Abstract—This paper presents a design of fuzzy logic control for 2DOF laboratory helicopter model (Humusoft CE 150) which represents a nonlinear and highly cross-coupled system. The controller is composed of two fuzzy logic controllers for azimuth and elevation controls. 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 quality 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.

I. INTRODUCTION HE helicopter control is a complicated and challenging task. Helicopter is inherently unstable, very nonlinear

and highly cross-coupled system. Also, the main problem with helicopter control is that a helicopter inherently a poorly damped MIMO system. Helicopter control requires the ability to produce moments and forces on the helicopter for changing the helicopter’s velocity, position and orientation and producing its equilibrium states [1].

The problem of helicopter control has received much attention and especially during the last two decade, its nonlinear version has been intensively developed [2]-[4]. The usage of the traditional PI, PD and PID is not satisfied because the helicopter parameters very dependent on the operating point. 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 is the cross-couplings of the system. The control performance of those controllers could be improved by using an output tracking based on approximate input-output linearization [3],[5]. 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 [6], a gain scheduling control of helicopter model was implemented. The model is being linearized at different set points along the elevation axis. Also, in [6] a MIMO control design based on Edmunds optimization method has been proposed. This method optimizes the numerators of the controller structure to achieve the desired frequency response of the closed-loop

Manuscript received May 12, 2010. J. Velagic is with the Faculty of Electrical Engineering, Department of

Automatic Control and Electronics, Sarajevo, Bosnia and Herzegovina (phone: +387 33 250 765; fax: +387 33 250 725; e-mail: jasmin.velagic@ etf.unsa.ba).

N. Osmic is with Faculty of Electrical Engineering, Department of Automatic Control and Electronics, Sarajevo, Bosnia and Herzegovina (e-mail: nedim.osmicr@etf.unsa.ba)

system. In that paper the control synthesis using a pole placement method with state observer is performed. Helicopter control design based on µ-synthesis is studied in [7]. Robust control algorithms design by an aggregation method of the state variables are proposed in [8]. 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 [9], [10] uses higher order output derivatives in the feedback loop. In general, linear controllers are designed in the flight envelope operating points [11]

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 fuzzy and neural controllers. The model predictive neural control of a helicopter is proposed in [12]. In [11] a nonlinear optimal control of helicopter using fuzzy gain scheduling is presented. Several fuzzy logic control and neural network control strategies are compared in [13]. The effectiveness of these controllers is verified in simulation modes only.

In our paper the proposed fuzzy controllers are applied to control of the helicopter model, which is treated as a multivariable system with significant cross coupling. We investigate behaviors of these controllers in both simulation and experimental conditions.

The paper is organized as follows. The section II introduces the azimuth and elevation fuzzy control system with descriptions of the main components. In section III the design of proposed fuzzy logic controllers based on Mamdani technique is performed. Simulation and experimental results are provided to verify the practicality of the fuzzy logic control of the laboratory helicopter model in section IV. Section V gives the conclusions.

II. CONTROL SYSTEM DESCRIPTION The main components of the proposed real-time

helicopter control system are shown in Fig. 1. The system is composed of three main components: PC based controller, hardware interface and helicopter model. The fuzzy controllers are designed in the Matlab/Simulink program package. The second component (MF624) represents the multifunctional card for data acquisition and transmission. It

Design and Implementation of Fuzzy Logic Controllers for Helicopter Elevation and Azimuth Controls Jasmin Velagic, Member, IEEE, and Nedim Osmic, Member, IEEE

T

2010 Conference on Control and Fault Tolerant SystemsNice, France, October 6-8, 2010

WeC3.3

978-1-4244-8154-5/10/$26.00 ©2010 IEEE 311

Ref.

