journal supervisory

1

Comparison the Performance of an

Automatic Landing System Using Fuzzy,

Classical and Supervisory Controllers

Masoud Shakeri

Department of Electrical Engineering, Malek Ashtar University of Technology, Tehran, Iran ([email protected])

Mohammad Ali Shahi Ashtiani

Assistant Professor Department of Electrical Engineering, Malek Ashtar University of

Technology, Tehran, Iran ([email protected])

Seyyed Hossein Sadati

Assistant Professor, Department of Electrical Engineering, Malek Ashtar University of

Technology, Tehran, Iran ([email protected])

Abstract

In this research, a Fuzzy, classical (PID) and a combination of them, as a fuzzy-classical

control method, are used in designing of the longitudinal motion controller for an aircraft.

The main objectives of each of these controllers are to reduce the vertical velocity and

altitude of the aircraft in glide slope and flare phases. In fact, each longitudinal controller

consists of two controllers. The first controller produces required pitch angle for aircraft

guidance to the specified trajectory, and the second one will produce elevator deflection for

aircraft rotation to the desired path. These controllers have proper performance in landing

phase but they are not more stable in presence of some wind disturbances. Therefore, by

adding an appropriate supervisory controller, the stability of the system against turbulence

will be increased. Simulation results show that the supervisory controller can successfully

raise the safety envelope to include more hostile environments such as wind disturbances.

Keywords—Automatic landing systems, Classical Control, fuzzy Control, supervisory

Control

1. INTRODUCTION After the realization of flight dream, flight safety was the most important issue for aircraft

designers. In this case, minimizing the human factors and moving toward automatic control

systems is an effective step in improving flight safety.

According to the reference released by Boeing, 47% of the aircraft crashes happened in final

approach and landing phase. On the other hand, 76% of all incidences were due to human factors

and 5% related to sudden changes in atmospheric conditions [1].

Considering the above points mentioned:

1. In terms of safety, the landing phase is the most critical phase of flight.

2. In terms of workload, this phase has a high percentage of total flight operations.

The earliest ILS systems were designed in 1943 and today have considerably progressed.

Although the ILS equipment provide facilities for pilots in the landing phase, but they are not fully

automated. Automatic landing systems include three sub-controllers:

1. Approach angle control systems

2. Flare phase control systems

3. Lateral-directional control systems

In this research, only the first two systems will be investigated.

mailto:[email protected]

mailto:[email protected]

Comparison the Performance of an Automatic Landing System Using Fuzzy, Classical and Supervisory Controllers


2

The first automatic landing system (ALS)1 developed, in the early years of making ILS, in

England. Early systems were only able to control the approach phase while newer models are also

able to control the Aircraft in next phases [2].

In designing of the aircraft automatic landing system, it is very important to determine the desired

trajectory from the beginning of landing until touching down the runway.

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].

In this research a longitudinal controller is designed to control the landing phase of Boeing 747

airplane. In The designed control system a combination of fuzzy and classical methods is used to

control the aircraft height and descent rate, in Flare and Glide phases.

This paper contains the following sections. First, the equations of motion of an aircraft and landing

phases are studied. Then, a reference model will be suggested for adjusting the height of the

aircraft. Then, fuzzy and classical controls are used in order to design the best longitudinal

controller. After that, supervisory controller will increase the stability of the auto land systems

against sudden weather conditions. 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 in landing phase. Here, using

the theory of small perturbation, the equations have been linear. Matrix of linear equations for

longitudinal variables has been described below [9].

0.021 0.122 0.000 0.322 0.01 1.0

0.209 0.530 2.210 0.000 0.064 0.044

0.017 0.164 0.412 0.000 0.378 0.544

0.000 0.000 1.000 0.000 0.000 0.000

E

T

u u

w w

q q

(1)

Where

q = pitch rate, θ = pitch angle, E = elevator deflection, T = throttle deflection; u and w are

respectively, the forward and downward velocity in the body coordinate system and the units are

in feet, seconds and radians.

3. DESIRED TRAJECTORY IN LANDING PHASE Figure 1 shows a simple pattern of landing phases. The desired landing trajectory for an aircraft

is mainly divided into glide path and flare.

Figure 1: General view of aircraft landing trajectory

1 Instrument Landing System

M. Shakeri, M. A. Ashtiani, S. H. Sadati

Volume 1 · Number 1 · 2014

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Glide path. A Glide path is a preferred descent path of an aircraft into the airport. In this phase,

flight path angle is between -2 and -5 degree and aircraft flies with a fixed descent rate. The

optimal height for this phase is expressed in equation (2).

0tan

Ch x (2)

In equation (3), x is aircraft position and 0 is flight path angle in the beginning of glide phase.

Usually, starting height of the glide slope depends on the aircraft, hence, for this case study

(Boeing 747), we considered 1200(ft) height for it [10].

Flare. A Flare path is a trajectory which the flight path angle changes to a more suitable angle for

smooth touchdown. During this phase the aircrafts rotates around their center of gravity and flight

path angle will change from negative to positive (e.g. 0 to 2 degree).

