fuzzy-genetic identification and control stuctures for nonlinear helicopter model

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Fuzzy-Genetic Identification and Control Stucturesfor Nonlinear Helicopter ModelJasmin Velagic a & Nedim Osmic aa Faculty of Electrical Engineering, University of Sarajevo, Zmaja od Bosne bb,71000, Sarajevo, Bosnia and HerzegovinaPublished online: 08 Mar 2013.

To cite this article: Jasmin Velagic & Nedim Osmic (2013) Fuzzy-Genetic Identification and ControlStuctures for Nonlinear Helicopter Model, Intelligent Automation & Soft Computing, 19:1, 51-68, DOI:10.1080/10798587.2013.771454

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FUZZY-GENETIC IDENTIFICATION AND CONTROL STUCTURESFOR NONLINEAR HELICOPTER MODEL

JASMIN VELAGIC* AND NEDIM OSMIC

Faculty of Electrical Engineering, University of Sarajevo, Zmaja od Bosne bb, 71000 Sarajevo,

Bosnia and Herzegovina

ABSTRACT—The paper exploits advantages of the genetic algorithm and fuzzy logic in identification

and control of 2DOF nonlinear helicopter model. The genetic algorithm is proposed for identification of

the helicopter system, which contains a helicopter body, main and tail motors and drivers. The quality of

helicopter model achieved was validated through simulation and experimental modes. Then, this model

is used to design of elevation and azimuth Mamdani type fuzzy controllers. The main objective of the

paper is to obtain robust and stable controls for wide range of azimuth and elevation angles changing

during the long time flight. The robustness and effectiveness of both fuzzy controllers were verified

through both simulations and experiments. Also, a comparative analysis of proposed fuzzy and

traditional PID controllers is performed.

Key Words: helicopter model; identification process; genetic algorithm; fuzzy control

1. INTRODUCTION

Identification and control of nonlinear systems are receiving considerable attention during last three

decades. In that context a helicopter is inherently unstable, very nonlinear and highly cross-coupled system.

Also, the helicopter is inherently a poorly damped MIMO system with the existence of great variations in

system dynamics, and in addition is exposed to severe disturbances. Hence, it is very important to make

correct modeling and parameters identification of this system.

The problem of parameter identification of nonlinear system is quite complex. A detailed description

of possible identification methods is given in [1]. In this paper we use a 2DOF Humusoft CE 150 laboratory

model helicopter was developed by Humusoft [2]. The identification method for this helicopter presented in

[2] and applied in [3] requires a specially prepared experiment for the determination of each individual

parameter. For more accurate identification, each experiment needs to be repeated many times. In order to

significantly reduce the number of conducted experiments and simplify the process of identification of the

helicopter, a simple genetic algorithm (GA) was used for identification of unknown parameters of

helicopter model.

The ordinary GA is binary-coded, where all the original real-number variables are encoded as binary

digits (genes) and then a string (chromosome) is formed by a collection of binary digits. GA makes no

limitation on the search space of optimization problems and searches for the optimum using a population of

potential solutions. It is very suitable for searching discrete, noisy, multimodal and complex spaces and

works with encoded parameters. A positive value, known as fitness, uses for evaluating the quality of

individual [4]. Identification of the parameters of the helicopter using GA is described in [5], but was used

q 2013 TSIw Press

*Corresponding author. Email: [email protected]

Intelligent Automation and Soft Computing, 2013

Vol. 19, No. 1, 51–68, http://dx.doi.org/10.1080/10798587.2013.771454

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for system identification in a closed loop. The paper [6] also describes the identification of parameters of

the helicopter using GA.

In recent years, a lot of effort has been undertaken to control of a nonlinear helicopter model [7]–[10].

The usage of the traditional PI, PD and PID is not satisfactory because the helicopter parameters are very

dependent on the operating point; therefore the controllers have to be very robust. These controllers only

work well in a very small area around that set point. Also, when dealing with multivariable systems, one of

the major concerns are the cross-couplings of the system. The control performance of these types of

controllers could be improved by using an output tracking based on approximate input-output linearization

[11]. This approach is constructed by first neglecting the coupling effect, then showing that the approximate

control results in bounded tracking on the exact model. In [12], a gain scheduling control of helicopter

model was implemented. The model is being linearized at different set points along the elevation axis. An

adaptive model-reference control with the reference model transfer function which is equal to the inverse of

the controller dynamics was designed in [13].

The multiple controllers for elevation and azimuth control designed by pole placement technique using

state feedback controller are shown in [14]. Helicopter control design based on m-synthesis is studied in

[15]. Robust control algorithms design by an aggregation method of the state variables are proposed in [16].

The method of aggregation of state variables enables designing a robust control algorithm with a high gain

and robust algorithms work in a slide mode. The robust control of the helicopter model based on

localization method [17], [18] uses higher order output derivatives in the feedback loop. The quality of

robust parallel PID controllers designed iteratively based on the method of Miyamoto method is

demonstrated in [19]. In general, linear controllers are designed in the flight envelope operating points [20].