Inputs Ψ, φMF 624 card

PWM drives DC motors

32-bit words Encoders

Computer

Matlab/ Simulink

bit/rad

Helicopter model

Interface

MF 624 card

RT Workshop

Fuzzy Controller

xPC Target

Helicopter body

Load

Fig.1. Block diagram of the proposed real-time control system for a laboratory helicopter model.

connects the PC and helicopter system and provides implementation control algorithm from the PC to the helicopter system. The helicopter system contains the DC motors with permanent stator magnets, power amplifiers (PWMs), encoders as sensors and axel gear (represents load). In the following subsections the mentioned components will be described.

A. Helicopter Model In this section a mathematical model of helicopter CE 150

by considering the force balances is presented [14]. Assuming that the helicopter model is a rigid body with

two degrees of freedom, the following output and control vectors are adopted:

T],[ ϕψ=y (1)

Tuu ],[ 21=u (2) where:

ψ - elevation angle (pitch angle), ϕ - azimuth angle (yaw angle), u1, u2 – voltages of main and tail motors.

Elevation dynamics considers the forces in the vertical plane acting on the vertical helicopter body, whose dynamics are given by the following nonlinear equations:

GmfI τττττψ ϕ +−−+=11 &&& (3)

ψτψψτ sinsinsin Gmm mgllF === (4)

ψϕψψϕτ ϕ 2sin21cossin 22 &&& mlml =⋅= (5)

211 1

ωτ ωk= , ψψτ ψψ && BsignCf +=1

(6)

11 for , cos ωϕψωϕτ <<= &&GG k (7)

where: I - moment of inertia around horizontal axis, τ1 - elevation driving torque, ϕτ & - centrifugal torque, τf1 - friction torque (Coulomb and viscous), τm - gravitation torque, τG - gyroscopic torque, ω1 - angular velocity of the main propeller, m - mass, g - gravity, l- distance from z-axis to main rotor, kω1 - constant for the main rotor,

kG - gyroscopic coefficient, Bψ - viscous friction coefficient (around y-axis), Cψ - Coulomb friction coefficient (around y-axis).

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 ϕ, whose dynamics are given by the following nonlinear equations:

rfI τττϕψ −−=22&& (8)

ψψ sinII = , 2222 sin

2ψωτ ω lk= , ϕϕτ ϕϕ && BsignCf −=

2 (9)

where: Iψ - moment of inertia around vertical axis, τ2 - stabilizing motor driving torque, τf2 - friction torque Coulomb and viscous, τr - main rotor reaction torque, kω2 - constant for the tail rotor, ω2 - angular velocity of the tail rotor, Bψ - viscous friction coefficient (around z-axis), Cψ - Coulomb friction coefficient (around z-axis).

B. DC Motor and Propeller Dynamics Modeling The propulsion system contains two independently working DC electrical engines. The model of a DC motor dynamics is obtained on the basis of following assumptions: 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 ω in low and ω2 in high rpm (revolutions per minute).

Taking this into account, the equations are following:

pjjjcjjjj BI τωττω −−−=& (10)

)(1jbjj

jj Ku

Ri ω−= (11)

jijj iK=τ , )( jjcj signC ωτ = , 2jpjpjpj j

DB ωωτ += (12)

where: 2,1=j - motor number (1- main, 2- tail), Ij - rotor and propeller moment of inertia, τj - motor torque, τcj - Coulomb friction load torque, τpj - air resistance load torque,

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Bj - viscous-friction coefficient, Kij- torque constant, ij - armature current, Rj - armature resistance, uj - control input voltage, Kbj - back-emf constant, Cj - Coulomb friction coefficient,

Bpj - air resistance coefficient (laminar flow), Dpj - air resistance coefficient (turbulent flow). Block diagram of nonlinear dynamics of a complete

system based on equations (1)–(12) is shown in Fig.2.

Fig. 2. Block diagram of a complete helicopter system dynamics.

We determined values of unknown parameters in Fig. 2. using a genetic algorithm [15]. These values are: a1=0.1165, b1=0.062, Bψ=0.08, τG =0.071, I=184, a2=0.268, b2=0.0408, Bphi=0.04, Iψ=494.3, a3=0.1959, b3=0.0202, kG= 0.3185, T1=0.1 s, T2=0.25 s.

