Mathematical Modeling and Experimental Identification … · International Journal of Basic &...

International Journal of Basic & Applied Sciences IJBAS-IJENS Vol: 12 No: 02 88

123002-7474 IJBAS-IJENS © April 2012 IJENS I J E N S

Mathematical Modeling and Experimental Identification of Micro Coaxial Helicopter Dynamics

Huynh Phuoc Thien1, Taufiq Mulyanto1, Hari Muhammad1, and Shinji Suzuki2

1Faculty of Mechanical and Aerospace Engineering, Institut Teknologi Bandung, Bandung, Indonesia

2School of Engineering, The University of Tokyo, Tokyo, Japan

This paper deals with the problem of development of the mathematical model of a micro coaxial helicopter using hybrid method of analytical and experimental approach. An analytical mathematical model of micro coaxial helicopter has been derived with the consideration of dynamics of rotating parts to the rigid body dynamics. Pre-flight simulation was carried out based on the derived mathematical model to simulate the flight test scenarios. A sensory system was developed and installed onboard to capture the helicopter state during the flight test for the purpose of identifying parameters. Two steps system identification based on flight test data was used to estimate the parameters in the mathematical model. The Extended Kalman Filter was applied to estimate the states of the helicopter. Subsequently, based on measured flight test data, Total Least Square method was used to estimate the aerodynamic parameters in the linearized model of force and moment coefficients in the longitudinal mode. As a result, a mathematical model of micro coaxial helicopter with adequate parameters has successful been obtained. The verifications show that the estimated model of force and moment coefficients fit well the corresponding measured quantities in both phase and amplitude.

Index Terms— Micro Coaxial Helicopter, Mathematical Modeling, Sensory System Development, Flight Test, System Identification

NOMENCLATURE

Parameter Definition

, ,x y z Helicopter position in inertial x, y, z direction

, ,φ θ ψ Roll, pitch and yaw attitude respect to inertial axis

, ,u v w Longitudinal, lateral & vertical velocity in body axis

, ,p q r Roll, pitch and yaw rate measured in body axis

,lon latδ δ Longitudinal and lateral tilt of swash-plate

,u lω ω Rotational speed of upper and lower rotor

,u lT T Thrust generated by upper and lower rotor

,u lQ Q Torque caused by upper, lower rotor

β Rotor disc tilt angle

, ,

,u l

u l

α αβ β

Rotor’s longitudinal, lateral flapping angle

m Total mass of the helicopter

R Rotor radius

Ixx, Iyy, Izz Inertial moment of helicopter

Ju, , Jl, Jf Inertial moment of rotor and fly-bar

,u l Subscript of upper rotor and lower rotor

Vi Induced velocity from upper rotor

V Translational speed of the helicopter

Afus Project area of fuselage

Dfus, CDfus Drag, and drag coefficient of fuselage

I. INTRODUCTION

icro coaxial helicopteroffers an excellent tool to support missions in indoor environment. A helicopter with

certain onboard intelligent can be used to perform the tasks that may be dangerous for human or tasks in which human presence is not possible. In order to operate in indoor environments with limited space and rich of obstacles of different size and shapes, the helicopter should be inherently stable to simplify the control. Control system should be designed and implemented to autonomously control the helicopter. Good understanding of the vehicle model should be obtained before the controller design is started. Hence, development of mathematical model of the MAV helicopter that is sufficiently accurate but simple enough was conducted.

There are several approaches to acquire the mathematical model of the micro coaxial helicopter. In general, they can be classified into three approaches, consisted of physical approach, system identification approach, and hybrid approach. In the first approach, the analytical dynamic modelwill be derived from the laws of mechanics and aerodynamics[1], [2]. Considerable knowledge on flight dynamics is required to obtain the governing equation. The advantage of the analytical model is that the nonlinear dynamic model could cover the entire flight envelop, and the flight test data is only need for the validation of the model. However, first principle model does not produce highly accurate results unless performed with extreme care.