All of mentioned adaptive and robust methods work well for small changes of azimuth and elevation

angles only. Some more sophisticated control methods could be tested on the helicopter model in order to

try to achieve better performance. An interesting option would be the use of intelligent controllers, like

fuzzy and neural. The model predictive neural control of a helicopter is proposed in [21]. In [20] a nonlinear

optimal control of helicopter using fuzzy gain scheduling is presented. Several fuzzy logic control and

neural network control strategies are compared in [22]. The helicopter control based on evolutionary

algorithm and particle swarm optimization is described in [23]. The effectiveness of these controllers is

verified in simulations only.

In our paper, the proposed fuzzy elevation and azimuth controllers provide the significantly good

control performance in cases of a wide region of rapidly set points changing during the long time flight.

Particular advantages of the proposed fuzzy controllers are effective and satisfactory simultaneous controls

of both elevation and azimuth angles with strong cross-coupling effects. For design of proposed fuzzy

controllers the existence of accurate helicopter model is very important. In our paper we demonstrate the

effective implementation of the genetic-based identification of fourteen unknown parameters of the

nonlinear helicopter model. We investigate behaviors of these controllers in both simulation and

experimental modes.

2. CONTROL SYSTEM DESCRIPTION

The proposed fuzzy logic control system of azimuth and elevation angles is shown in Figure 1. An overall

system contains azimuth and elevation fuzzy controllers, interface and complex helicopter system. The

communication between PC and helicopter system is established by MF 624 card, which is integral part of

Humusoft CE 150 helicopter system. The helicopter system contains the helicopter body, DC motors with

permanent stator magnets, power amplifiers (PWMs), encoders as sensors and axel gear (represents load).

The helicopter body is driven by the main and tail motors. In the rest of this section the mentioned

Intelligent Automation and Soft Computing52

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components of helicopter system will be described, except fuzzy logic controllers design procedures given

in the Section 4.

2.1 Helicopter Model

The derivation of themathematicalmodel for a helicopter system is based on a direct derivation of themodel by

computing the force balances in the form of nonlinear differential equations. Because the helicopter model

dynamics is extremely complicated and too large, in this paper only main results of it will be presented. The

mathematical derivation of Humusoft CE 150 helicopter is shown in more details in [2]. Also, some parts of

nonlinear helicopter system are linearized, especially nonlinear dynamics of the helicopter body in both

elevation and azimuth. The main reason for that is dependence of the resistive torque generated by rotating

propeller on the laminar air flow in low and turbulent air flow in high speed.

The helicopter model is a rigid body with two degrees of freedom. The axes of the main and tail motor

and the vertical (elevation) and horizontal (azimuth) helicopter axes are perpendicular to each-other. These

motors drive the propellers which influence changing azimuth (w) and elevation (c) angles simultaneously.

The helicopter model can be represented as a nonlinear multi-variable system with two inputs (u1 and u2)

and two outputs (c and w) by the following equations:

u ¼ ½u1; u2�T ð1Þ

y ¼ ½c;w�T ð2Þ

where u1, u2, c and w are voltage of the main motor, voltage of the tail motor, elevation angle (pitch angle)

and azimuth angle (yaw angle), respectively.

Elevation dynamics considers the forces in the vertical plane acting on the vertical helicopter body

(Figure 2), whose dynamics are given by the following nonlinear equation:

I €c ¼ t1 þ t _w 2 tf 1 2 tm þ tG ð3Þ

Tailmotor

Amplifier

Helicopter body

M624card

d

Encoder

d

y

y

e

u2

_

e

d/dt

PC Interface

d/dt

Fuzzyazimuth

controller

Fuzzyelevatio

controller

u1

Amplifier

Encoder

u2

u1

Mainmotor

Figure 1. Fuzzy helicopter control system.

Fuzzy-Genetic Identification and Control Stuctures for Nonlinear Helicopter Model 53

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where tm ¼ Fml sinc ¼ mgl sinc ¼ tG sinc, t _w ¼ ml _w2 sinc� cosc ¼ 12ml _w2 sin 2c, t1 ¼ kv1

v21 tf 1 ¼

Ccsign _cþ Bc_c, tG ¼ kG _wv1 cosc for _w ! v1, I is moment of inertia around horizontal axis, t1 is

elevation driving torque, t _w is centrifugal torque, tm is gravitation torque, tf1 is friction torque (Coulomb

and viscous), tG is gyroscopic torque, v1 is angular velocity of the main propeller, m is mass, g is gravity, l

is distance from z-axis to main rotor, kv1is constant for the main rotor, kG is gyroscopic coefficient, Bc is

viscous friction coefficient (around y-axis) and Cc is Coulomb friction coefficient (around y-axis).

Some influences are neglected in the above equations [2], e.g. stabilizing motor reaction torque and

varying air resistance depending on the turnings of the main propeller. While the influence of the tail motor

on the elevation angle is almost negligible, varying damping of body oscillation in elevation is noticeable.