C. Control Interface The MF 624 multifunction I/O card is designed for

connecting PC compatible computers to real world signals. 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 Simulink®. MF 624 features fully 32 bit architecture for fast throughput.

III. FUZZY LOGIC CONTROLLERS DESIGN This section considers design procedures of Mamdani

fuzzy logic controllers for elevation and azimuth angles controls.

A. 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 (ref)), elevation angle error (elevation error (e)) and change elevation angle error (error derivative (de)). The output is control output (u).

The membership functions of input and output variables are shown in Figs. 3-8.

-80 -60 -40 -20 0 20 40 60 800

0.2

0.4

0.6

0.8

1

Elevation error [deg]

Deg

ree

of m

embe

rshi

p

NB PB

Fig. 3. Membership functions of the elevation error input.

-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

NB

PB

N P

Elevation error

Fig. 4. Membership functions of elevation error input around zero point.

-40 -30 -20 -10 0 10 20 30 40

0

0.2

0.4

0.6

0.8

1

Deg

ree

of m

embe

rshi

p

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

Referent value [deg]

Fig. 5. Membership functions of the referent value input.

-10 -8 -6 -4 -2 0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1

Error derivative [deg]

Deg

ree

of m

embe

rshi

p

N P

Fig. 6. Membership functions of the error derivative input.

313

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

0

0.2

0.4

0.6

0.8

1 D

egre

e of

mem

bers

hip

ZENeg N01 P01 PozN03 P03 N08 N05 P05 P08

Control output [V]

Fig. 7. Membership functions of the control output variable.

-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

of m

embe

rshi

p

0N01 P01

N005

N03 P03

P005

N002 P002

Fig. 8. Membership functions of control output variable around zero point.

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.

The main part of fuzzy controller is called the fuzzy rulebase or fuzzy-associative-memory (FAM) rules, which contains the input/output relationships that define the control strategy. The fuzzy elevation controller uses 90 rules, corresponding to different combinations of the three input fuzzy sets (Table I-V). Each FAM rule represents ambiguous expert knowledge or learned input/output transformations. The FAM rules of the fuzzy elevation controller were obtained under different simulation and experiment conditions based on the PID controller behaviors. The main objective is to improve its control performance, such as an overshoot, undershoot and oscillations. Each of the table is based on different intervals of the referent value input.

TABLE I

FAM OF ELEVATION CONTROLLER FOR REF. INPUT INTERVAL [-45,-30]

TABLE II

FAM OF ELEVATION CONTROLLER FOR REF. INPUT INTERVAL [-30,-20] de/e N NB NM NS ZE PS PM PB P N Neg N05 N01 N005 0 P005 P01 P05 N05 P Poz N05 N01 N005 0 P005 P01 P05 Poz

TABLE III FAM OF ELEVATION CONTROLLER FOR REF. INPUT INTERVAL [-20,10]

de/e N NB NM NS ZE PS PM PB P N Neg N03 N01 N005 0 P005 P01 P03 N05 P Poz N03 N01 N005 0 P005 P01 P03 P08

TABLE IV

FAM OF ELEVATION CONTROLLER FOR REF. INPUT INTERVAL [10,20] de/e N NB NM NS ZE PS PM PB P N Neg N03 N01 N002 0 P002 P01 P03 N05 P Poz N03 N01 N002 0 P002 P01 P03 P05

TABLE V

FAM OF ELEVATION CONTROLLER FOR REF. INPUT INTERVAL [20,45] de/e 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

Properties of Mamdani type elevation angle controller are

given in Table VI.

TABLE VI FIS (FUZZY INFERENCE SYSTEM) PARAMETERS OF ELEVATION

CONTROLLER FIS TYPE Mamdani AND method min OR method max Implication min Aggregation max Defuzzyfication centroid

B. Fuzzy Azimuth Controller The fuzzy azimuth controller has two inputs and one

output. The input variables are: azimuth angle error (azimuth error) and change azimuth angle error (error derivative). The output is control output (u). The membership functions of input and output variables are shown in Figs. 9-11.