In the second approach, named system identification approach, the dynamic model is identified from flight test data. Theoretically, no prior model is required[3]. In the third approach, the advantages of the analytical approach and system identification approach will be combined. The

M

This research was sponsored by Japan International Cooperation Agency (JICA) under Collaborative Research Program of AUNSeed-Net.

Manuscript received March 7, 2012. Corresponding author: Huynh Phuoc Thien (e-mail: [email protected], [email protected])



mathematical model of the helicopter is preliminary derived by the analytical approach. The parameters in the mathematical model will be determined by direct measurement on the MAV, estimated using CAD model, estimated through experiment on test-bench, or determined through the flight-test-based identification process[4], [5].

By study on the literature of the development of the mathematical model of the micro coaxial helicopter, some gaps have been found. Firstly, most of the researches have concentrated on the MAV coaxial helicopter with the small size (rotor radius < 20 cm). Secondly, although flight test have been conducted to collect data for parameter estimation, there still lacked the standard procedure in carrying out of the flight test for this kind of MAV. Therefore, the research in this paper was aimed to the development of the mathematical model of micro coaxial helicopter in the class of 20-30 cm rotor radius by using the combination of analytical modeling and experimental system identification.

In this paper, the development of appropriate mathematical model of a 25cm radius rotor micro coaxial helicopter will be presented. The main scope will be concentrated on describing the procedure to establish the mathematical model of the helicopter by combining the analytical modeling, pre-flight simulation, flight test, and estimation of parameters based on flight test data.

The paper is managed into 6 sections, started with the current one. In the second section, the formulation of the analytical mathematical model is introduced. The simulation of the flight test scenarios using the derived mathematical model is discussed in section III. In section IV, the issue in obtaining of real flight test data and processing of data will be presented. Section V deals with the process to estimate parameters in the aerodynamic force and moment model using flight test data. The paper ends with conclusions and ideas for future works in section VI.

II. FORMULATION OF THE MATHEMATICAL MODEL OF THE MICRO COAXIAL HELICOPTER

A. Micro Coaxial Helicopter Platform An available commercial micro coaxial helicopter named

Lama 400D was chosen as the platform of the research. The Lama 400D has two sets of rotor in coaxial arrangement. Two electric motors are used to separately drive the two rotors in opposite direction. The lower rotor rotates in the clockwise direction; while the upper rotor rotates in the counter clockwise. On the upper rotor, a fly-bar is attached to rotor shaft, and driven at the same speed as the upper rotor to create passive control through its augmentative input to the rotor cyclic pitch. On the lower rotor, a swash-plate system is used to control the pitch and roll of the helicopter through the mechanical linkages with the servo system. Several modifications have been done to increase payload capacity, and to allow the housing of the instrumentation system. Main specification of the helicopter is described inTABLE I; while illustration of helicopter platform and its modified model is

shown inFig. 1.

TABLE I PHYSICAL CHARACTERISTIC OF MICRO COAXIAL HELICOPTER

Characteristics Data

Main rotor radius 25 cm

Total weight 800g

Engine type Electric motor

Distance between rotor 80mm

Fig. 1. Lama 400D and the modified model

The control of the micro coaxial helicopter was done by four control input channels, i.e. the RPM of the upper and lower rotors, and the pitch and roll servos. In detail, simultaneous increase or decrease of the rotor RPM will initiatea vertical flight; while differential variation of RPM of the upper and lower rotors causes a yaw motion of the helicopter. By giving control input into the pitch servo, the swash-plate will be deflected, which leads to the tilting of rotor Tip Path Plane. As a result, a pitching momentwill be generated to activate a pitch motion of the helicopter. In the same manner, a roll motion of micro coaxial helicopter can be achieved by giving command to the roll servo.

B. Nonlinear Mathematical Model of Micro Coaxial Helicopter

The mathematical model of the micro coaxial helicopter was derived under the following assumptions:

−−−− The upper rotor is assumed to rotate in the counter – clockwise direction when viewed from above, and the lower rotoris rotated in the clockwise direction;

−−−− In rigid body model, the two rotors are considered to be hinged directly to the hub. Hence, no hinge offset associates with the rotor flapping. The rotor is then considered to rotate in a disk;

−−−− The air resistance is modeled as simple drag force opposing to the rotation of the two rotors;

−−−− The aerodynamic forces generated by the relative wind or due to ground effect are not considered.