The influence of the speed of the main propeller on friction torque in elevation is hardly to be modeled

analytically and must be evaluated by an experiment and, if significant, nonlinear coupling must be

introduced. The gyroscopic effect is to be considered, however the equation for gyroscopic torque

computation is simplified due to the assumption according to tG ¼ kG _wv1 cosc ; for _w ! v1.

Azimuth dynamics considers the forces in the horizontal plane, taking into account the main forces

acting on the helicopter body in the direction of angle w, whose dynamics are given by the following

nonlinear equation:

Ic €w ¼ t2 2 tf 2 2 tr ð4Þ

where Ic ¼ I sinc, t2 ¼ kv2l2 sincv2, tf 2 ¼ Cwsign _w2 Bw _w, Ic is moment of inertia around vertical axis,

t2 is stabilizing motor driving torque, tf2 is friction torque Coulomb and viscous, tr is main rotor reaction

torque, kv2is constant for the tail rotor, v2 is angular velocity of the tail rotor, Bw is viscous friction

coefficient (around z-axis) and Cw is Coulomb friction coefficient (around z-axis).

Similar to the body dynamics in elevation, no connection between the speed of the side propeller and

friction torque around vertical rotational axis has been introduced into the derivation of an analytical model

of the helicopter dynamics. Torque tr is significant and arises from the torque generated by the main motor

acting on rotating body [2].

2.2 DC Motor and Propeller Dynamics Modelling

The propulsion system contains two independently working DC electrical engines. The model of a DC

motor dynamics is obtained on the basis of assumptions that the armature inductance is very low, Coulomb

friction and resistive torque generated by rotating propeller in the air are significant and the resistive torque

generated by rotating propeller depends on v in low and v2 in high rpm.

Figure 2. Torques acting on the body of the helicopter in the vertical (a) and horizontal (b) axis


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Taking this into account, the equations are following:

Ij _vj ¼ tj 2 tcj 2 Bjvj 2 tpj ð5Þwhere ij ¼ 1

Rjðuj 2 KbjvjÞ, tj ¼ Kijij, tcj ¼ Cjsign(vj), tpj ¼ Bpjvj þ Dpj

vj2, j ¼ 1,2 - motor number (1-

main, 2- tail), Ij is rotor and propeller moment of inertia, tj is motor torque, tcj is Coulomb friction load

torque, tpj is air resistance load torque, Bj is viscous-friction coefficient, Kij is torque constant, ij is armature

current, Rj is armature resistance, uj is control input voltage, Kbj is back-emf constant, Cj is Coulomb

friction coefficient, Bpj is air resistance coefficient (laminar flow) and Dpj is air resistance coefficient

(turbulent flow).

2.3 Dynamics of the System as a Whole

The mathematical model of helicopter is described by (1)–(5). However, its block diagram will be

achieved by neglecting certain aspects of the helicopter model (without loss of generality) and using a

linearization of some parts of the helicopter model. The particular attention is paid to the interconnection

between the inputs (u1, u2) and the speed of rotation of the propeller (v1, v2). This relation yields the

following transfer function:

Gj ¼ 1

ðTjsþ 1Þ2 ð6Þ

Then, the transfer function output is multiplied by the following square term:

aju2j þ bj ð7Þ

where uj is output from transfer function given by (6) and j ¼ 1,2,3 (1- main motor, 2- tail motor, 3- cross-

coupling).

The terms (1)–(7) describe the whole helicopter system, which is shown in Figure 3.

For a simulation of the helicopter HUMUSOFT CE 150 it is necessary to perform the identification of

14 unknown parameters: T1, T2 (time constants of main and tail motor, respectively), ai, bi (parameters of

square functions, i ¼ 1,2,3), I;Bc; tG; kG; Ic andBw.

Figure 3. Block diagram of a complete system dynamics (body, motors and propeller).


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For the identification and design of fuzzy logic controllers, the Simulink computational model of the

complete helicopter system dynamics is used.

3. HELICOPTER MODEL IDENTIFICATION

Identification process of the complete physical helicopter system using GA is represented in Figure 4.

The inputs and outputs of the 2DOF helicopter model are:

uðkÞ ¼ ½u1; u2�T ð8Þ

yðkÞ ¼ ½c;w�T

In the identification procedure both physical structure of the helicopter and its model are excited by the

same input signals (see Figure 4). Then, we compute the output signals yðkÞ from the helicopter. An error

signal e(k) is calculated as the difference between the physical structure of the helicopter and the helicoptermodel outputs. The parameter k denotes the time instant t ¼ kT, where T is a constant sampling period. For

the evaluation of helicopter parameters a performance index J(e(k),Q) is used. It represents measure of the

errors size and expresses its dependence on the model parameters Q. In this paper, we use the genetic

algorithm (GA) to minimize the performance index.