-300 -200 -100 0 100 200 300

0

0.2

0.4

0.6

0.8

1

Deg

ree

of m

embe

rshi

p

NB PB

Azimuth error [deg]

Fig. 9. Membership functions of the azimuth error input.

-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 PS NM PM

N P

Azimuth error [deg]

NB PB

Fig. 10. Membership functions of azimuth error input around zero point.

de/e 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

314

-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

ZENeg N01 P01 PozN03 P03 N05 P05

Control output [V] Fig. 11. Membership functions of control output variable.

The membership functions of the error derivative input variable are the same as in case of fuzzy elevation controller.

The FAM rules are given in Table VII. The FIS properties of this controller are given in Table VI.

TABLE VII

FAM OF AZIMUTH CONTROLLER FOR REF. INPUT INTERVAL [-135, 135] de/e 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

IV. SIMULATION AND EXPERIMENTAL RESULTS In this section, the simulation and experimental results of

the helicopter model HUMUSOFT CE 150 (Fig. 12) are presented. As the user communicates with the system via Matlab Real Time Toolbox interface, all input/output signals are scaled into the interval <-1,+1>, where value ”1” is called Machine Unit (MU) and such a signal has no physical dimension.

A. Simulation Results In this subsection we investigate the effectiveness of the

proposed fuzzy logic control system. Simulation results obtained using the helicopter models (Fig. 2) are shown in Figs. 13 and 14. Azimuth and elevation angle responses are smoothed without oscillations. There is small 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.

Fig. 12. Laboratory model of helicopter (HUMUSOFT CE 150).

0 20 40 60 80 100 120 140 160-45

-40

-35

-30

-25

-20

-15

-10

-5

Time [s]

Elev

atio

n an

gle

[deg

]

DesiredActual

Fig. 13. Elevation angle response on a complex input excitation.

0 50 100 150 200-120

-100

-80

-60

-40

-20

0

Time [s]

Azi

mut

h an

gle

[deg

]

DesiredActual

Fig. 14. Azimuth angle response on a complex input excitation.

B. Experimental Results The xPC Target Toolbox under Matlab/Simulink was

used to perform the experiments in real-time with a stand-alone computer. The experimental results demonstrate the effectiveness of the proposed control system for real-time applications. The experimental evaluation of the proposed fuzzy logic controllers are performed through comparisons with previous designed PID controllers [6]. The step responses of both elevation and azimuth angles are shown in Figs. 15 and 17. The better tracking performance is achieved by fuzzy logic controllers with significant smaller voltage values of main motors and their variations during a transition process (Figs. 16 and 18), especially in elevation angle control. The superiority of the proposed fuzzy elevation and azimuth controllers in comparisons to PID controllers are illustrated in cases of a wide region of set points changing (Figs. 19 and 20).

0 10 20 30 40 50 60

-40

-30

-20

-10

0

10

20

30

Time [s]

Ele

vatio

n an

gle

[deg

]

DesiredFuzzyPID

Fig. 15. Step responses of PID and fuzzy elevation control systems.

315

0 10 20 30 40 50 600

0.5

1

1.5

2

Time [s]

Vol

tage

[MU

]

PIDFuzzy

Fig. 16. Main motor voltage responses during elevation angle control.

0 10 20 30 40 50 60 70 80

-100

-80

-60

-40

-20

0

20

Time [s]

Azi

mut

h an

gle

[deg

]

FuzzyDesiredPID

Fig. 17. Step responses of PID and fuzzy azimuth control systems.

0 10 20 30 40 50 60 70 800

0.1

0.2

0.3

0.4

0.5

Time [s]

Vol

tage

[MU

]

FuzzyPID

Fig. 18. Main motor voltage responses during azimuth angle control.

0 100 200 300 400 500 600-40-30

-20-10

010

2030

4050

Time [s]

Ele

vatio

n an

gle

[deg

]

DesiredFuzzyPID

Fig. 19. Elevation angle responses under interval of [-45°, 45°].