Usually, this phase begins at less than 70 feet height above the ground. In this situation, aircraft

descent rate should be between 2 and 3 (ft/s) for a smooth landing. Therefore, the aircraft’s

altitude changes in an exponential curve which is expressed in equation (3).

/

0

t

flare fh h e (3)

In equation (3), 0fh is flare starting altitude, is the time constant of flare [11].

4. LONGITUDINAL CONTROLLER DESIGN

Selecting an appropriate configuration and choosing the best variables as input or output are the

most important steps in order to attain the best performance in controller design. Hence, a

combination of two controllers is used for longitudinal motion control. Input variables in the first

controller are eh and eh (difference values of aircraft altitude and descent rate compared to the

desired value) 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 values of

elevator deflection. Figure 2 shows a general block diagram of this aircraft longitudinal controller.

Figure 2: general block diagram of an aircraft landing controller

4.1. Fuzzy Controller Systems

Fuzzy logic was first introduced by Lotfi Zadeh in the 60s. Later, he continued with fuzzy sets

described by linguistic variables [12]. Fuzzy logic procedures are quite different from classical

logic [13]. 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 [14], genetic algorithm [15], Kalman filter [16] or numerical optimization techniques

[17]. This section, presents the implementation of a fuzzy controller which analyzes the inputs in

order to generate elevator deflection for aircraft.

The two-dimensional table of rules is the most common and appropriate method for presentation

and structure of database rules. In this research, the structures of these tables are also used. On the

other hand, we choose the triangular-type membership functions that are suitable in terms of

calculations and also robust against perturbed noises.

Fig. 3 shows an example of input and output defined membership functions. The triangular



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membership functions, defined for all longitudinal variables, are completely symmetrical.

Figure 3 : An example for 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

NM = Negative Large NL = Negative Medium

Table 1 and table 2, respectively, show defined fuzzy rules for first and second fuzzy controller.

The first controller outputs equal to a proper pitch angle and the second controller outputs are the

elevator deflection. 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.

PL

PM

PS

ZE

NS

NM

NL

eh

ehdot

PL PL PM PS ZE NS NS PL PL PM PS ZE NS NS NM PM

PM PS ZE NS NS NM NM PS PS ZE NS NS NM NM NM ZE ZE NS NS NM NM NM NL NS NS NS NM NM NM NL NL NM

NS NM NM NM NL NL NL NL

Table 2: Fuzzy rules for the second controller.

PL

PS

ZE

NS

NL

eθ

q

ZE PS PL PL PL PL

NS ZE PS PL PL PS

NL NS ZE PS PL ZE

NL NL NS ZE PS NS

NL NL NL NS ZE NL



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4.2. Classical Controller Design

Classical controls are the simplest method for designing an aircraft controller by using linear

equations of the plant. For linearization, a series of simplifying assumptions are regarded to obtain

simple mathematical equations. These simplifications lead to a great difference between the

considered and actual conditions. Therefore, their usage is not applicable for all real conditions.

However, the classical controllers are used in most industrial systems because of their speed and

simplicity [18].

Fig. 4 and figure 5 show the designed PID controllers. The first controller generates the desired

pitch angle by using eh , eh and the second controller generates the elevator deflection by

using e , q as input variables.

Figure 4: An overview of the first PID controller which generates the desired pitch angle

As can be seen, the gains of altitude error and descent rate are constant, but the gains of pitch

angle error and pitch rate are different in flare and glide phases [19].

Figure 5: An overview of the second PID controller that generates required elevator

deflection

4.3. Fuzzy-Classical Controller Design

After designing the fuzzy and classical controllers separately, we want to combine these

controllers to gain the best performance and obtain the best controller for landing phase.

At this time, we use the fuzzy controller, designed in section (4-1), for producing command pitch

angle and the PID controller, designed in section (4-2), for producing elevator deflection, fig. (6).

We call this controller as a Fuzzy-Classical Controller which Fuzzy controller performs as the first

controller and Classical controller acts as the second one.



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Figure 6: An overview of the fuzzy-classical controller

4.4. Classical-Fuzzy Controller Design

This section is similar to the last section (4-3) but in reverse. We use the PID controller for

producing command pitch angle and fuzzy controller for producing elevator deflection, fig. (7).

We call this controller as a Classical-Fuzzy controller which classical controller performs as the

first controller and fuzzy controller acts as the second one.

Figure 7: An overview of the Classical-Fuzzy controller

4.5. Supervisory Controller Design In complex operational systems, single-loop control systems are not able to effectively solve the

issue of control, so a multi-level control structures can be very useful.

There are two possibilities in the two-level control structure:

1. The first level of controller is a fuzzy controller and the second level is a non-fuzzy

supervisory controller.

Figure 8: Structure of a two levels fuzzy control system, the main controller is fuzzy and

supervisory controller is non-fuzzy

2. The first level of controller is a non-fuzzy controller (for example PID) and the second

level is a fuzzy supervisory controller.