The parameters of the helicopter model are determined through series of experiments. If we want to

identify the main parameters of the motor, the input signal u1 is changing, while the input signal u2 is kept

constant (i.e., u2 ¼ 0). During that procedure, a horizontal axis (i.e., angle w) must be artificially fixed by

tightening the screw, i.e., by physical fixation, were the screw is located on the helicopter body. For the

evolution of these parameters a simple GA was used [24]. Taking into account the known value of the time

constant of the main motor (given by manufacturer of the motor, T1 ¼ 0.1 s), the input u2 ¼ 0 and the

physical stabilization of the horizontal axis ( _w ¼ 0), then the values of the remaining parameters a1, b1, Bc,

tG, I are to be determined. All of the above coefficients are encoded in a binary chromosome, where each

coefficient was represented using a different number of bits (Figure 5). Number of bits depends on the range

of the parameters and the size of the quantization steps.

Number of bits written in chromosome for this case is 96 with a quantization step of 1026, with the

length of the individual bits: m ¼ 17, p ¼ 16, r ¼ 20, s ¼ 15, t ¼ 26.

Figure 4. Block diagram of identification structure.


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A binary number is decoded in real by using equation:

ka ¼ kmin þ b

ð2n 2 1Þ kmax 2 kminð Þ ð10Þ

where kmin and kmax represent upper and lower limits of the coefficient values ka, n is the number of bits and

b is a binary number written in following way:

b ¼Xn21

i¼0

Bi2i ð11Þ

The binary representation (11) is converting into a potential solution in the interval [kmin, kmax] using

(10). In this case, the evolution is done on the basis of differences between a step response y(k) and the

simulated response yðkÞ to the set inputs. At any time, an error of response of the real system compared to

the simulated response of the system is computed as:

eiðkÞ ¼ yiðkÞ2 yiðkÞ

where the criterion J is:

J ¼XN

i¼1

eij j

In order to evaluate the fitness of the individual it is necessary to run the simulation of the helicopter

model (Figure 3.). N is number of point of experiment and i is current point. It is important to emphasize

that the model obtained using the GA can be used for the synthesis of various controllers on the simulation

model, which will be transferred to the physical helicopter model.

The proposed GA has the following parameter values: population size: 50, type of selection: roulette

wheel, chromosome length: 96 bit [a1 ¼ 17, b1 ¼ 16, Bc ¼ 20, tG ¼ 15, I ¼ 26], quantization step size:

1026, crossover probability: 0.75, probability of mutations: 0.1, Fitness: 10000-J. The diagram of the

evolution process is shown in Figure 6. This evolution yielded the following values for coefficients:

a1 ¼ 0.1165, b1 ¼ 0.062, Bc ¼ 0.08, tG ¼ 0.071, I ¼ 184.

To determine the correlation of the tail motor voltage (u2) and the azimuth angle (w), the above

described procedure was used. Since there is data on the time constants of the tail motor (T2 ¼ 0.25 s)

voltage u2 changes while voltage on u1 is constant (u1 ¼ const). So using the GA is necessary to determine

the coefficients a2, b2, Bw, Ic. Parameters obtained using described genetic algorithm are: a2 ¼ 0.268,

b2 ¼ 0.0408, Bw ¼ 0.04, Ic ¼ 494.3

To investigate an influence of the main motor voltage u1 on the azimuth angle w it is necessary to

determine the unknown parameters a3 and b3. In order to do this, voltage u2 was held constant, while

voltage u1 was changing. Parameters obtained using GA are: a3 ¼ 0.1959, b3 ¼ 0.0202.

a1 I

100.........01

m bits p bits r bits s bits b bits

001.........11 101.........10 011.........00 110.........10

b1 By tG

Figure 5. Chromosome structure.


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For determining the influence of the tail motor voltage motor u2 on the elevation angle w (Figure 3) it is

necessary to find unknown parameter kG. In this process both voltages were changing. Parameter obtained

using GA is kG ¼ 0.3185.

The quality of the identification procedure performed will be analyzed in Section 5.

4. FUZZY LOGIC CONTROLLERS DESIGN

This section considers design procedures of Mamdani type fuzzy logic controllers for the elevation and

azimuth angles controls.

4.1 Fuzzy Elevation Controller

This controller has three input and one output variables. The inputs of the elevation fuzzy controller are:

referent elevation angle value (referent elevation (cd)), elevation angle error (elevation error (ec)) and

change elevation angle error (error derivative (dec)). The output is control output (u2).

The motivation to design fuzzy logic controllers for elevation and azimuth controls lies in the

improvement of control performance achieved by PID controllers in [2]. These PID controllers exhibit a

poor control performance, such as an overshoot and undershoot due to a referent operating point changing.

We have determined the fuzzy rules based on the existing PID controllers with aim to improve the control

performance. The fuzzy rules were obtained through many simulations and experiments.