The micro coaxial helicopter is a complicated nonlinear

system with high order dynamics. There are coupling between components, e.g. rotor-fuselage coupling, rotor-fly-bar coupling. In addition, other systems such as swash-plate, electric motor also contribute into the total dynamics. Hence, the rigid body dynamic approach that is typically used for fixed wing aircraft is insufficient to capture the key dynamics of the helicopter.



In order to capture the key dynamics of micro coaxial helicopter, the rotor and fly-bar dynamics will be taken into account besides the rigid body dynamics[6]. Details of these dynamics are presented in following paragraphs.

The rigid body dynamicscan be derived from Newton-Euler equation as:

( )+ Ω× =&mV m V F (1)

( )I I MΩ + Ω × Ω =& & & (2)

where [ ] [ ],= Ω =T TV u v w p q r are the fuselage velocity

and angular rate in the body fixed frame.

[ ],T T

X Y ZF F F F M L M N = = are the vector of the

external force and moment acting on the vehicle. The force equation (1) can be expanded and rearranged as

Xu rv qw F m= − +& (3)

Yv pw ru F m= − +& (4)

Zw qu pv F m= − +& (5)

Expanding equation (2) and neglecting of small multiplication term, i.e. pq, pr, rq, p2, q2, r2, yields

xxp L I=& (6)

yyq M I=& (7)

zzr N I=& (8)

In the body coordinate system, the total force acting on the helicopter consists of thrust force from rotor system Tu, Tl, the aerodynamic drag on fuselage Dfus, and the gravitational force caused by the mass of the helicopter G. The torques acting on helicopter consist of the drag torque from two rotary rotor Qu, Ql, the torque caused by the thrust of rotor system and the torque cause by the gyroscopic effect of the rotors and fly-

bar( )gyroτ . In summary, the total force and moment acting on

the helicoptercan be described as

u l fusF T T D G= + + + (9)

u l u u l l gyroM Q Q d T d T τ= + + × + × + (10)

In which Tu, Tlare the vector of thrust acting on the upper and lower rotors, calculated from the total thrust magnitude and its direction vector.

( ), .Tu u u

u X Y Z u u uT T T T G Tα β = =

(11)

( ), .Tl l l

l X Y Z u u uT T T T G Tα β = =

(12)

In (11) and (12), ( ),u uG α β and ( ),l lG α β are the direction

vector of the upper and lower rotors’ thrust vector,defined fromthe tilted angle of the rotor Tip Path Plane with respect to the body fixed frame.

( )2 2

sin cos1

, sin cos1 sin sin cos cos

u u

u u u u

u u u u

G

α βα β β α

α β α β

− = − −

(13)

( )2 2

sin cos1

, sin cos1 sin sin cos cos

l l

l l l l

l l l l

G

α βα β β α

α β α β

− = − −

(14)

u lT and T are the magnitude of the thrusts on the upper

and lower rotors, defined by 2 2

u T R b T T uu uT C V A C kρ ω= = (15)

2 2l T R b T T ll l

T C V A C kρ ω= = (16)

with 4Tk Rρπ=

The torque vector generated by the rotor system can be calculated as follows

0 0u uQ Q = (17)

0 0l lQ Q = − (18)

where the magnitudes of the torque are defined as 2

u Q Q uuQ C k ω= (19)

2l Q Q ll

Q C k ω= (20)

5Qk Rρπ=

The other components ofthe force and moment inequations(9) and(10)can be expressed by

( ) 21 2 ρ=fus i fus DfusD V A C (21)

TX Y Z

gyro gyro gyro gyroτ τ τ τ =

(22)

( )Xgyro l l u u u fJ J J qτ ω ω ω= − + + (23)

( )Ygyro l l u u u fJ J J pτ ω ω ω= − − (24)

0Zgyroτ = (25)

The flapping angles of the lower rotor and fly-bar in (13) and (14)can be defined from the rotor dynamics as follows [5], [7], [8]