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Figure 9: Structure of a two levels fuzzy control system, the main controller is non-fuzzy

and supervisory controller is fuzzy

In this research, the first kind of supervisory controller is considered. On the other hand, as will be

shown, the fuzzy-classical controller has the best performance in landing phase, hence for this

case, the first level controller is fuzzy and the second-level controller is classic.

Figure 10 shows the inside of the supervisory controller. As can be seen, the fuzzy-classical

controller is used for the process and a non-fuzzy (PID) controller supervises of the performance

of fuzzy controller, which produces the value of the command pitch angle.

Figure 10: Structure of a two levels fuzzy supervisory control system

4.5.1. Obtaining the Control Law Equation (4) shows the general form for obtaining the control law.

*( ) ( )fuzz su u X I u X (4)

1( ) ( )[ ( ( ) ]T u T

s fuzz

L

u X sign X pb f K X u Xg

(5)

The coefficients, in equation (5), can be obtained in [20]. If xX M then * 1I else

* 0I . In fact, *I is a switching function. For elimination of chattering, *I is considered as:

*

0

1

x

x

x

X a

X aI a X M

M a

X M

(6)



8

That (0, )xa M and is obtained by control designer [20]. The value of parameters is considered

as 35( ), 10xM ft a .

It means, if eh would be more than 35 (ft) then *I function operates in control loop and affects on

the value of command pitch angle (C ).

Fuzzy-Classical controllers are able to properly control the aircraft in landing phase by itself [21].

Therefore, the fuzzy-supervisory controller is designed to control aircraft in bad weather

conditions, especially in sudden gusts that are mentioned below.

4.6. Gust Model

Fig. 11 shows Wind speed diagrams in Dryden model. As can be seen, the horizontal wind

speed equal to -50 (ft/s), which is a relatively as a powerful gust ( gcu 50( / )ft s ).

Figure 11: graphs of vertical and horizontal wind speeds

5. Simulation Results

In this section, the controller performances have been investigated. Linear dynamic model of the

Boeing 747 is used that its initial velocity and height are mentioned below [10]. The initial

Conditions of some parameters are considered in equation (7):

01200( ), 221( / )h ft V ft s (7)

The graphs of aircraft flight path are shown in the following figures (12,14,16,18). As these

figures show, aircraft started approaching from 1200 (ft) height above the ground and touched

down on the runway in approximately 180 seconds. As you can see, the aircraft tracks the desired

path very well and there are only some small oscillations around desired trajectory.

Figure 12: aircraft flight path graph with fuzzy controller



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Figure 13: aircraft rate of descent graph with fuzzy controller

Figure 14: aircraft flight path graph with Classical controller

Figure 15: aircraft rate of descent graph with Classical controller

According to the aircraft descent rate graphs (Figs. 12,14,16,18) can be observed that rates of

descent are almost constant in Glide phase and acceptably follow the command rate of descent.

Most oscillations in these graphs are related to beginning of the glide path because of difference

between desired and the aircraft initial descent rate.

By comparing these graphs, can be found out that the classical controllers (PID) has the best

performance in tracking of desired landing trajectory but its descent rate overshoot is more than

the others. For the passenger aircraft, like Boeing 747, rate of descent is the most important



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parameter that has a major influence on passengers. So, the best performance, in terms of time

response and overshoot, belongs to classical-fuzzy controller that provides comfortable landing for

passengers but it is a bit slow rather than fuzzy-classical controller. Therefore, with considering all

the parameters, we can choose fuzzy-classical controller as an appropriate controller for landing

phase.

Figure 16: aircraft flight path graph with Fuzzy-Classical controller

Figure 17: aircraft rate of descent graph with Fuzzy-Classical controller

Figure 18: aircraft flight path graph with Classical-Fuzzy controller



11

Figure 19: aircraft rate of descent graph with Classical-Fuzzy controller

Figures 20 and 21 show the descent rate and landing trajectory graphs by using fuzzy-

supervisory controller, in presence of the wind disturbances. As can be seen, the wind turbulences

affect the rate of descent but finally the fuzzy-classical supervisory controller keeps the aircraft

stable and brings it landed very well.

Figure 20: aircraft flight path graph with Fuzzy - supervisory controller in presence of the

wind disturbances

Figure 21: aircraft rate of descent graph with Fuzzy-supervisory controller in presence of

the wind disturbances



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6. Conclusion

The main purpose of this paper is to compare the performance of the fuzzy, classical and the

combined classical-fuzzy and fuzzy–classical controller performance in landing phase.

Simulation results show that classical controller tracks commands, have sent from the runway,

very well. So we can conclude that classical controller, because of its high speed command

tracking, is the best choice to control different motions of UAV.

Considering the overshoot of the descent rate shows that the classical-fuzzy controllers have the

best performance in landing phase.

The controller stability against wind disturbance was not very well [22]. Therefore, the fuzzy–

Supervisory controllers has been designed that resulting graphs show the proper performance of

this controllers in the bad weather conditions.

In future work, improving the range of input and output membership functions, in classical-

fuzzy controller, and also adaptive-fuzzy controller for improving the aircraft response and

reliability against sudden and stronger wind disturbance will be considered.

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journal supervisory

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