In the case of fuzzy elevation controller the following fuzzy rules are:

For large elevation error values obtained rules are:

1. IF ec is big and negative THEN u2 is big and negative

2. IF ec is big and positive THEN u2 is big and negative

Using similar observations the next fuzzy rules are adopted for middle and small errors:

3. IF ec is middle and negative THEN u2 is middle and negative

4. IF ec is middle and positive THEN u2 is middle and positive

5. IF ec is small and negative THEN u2 is small and negative

6. IF ec is small and positive THEN u2 is small and positive

0 50 100 1508.4

8.6

8.8

9

9.2

9.4

9.6x 104

Generation

Fit

nes

s

Figure 6. Evolution process.


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If there is no error between the actual and the reference response (absolute value of error is less than 0.5

degrees) then the following rule is active:

7. IF ec is zero THEN control output is zero

To avoid overshoot and undershoot we have introduced next rules:

8. IF ec is negative and dec is negative THEN u2 is negative

9. IF ec is positive and dec is negative THEN u2 is negative

10. IF ec is positive and dec is positive THEN u2 is positive

11. IF ec is negative and dec is positive THEN u2 is positive

These rules are derived from the existing PID controller behaviors and they provide good results in the

elevation angle range [245, 230]. However, for angles above 230 degrees, the control was not

satisfactory and the improvements to the initial rules yielded five regions for the desired input elevation.

The eleven basic rules are repeated for different working ranges with different control output. In this way a

total number of fuzzy rules for elevation control is determined to be 90. In the same manner we created

rules for azimuth controller.

The membership functions of input and output variables are shown in Figures 7–9. Labels for the input

and output membership functions are: NB – negative big, NM – negative medium, NS – negative small,

ZE – zero, PS – positive small, PM – positive medium, PB – positive big, N – negative, P – positive.

As mentioned before, the fuzzy elevation controller uses 90 rules, corresponding to different

combinations of the three input fuzzy sets (Tables I–V). Each of the table is based on different intervals of

–40 –30 –20 –10 0 10 20 30 40

0

0.2

0.4

0.6

0.8

1

(a) (b)

Deg

ree

of m

embe

rshi

p N45-30 N30-20 N20-P10 P10-20 P20-45

–10 –8 –6 –4 –2 0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1

Error derivative[deg]

N P

Referent value [deg]

Deg

ree

of m

embe

rshi

p

Figure 8. Membership functions of referent elevation value (a) and error derivative (b).

–80 –60 –40 –20 0 20 40 60 800

0.2

0.4

0.6

0.8

1

(a) (b)

Elevation error [deg]

Deg

ree

of m

embe

rshi

p NB PB

–20 –15 –10 –5 0 5 10 15 200

0.2

0.4

0.6

0.8

1

Deg

ree

of m

embe

rshi

p NS ZE PSNM PM

NBPB

N P

Elevation error [deg]

Figure 7. Membership functions of elevation error (a) and its representation around zero (b).


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–2 –1.5 –1 –0.5 0 0.5 1 1.5 2

0

0.2

0.4

0.6

0.8

1

Deg

ree

of m

embe

rshi

p ZEP01Neg N01 PozN03 P03N08 N05 P05 P08

Control output[V]–0.4 –0.3 –0.2 –0.1 0 0.1 0.2 0.3 0.40

0.2

0.4

0.6

0.8

1

Control output[V]

Deg

ree

ofm

embe

rshi

p

0N01 P01

N005

N03 P03

P005N002 P002

(a) (b)

Figure 9. Membership functions of control output (a) and its representation around zero (b).

Table I. FAM of fuzzy elevation controller for referent elevation input interval [245, 230]

dec /ec N NB NM NS ZE PS PM PB P

N Neg N05 N01 N005 0 P005 P03 P05 Neg

P P08 N05 N01 N005 0 P005 P03 P05 Poz

Table II. FAM of fuzzy elevation controller for referent elevation input interval [230, 220]


N Neg N05 N01 N005 0 P005 P01 P05 N05

P Poz N05 N01 N005 0 P005 P01 P05 Poz

Table III. FAM of fuzzy elevation controller for referent elevation input interval [220, 10]


N Neg N03 N01 N005 0 P005 P01 P03 N05

P Poz N03 N01 N005 0 P005 P01 P03 P08

Table IV. FAM of fuzzy elevation controller for referent elevation input interval [10, 20]


N Neg N03 N01 N002 0 P002 P01 P03 N05

P Poz N03 N01 N002 0 P002 P01 P03 P05

Table V. FAM of fuzzy elevation controller for referent elevation input interval [20, 45F]

dec /Fec N NB NM NS ZE PS PM PB P

N N08 N01 N005 N002 0 P002 P005 P01 N05

P Poz N01 N005 N002 0 P002 P005 P01 Poz


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the referent elevation input value. The Mamdani type elevation angle controller uses the max-min

implication and centroid defuzzyfication method.

4.2 Fuzzy Azimuth Controller

The fuzzy azimuth controller is also Mamdani type with two inputs and one output. The input variables are:

azimuth angle error (elevation error (ew)) and change azimuth angle error (error derivative (dew)).

The output is control output (u1). The membership functions of input and output variables are shown in

Figures 10 and 11. The FAM rules are given in Table VI. The properties of this controller are the same as

the fuzzy elevation controller.