, , ,

l bl lon l

f l f l f l

AKq

βαα δ βτ τ τ

= − + − −& (26)

, , ,

l bl lat l

f l f l f l

K Bpαββ δ α

τ τ τ= − + + −& (27)

,

ff

f fq

αα

τ= − −& (28)

,

ff

f fp

ββ

τ= − −& (29)

The upper rotor flapping motion can be expressed through the relation with the fly-bar by[7]

u q fKα α= (30)

u q fKβ β= (31)



Inthe equations (26), (27), (30), (31)Kb is the ratio of the deflection angle of the swash-plate to the tilted angle of the lower rotor Tip Path Plane. And, Kq, Kpare the ratio of the tilted angle of the fly-bar to the tilted angle of the upper rotor Tip Path Plane with respected to the longitudinal and lateral axes expressed in the helicopter body fixed frame.

By substituting(9)-(25)into(3)-(8),the mathematical model of the MAV coaxial helicopter can be written in term of the translational equation and rotational equations as follows.

−−−− Translational dynamics

2

2 2

2

2 2

sin cos

1 sin sin1sin

sin cos

1 sin sin

u uT T uu

u u

l lT T ll

l l

C k

u rv qw gm

C k

α βωα β

θα βω

α β

− = − − −

+ −

& (32)

2

2 2

2

2 2

sin cos

1 sin sin1cos sin

sin cos

1 sin sin

u uT T uu

u u

l lT T ll

l l

C k

v pw ru gm

C k

β αωα β

θ φβ αω

α β

+ −

= − + + + −

&(33)

2

2 2

2

2 2

2

cos cos

1 sin sin

cos cos1cos cos

1 sin sin

1

2

u uT T uu

u u

l lT T ll

l l

i fus D fus

C k

w qu pv g C km

V A C

α βωα β

α βθ φ ωα β

ρ

− = − + − + − −

−

&(34)

−−−− Rotational dynamics

( )

2

2 2

2

2 2

sin cos

1 sin sin

sin cos1

1 sin sin

u uu T T uu

u u

l ll T T ll

xx l l

l l u u u f

d C k

p d C kI

J J J q

β αωα β

β αωα β

ω ω ω

− − −

= − + − + − + +

& (35)

( )

2

2 2

2

2 2

sin cos

1 sin sin

sin cos1

1 sin sin

u uu T T uu

u u

l ll T T ll

yy l l

l l u u u f

d C k

q d C kI

J J J p

α βωα β

α βωα β

ω ω ω

− − −

= − + − + − −

& (36)

( )2 21Q Q u Q Q lu l

zz

r C k C kI

ω ω= −& (37)

In order to transform the angular velocity and the translational velocity from the body fixed frame to the inertial frame, kinematic equation and navigation equation are used[9]

−−−− Kinematic equation

( )tan sin cosp q rφ θ φ φ= + +& (38)

cos sinq rθ φ φ= −& (39)

sin / cos cos / cosq rψ φ θ φ θ= +& (40)

−−−− Navigation equation

( )( )

cos cos cos sin sin sin cos

cos sin cos sin sin

Ex u v

w

ψ θ ψ θ φ ψ φψ θ φ ψ φ

= + −

+ +

&

(41)

( )( )

sin cos sin sin sin cos cos

sin sin cos cos sin

Ey u v

w

ψ θ ψ θ φ ψ φψ θ φ ψ φ

= + +

+ −

&

(42)

sin cos sin cos cosEz u v wθ θ φ θ φ= − + +& (43)

The equations of motion(26)-(29) and (32)-(43) represent the complete mathematical model of the micro coaxial helicopter. They can berewritten in the form of

( ) ( ) ( )( ) ( )0 0, ;Χ Χ= =&mt f t u t X t X (44)

In (44)the state vector and the input vector can be detailed as follows:

−−−− State vector :, , , , , , , ,

, , , , , , ,

α βα β φ θ ψ

Χ

=

Tl l

f f

u v w p q r

x y z

−−−− Input : , , ,ω ω δ δ= m l u lon latu

The differential equation (44)can beused to simulate the flight test scenarios, see section III. Besides that, based on (44) longitudinal and lateral mathematical modelcould also be derived to govern the estimation of linearized aerodynamic force and moment model, see section V.

