of fuzzy if-

then rule bases by evolutionary tuning of the operations,” 39th Int.

Symposium on Multiple-Valued Logic, 2009. ISMVL '09, 21-23 May

2009 pp. 221 – 226.

[21] P. Ramaswamy, M. Riese, R.M. Edwards, K.Y. Lee, “Two

approaches for automating the tuning process of fuzzy logic

controllers,” Proc. of the 32nd IEEE Conference on Decision and

Control, San Antonio, Texas, 15-17 Dec. 1993.