5. SIMULATION AND EXPERIMENTAL RESULTS

The experimental validation of the identification procedure performed in Section 3 will be done in the

subsection 5.1. In subsection 5.2 both simulation and experimental results of the fuzzy elevation and

azimuth controls will be presented.

–10 –5 0 5 10

0

0.2

0.4

0.6

0.8

1

Error derivative[deg]

ZEN P

Deg

ree

of m

embe

rshi

p

–2 –1.5 –1 –0.5 0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

Deg

ree

of m

embe

rshi

p ZENeg N01 P01 PozN03 P03N05 P05

Control output[V]

Figure 11. Membership functions of error derivative (a) and control output (b).

Table VI. FAM of azimuth fuzzy controller for referent azimuth input interval [2135, 135]

dew /ew N NB NM NS ZE PS PM PB P

P Poz Bneg N05 N03 ZE P03 P05 Poz Poz

N Neg Bneg N05 N03 ZE P03 P05 Poz Neg

–300 –200 –100 0 100 200 300

0

0.2

0.4

0.6

0.8

1

Deg

ree

ofm

embe

rshi

p

NB PB

Azimuth error [deg]–20 –15 –10 –5 0 5 10 15 20

0

0.2

0.4

0.6

0.8

1

Deg

ree

of m

embe

rshi

p

NS ZE PSNM PM

N P

Azimuth error [deg]

NB PB

Figure 10. Membership functions of azimuth error (a) and its representation around zero (b).


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5.1 Validation of the Helicopter Model Obtained by Identification

The quality of the identification procedure performed is tested through comparisons of the simulation

model to the real (experimental) helicopter model. The time responses of elevation angle of simulated and

real models are shown in Figure 12a, where the input voltage was slowly changing from value 0 to 0.6

[MU].

From the results shown in Figure 12a it can be concluded that there is almost no change in the elevation

angle response in the range of [0, 0.47] [MU]. When an input voltage of the main motor exceeds value of

0.6 [MU], the effect of helicopter crashing occurs. This follows from the fact that the helicopter is naturally

unstable system and there is no possibility for feed-forward control.

The elevation angle step responses of both simulated and real helicopter models are depicted in

Figure 12b. The voltage of the main motor (input signal) is u1 ¼ 0.53 [MU]. This comparison gives good

matching of simulated and real models.

The azimuth angle responses are shown in Figure 13a. These results are obtained when the tail motor

voltage u2 takes the constant value of 0.15 [MU] and the main motor voltage u1 is changing as a slow

ramp. Assuming that a horizontal axis of the helicopter is naturally unstable with respect to voltage u2, then

the validation of tail motor voltage (u2) and azimuth angle (w) correlation requires constant voltage u1 and

voltage u2 step change. Azimuth angle step responses on voltage u2 are shown in Figure 13b.

Shapes of the main and tail motors voltages signals u1 and u2 used for investigation of their

simultaneous influence on the azimuth angle are shown in Figure 14a. The azimuth angle responses on the

mentioned excitations are depicted in Figure 14b.

0.45 0.5 0.55 0.6

–40

–20

0

20

40

Voltage on main motor u1 [MU]

Ele

vatio

nang

le[d

eg]

ExperimentSimulation

0 5 10 15 20–50

–40

–30

–20

–10

0

Time [s]

Ele

vatio

nang

le[d

eg]

(b)(a)


Figure 12. Elevation angle dependence on main motor voltage (a) and validation of elevation angle response on voltage u1 excitation

(step signal) (b).

0 0.1 0.2 0.3 0.4–150

–100

–50

0

50

100

150

Voltage on main motor u1 [MU]

Azi

mut

hang

le[d

eg]

(a) (b)

0 20 40 60 80 100 120–150

–100

–50

0

50

100

150

Time [s]

Azi

mut

h an

gle

[deg

]

ExperimentSimulation Experiment

Simulation

Figure 13. Dependence of azimuth angle on input voltage u1 changing (a) and azimuth angle step responses on voltage u2 input

excitation (b).


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Simulation and experimental results illustrated in Figures 12–14 justify the conclusion that model

obtained by identification with simple GA can be successfully used for further research in synthesis of

various classes of controllers. The controllers obtained in this manner can be transferred on real

(experimental) models which reduce the time for controllers synthesis and avoids possible defects arising

from working with the physical model.

5.2 Fuzzy Logic Control of Helicopter Model

In this subsection we investigate the effectiveness of the proposed fuzzy control system of elevation and

azimuth angles on the helicopter model HUMUSOFT CE 150 (Figure 15). As the user communicates with

the system via Matlab Real Time Toolbox interface, all input/output signals are scaled into the

interval ,21,þ1., where value ”1” is called Machine Unit (MU). In the next two subsections, simulation

and experimental results of the proposed fuzzy logic controllers are given respectively.