III. PRE-FLIGHT SIMULATION OF MICRO COAXIAL HELICOPTER

This section introduces the implementation of the derived mathematical model of the micro coaxial helicopter obtained in section II into the simulation. Pre-simulation will be carried out to simulate the fight test scenarios.

A. Implementation of the Helicopter Mathematical Model into Simulation

The equations of motion of the micro coaxial helicopter expressed in (26)-(43)can be implemented into simulation to simulate the behavior of the helicopter. In order to simulate the observation, the sensor model is added as follows

obs y

obs y

obs z

obs V

obs E h

obs p

obs q

obs r

x x a

y y a

z z a

V V

h z

p p

q q

r r

a a

a a

a a

ηη

ηη

ηη

η

η

= += − += +

= +

= += +

= +

= +

(45)



The schematic diagram for the implementation of the mathematical model of the MAV helicopter is shown in Fig. 2.

Fig. 2. Schematic diagram for implementation of mathematical model of Coaxial Helicopter into simulation

In (45), Vobs, hobs, pobs, qobs, robs, obsxa ,

obsya and obsza are the

observed velocity, observed altitude, observed angular rate and observed acceleration respectively. Vη , hη , ,p qη η , rη ,

, ,x y za a aη η η are the noise model of velocity, altitude, angular

rates and accelerations.

The physical parameter of the helicopter used in the simulation is detailed inTABLE II.

TABLE II

PHYSICAL PARAMETER OF MICRO COAXIAL HELICOPTER

No. Parameter Description Value Unit

1 m Total weight 0.8 [kg]

2 R Main rotor radius 0.25 [m]

3* kT 4Rρπ 1.40E-02 [kg.m.rad]

4* kQ 5Rρπ 3.49E-03 [kg.m.rad]

5 lfus Fuselage length 0.14 [m]

6 wfus Fuselage width 0.04 [m]

7 du Distance from upper rotor hubto center of gravity

0.185 [m]

8 dl Distance from upper rotor hubto center of gravity

0.105 [m]

9 Ixx Inertia about X-axis 5.33E-03 [kg.m2]

10 Iyy Inertia about Y-axis 6.26E-03 [kg.m2]

11 Izz Inertia about Z-axis 2.50E-03 [kg.m2]

12 Ju Upper rotor inertial moment 7.66E-04 [kg.m2]

13 Jl Lower rotor inertial moment 7.66E-04 [kg.m2]

14 Jf Fly-bar inertial moment 2.55E-04 [kg.m2]

*kT, kQ is calculated for the case of 31.14 /kg mρ = (Bandung, Indonesia)

The rotor and fly-bar parameters are shown in TABLE III.

TABLE III PARAMETERS OF ROTOR AND FLY-BAR

Parameter Description Value Unit

,f lτ Lower rotor time constant 0.05 [s]

,f fτ

Fly-bar time constant 3.0 [s]

bK Ratio of swash-plate tilt angle to the Tip Path Plane tilt angle

0.91 [-]

qK

Ratio of fly-bar tilt angle to longitudinal tilt angle of upper rotor Tip Path Plane

0.54 [-]

pK

Ratio of fly-bar tilt angle to lateral tilt angle of upper rotor Tip Path Plane

0.54 [-]

The thrust and torque coefficients of rotor system are described inTABLE IV.