700 800 900 1000 11000

20

40

60

80

100

120

Time [s]

Azi

mut

h an

gle

[deg

]

FuzzyDesiredPID

Fig. 20. Azimuth angle responses under interval of [0°, 120°].

V. CONCLUSION This paper focuses on design and implementation of fuzzy

elevation and azimuth controllers for real-time control of 2DOF laboratory helicopter model. The fuzzy controllers are chosen due to nonlinearity and highly cross-coupled dynamics of the helicopter model. Mamdani type fuzzy controllers are used in both elevation and azimuth control systems. Simulation and experimental results are given to demonstrate the effectiveness and robustness of the proposed fuzzy logic controlled system.

REFERENCES [1] R. W. Prouty, Helicopter Performance, Stability, and Control, Krieger

Publishing Co., Inc., 1995. [2] A. Isidori and C. I. Byrnes, “Output regulation of nonlinear systems,”

IEEE Transactions on Automatic Control, vol. 35, pp. 131-140, 1990. [3] J. K. Yi, Y. Ma, and S. S. Sastry, “Nonlinear Control Of A Helicopter

Based Unmanned Aerial Vehicle Model,” [4] T. J. Koo and S. Sastry, “Output tracking control design of a

helicopter model based on approximate linearization,” in Proc. 37th IEEE Conference on Decision and Control, Tampa, FL, 1998, pp. 3635-3640.

[5] C. Tomlin, J. Lygeros, L. Benvenuti, and S. Sastry, “Output tracking for a non-minimum phase dynamic CTOL aircraft model,” in Proc. 1995 IEEE Conference in Decision and Control, Kobe, Japan, 1996, pp. 1867–1872.

[6] U. Legat, R. Gajšek, and M. Gašperin, “Simulation and Control of a helicopter pilot plane,” in Proc. 11th International Cultural and Academic Meeting of. Engineering Students,Tel Aviv, 2005.

[7] H. Shim, J. Koo, F. Hoffmann, and S. Sastry, “A comprehensive of a control design for an autonomous helicopter,” in Proc. 37th IEEE Conference on Decision and Control, Tampa, FL, 1998, pp. 3653-3658.

[8] T. Kudela and R. Wagnerova, “Position control with robust algorithms“, Sbornik vedecksch prací Visoke školy banske - Technicke univerzity Ostrava, paper no. 1542, vol. 52, no. 2, 2006.

[9] V. D. Yurkevich, Design of Nonlinear Control Systems with the Highest Derivative in Feedback. World Scientific Publishing, 2004.

[10] R. Czyba and M. Serafin, “Robust Regulation of Helicopter Model Based on the Highest Derivative in Feedback,” in Proc. Advanced Intelligent Mecahtronics, Zurich, 2007, pp. 1-6.

[11] Y. Bai, H. Zhuang, and D. Wang, “Fuzzy Logic for Flight Control I: Nonlinear Optimal Control of Helicopter Using Fuzzy Gain Scheduling,” in book: Advanced Fuzzy Logic Technologies in Industrial Applications, London: Springer, 2006, pp. 207-221.

[12] E.A. Wan. and A.A. Bogdanov, “Model predictive neural control with applications to a 6 DOF helicopter model,” in Proc. 2001 American Control Conference, Arlington, Virginia, 2001, pp. 488-493.

[13] D. McLean, and H. Matsuda, “Helicopter station keeping: comparing LQR, fuzzy logic and neural-net controllers,” Engineering Applications of Artificial Intelligence, vol.11, pp. 411-418, 1998.

[14] User Manual, CE150 Helicopter model. Praha: HUMUSOFT s.r.o., 2008.

[15] N. Osmic, J. Velagic, and S. Konjicija, “Genetic Algorithm Based Identification of a Nonlinear 2DOF Helicopter Model,” in Proc. IEEE Mediterranean Conference on Control and Automation (MED10), Marrakech, Morocco, 2010, pp. 333-338.

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