5.2.1 Simulation Results

Simulation results of the fuzzy logic control obtained using the helicopter model (Figure 3) are shown in

Figure 16. Azimuth and elevation angle responses are smoothed without oscillations. There is small

0 10 20 30 40 50 60 700

0.2

0.4

0.6

0.8

Time [s]

Vol

tage

[MU

]

(a) (b)

0 20 40 60

–100

0

100

Time [s]

Azi

mut

hang

le[d

eg]U1

U2


Figure 14. Shapes of voltages u1 and u2 for azimuth angle validation (a) and azimuth responses for simultaneous change of voltages

u1 and u2 (b).

Figure 15. Laboratory model of helicopter (HUMUSOFT CE 150).


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overshoot in the elevation angle response. The azimuth and elevation angle errors were not exceeding a one

degree (between 0.5 and 1 degree). Finally, simulation results indicate the good control performance of the

proposed control system.

5.2.2 Experimental Results

The experiments were performed using the laboratory helicopter model Humusoft CE 150 (Figure 15).

The fuzzy logic based system for real-time control of helicopter is shown in Figure 17.

The xPC Target Toolbox was used to perform the experiments in real-time with a stand-alone

computer. The helicopter is connecting to PC compatible computer with MF 624 multifunction I/O card.

The MF 624 contains 8 channel fast 14 bit A/D converter with simultaneous sample/hold circuit, 8

independent 14 bit D/A converters, 8 bit digital input port and 8 bit digital output port, 4 quadrature encoder

inputs with single-ended or differential interface and 5 timers/counters. The card is designed for standard

data acquisition and control applications and optimized for use with Real Time Toolbox for Simulinkw.

MF 624 features fully 32 bit architecture for fast throughput.

The experimental results demonstrate the effectiveness of the proposed control system for real-time

application. The strong cross-coupling effects between two axes (azimuth and elevation) are considered as

follows. The influence of tail motor voltage u2 changing on elevation and azimuth angles with the constant

main motor voltage u1 (u1 ¼ 0.48 MU) in the open-loop, uncontrolled system is depicted in Figure 18a.

There are significant oscillations in both angles responses when voltage u2 changes. After the oscillation

period, the elevation angle tends to obtain the previous value. The similar effects occur (Figure 18b) when

the voltage u1 is changed while the voltage u2 is kept constant (u2 ¼ 0.21 MU). However, an influence of

0 50 100 150–50

–40

–30

–20

–10

0(a) (b)

Time [s]

Ele

vatio

n an

gle

[deg

]

0 50 100 150 200–120

–100

–80

–60

–40

–20

0

Time [s]

Azi

mut

h an

gle

[deg

]

DesiredActual

DesiredActual

Figure 16. Elevation and azimuth angle responses on complex input excitations.

Ref.Input ,MF 624

cardPWMdrives

DCmotors

32-bit words Encoders

Computer

Matlab/Simulink

bit/rad

Helicopter model

Interface

MF 624card

RTWorkshop

FuzzyController

xPCTarget

Helicopterbody

Load

Figure 17. Block diagram of the proposed real-time control system for the helicopter model.


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elevation angle is stronger and consequently the azimuth angle significantly deviates from its earlier value,

i.e., value before the input voltage u1 jump.

The experimental evaluation of the proposed fuzzy logic controllers are performed through

comparisons with previously designed PID controllers [12]. The step responses of both elevation and

0 50 100 150–200

0

200

400

Time [s]

–40

–20

0

Time [s]

0.15

0.2

0.25

(a) (b)

Time [s]

0 50 100 150–200

0

200

Time [s]

Time [s]

–40

–20

0

0.4

0.6

0.8

Azi

mut

h [d

eg]

Ele

vatio

n [d

eg]

Vot

ageu

2 [V

]

Azi

mut

h [d

eg]

Ele

vatio

n [d

eg]

Vot

ageu

2 [V

]

0 50 100 150

0 50 100 150Time [s]

0 50 100 150

0 50 100 150

Figure 18. The influence of azimuth angle on elevation angle when voltage u2 acts on helicopter model with u1 ¼ const. (u1 ¼ 0.48

MU) (a) and the influence of elevation angle on azimuth angle when voltage u1 acts on helicopter model with u2 ¼ const. (u2 ¼ 0.21

MU) (b).

0 10 20 30 40 50 60

–40

–20

0

20(a) (b)

Time [s]

Ele

vatio

n an

gle

[deg

]

0

0.5

1

1.5

2

Time [s]

Vol

tage

[MU

]

DesiredFuzzyPID

PIDFuzzy

0 10 20 30 40 50 60

Figure 19. Step responses of PID and fuzzy elevation control systems (a) and main motor voltage responses during elevation angle

control (b).

0 20 40 60 80

–100

–50

0

(a) (b)

Time [s]

Azi

mut

h an

gle

[deg

]

0

0.1

0.2

0.3

0.4

0.5

Vol

tage

[MU

]

Time [s]0 20 40 60 80

FuzzyDesiredPID

FuzzyPID

Figure 20. Step responses of PID and fuzzy azimuth control systems (a) and main motor voltage responses during azimuth angle

control (b).


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100 200 300 400 500 600–120

–100

–80

–60

–40

–20

0

Time [s]

Azi

mut

h an

gle

[deg

]

FuzzyDesiredPID

Figure 22. Azimuth angle responses under interval of [21208, 08].

0 200 400 600 800 1000 1200

–40

–20

0

20

40

Time [s]

Ele

vatio

n an

gle

[deg

] DesiredFuzzyPID

Figure 21. Elevation desired angle tracking in wide region (1808).

0 50 100 150 200 250 300 350 400 450

–40

–30

–20

–10

0

Time [s]

Ele

vatio

n [d

eg]

–100

–50

0

50

100

Azi

mut

h [d

eg]

0 50 100 150 200 250 300 350 400 450

Time [s]

Desired

Actual

Actual

Desired

Figure 23. Simultaneous fuzzy controls of both azimuth and elevation angles.


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azimuth angles are shown in Figures 19a and 20a. Better tracking performance is achieved by using fuzzy

logic controllers with significantly smaller voltage values of the main motors and their variations during a

transition process (Figures 19b and 20b), especially in elevation angle control.

The superiority of the proposed fuzzy elevation and azimuth controllers in comparison with PID

controllers has illustrated in cases of a wide region of set points changing with independent real-time

elevation and azimuth controls (Figures 21 and 22). The fuzzy controllers exhibit good control performance

when referent values (set-points) rapidly change. These are represented by smaller oscillations and

overshot/undershoot during transient period with small settling times. In referent literature some authors

verified the effectiveness and robustness of their elevation and azimuth controllers only in simulation

mode [3], [13], [16]–[18], [20]–[22]. There are several papers which considered experimental

verification of proposed helicopter controllers, but within smaller azimuth and elevation angle intervals

[10], [14], [19], [23]. Our fuzzy elevation and azimuth controllers are tested in significant larger interval of

elevation and azimuth angles ([2120, 0] and [245, 45]) with their faster changing in experimental mode

(complex excitations). Particular advantages of the proposed fuzzy controllers are effective and satisfactory

simultaneous controls of both elevation and azimuth angles (Figure 23) with strong cross-coupling effects

illustrated in Figure 18.

6. CONCLUSION

The identification and control of physical helicopter model based on soft computing methodologies are

addressed in this paper. Identification process required the determination of fourteen unknown parameters

in nonlinear, cross-coupled and complex helicopter system. Due to complexities of the considered

helicopter system, a genetic algorithm is used to determine those parameters. The complete design

procedure of fuzzy elevation and azimuth controllers based on identified helicopter model are considered

and performed. The main objectives in control design are to reduce the cross-coupling dynamics effects and

nonlinearity terms acting on the control performance, especially during simultaneous control of both

elevation and azimuth angles. The effectiveness and robustness of the proposed fuzzy elevation and

azimuth controllers are verified in both simulation and experimental modes within a wide region of set

points changing during a long time flight. The superiority of fuzzy controllers is demonstrated through

comparison with existing PID controllers.

Topics of further research include the consideration of external disturbances acting on the control

performance, design of disturbance observers (especially fuzzy observers) and rigorous stability

analysis.

NOTES ON CONTRIBUTORSJ. Velagic received his M.Sc. degree in 1999 from the Faculty of Electrical Engineering and Computing,

University of Zagreb and his Ph.D. degree from the Faculty of Electrical Engineering, University of

Sarajevo, in 2005. From 2006 to 2009 he was an Assistant Professor with the Faculty of Electrical

Engineering, University of Sarajevo. He is currently an Associate Professor at the same faculty. His

research interests include intelligent control, mobile robotics, mechatronics, marine systems, distributed

control systems and adaptive and robust control. Prof. Velagic is a member of IEEE Control System, IEEE

Robotics and Automation and IEEE Systems, Man and Cybernetics Societies.


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N. Osmic received his B.Sc. degree in electrical engineering in 2003 and his M.A.Sc. degree in electrical

engineering in 2009 from University of Sarajevo, Sarajevo, Bosnia and Herzegovina, where he is

currently working like teaching assistant. He is currently a Ph.D. student. His research interests include

adaptive process control, applications of modern control, Fuzzy logic and intelligent control.

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[3] Karer, G., & Zupancic, B. (2006). Modelling and identification of a laboratory helicopter. Proceedings of 5th mathmod

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[4] Beyer, H. G. (2001). The theory of evolution strategies. Berlin: Springer Verlag.

[5] Tahersima, H., & Fatehi, A. (2008). Nonlinear identification and mimo control of a laboratory helicopter using genetic algorithm.

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[13] Czyba, R., & Serafin, M. (2010). Application of higher order derivatives to helicopter model control. Mechatronic systems,

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[14] Nazarzehi, V., Fatehi, A., & Zamanian, M. (December 2010). Investigation of the performance of multiple modeling and control

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fuzzy-genetic identification and control stuctures for nonlinear helicopter model

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