TABLE IV THRUST AND TORQUE COEFFICIENTS OF ROTOR SYSTEM

Parameter Description Value Unit

TuC Thrust coefficient of upper rotor 7.18E-03 [rad-1]

TlC Thrust coefficient of lower rotor 4.98E-03 [rad-1]

QuC Torque coefficient of upper rotor 5.98E-04 [rad-1]

QlC Torque coefficient of lower rotor 5.20E-04 [rad-1]

The information of noise assumption is shown inTABLE V

TABLE V ASSUMPTION OF NOISE IN THE OBSERVATION

Deviation of noise Value Unit

( )Vσ η 0.5 [m/s]

( )hσ η 0.05 [m]

( )pσ η 2 [deg/s]

( )qσ η

2 [deg/s]

( )rσ η

2 [deg/s]

( )axσ η

0.1 [m/s2]

( )ayσ η

0.1 [m/s2]

( )azσ η

0.1 [m/s2] The simulation was carried out at air density ofρ = 1.14

kg/m3, gravitational acceleration ofg = 9.804 m/s2. The time step of simulation is 10 ms, which is corresponding to the update rate of the sensory system (100 Hz).

B. Pre-flight Simulation

The purpose of the pre-flight simulation is to obtain the reference value of the control inputs of the rotor and servo systems for later use in the real flight test. From the simulation, study of the response of the helicopter to the control input can be obtained. Therefore, the pre-flight simulation can minimize the flight test envelop as well as increase the efficiency of the flight test.

In this section, the simulation of longitudinal maneuver is presented as an example of pre-flight simulation. A control

,lon latδ δMicro Coaxial Helicopter

Mathematical Model:(26)-(29) and

(32)-(43)

Environmental Data:ρ, g

Helicopter Parameters: m, R, l fus, wfus, du, dl, Ixx, Iyy, Izz, Ju, Jl, Jf,

Kb, Kq, Kp

,l uω ωState: u, v, w p, q, r

,

,l l

f f

α βα β

, ,φ θ ψ xE,yE, h

Sensor Model: (45)

V, h, p, q, r ax, ay, az

Observation

, , ,

, , ,

V h p q

r a a ax y z

η η η ηη η η η



input is given to the pitch servo to study the behaviour of the helicopter in the longitudinal mode. The helicopter is expected to move in the longitudinal plane with the change in pitch angle, longitudinal and lateral translation.

The control inputs of the rotor and servo systems are shown in Fig. 3

Fig. 3. Control input of rotor and servo system in longitudinal maneuver pre-flight simulation

As shown in Fig. 3, during the simulation of the longitudinal maneuver, the RPM of rotor are set at constant value, i.e. RPM of 2000 and 2150 for the upper and lower rotors respectively. These RPM values are the corresponding values obtained in the hover flight simulation. The control input of the roll servo latδ is set zero to make sure no active

input is given to the roll channel. The input of the pitch servo

lonδ is the active input. In the first 2 s of the simulation, lonδ is

set to zeros to simulate the hover flight. A doublets input with the pulse width of 2 s and amplitude of 5 deg is then given to the lonδ to initiatethe pitch down and up motion. In the rest of

simulation time, the value of lonδ is reset to zero to see the

response of the helicopter after giving a command in the pitch channel.

The corresponding response of the helicopter is shown in Fig. 4 to Fig. 7.

Fig. 4. Response of translational velocity

Fig. 5. Response of translational velocity (v, w), angular rates (p, q, r) in pre-flight simulation of longitudinal maneuver

Fig. 6. Response of rotor, fly-bar flapping angles( ), , ,l l f fα β α β in pre-flight

simulation of longitudinal maneuver

-10

-5

0

5

10

0 2 4 6 8 10dla

t (d

eg)

Time (s)

-10-505

10

0 2 4 6 8 10dlo

n (d

eg)

1800

2000

2200

0 2 4 6 8 10RP

M_

uppe

r ro

tor

2000

2200

2400

0 2 4 6 8 10RP

M_

low

er

roto

r

-5

0

5

0 2 4 6 8 10bf(d

eg)

-5

0

5

0 2 4 6 8 10af(d

eg)

-2

0

2

0 2 4 6 8 10

bl(d

eg)

-5

0

5

0 2 4 6 8 10al(d

eg)

-5

0

5

0 2 4 6 8 10r(d

eg/s

)

Time (s)

-20

0

20

40

0 2 4 6 8 10q(d

eg/s

)

-30

0

30

0 2 4 6 8 10p(d

eg/s

)

-1

0

1

0 2 4 6 8 10w(m

/s)

-1

0

1

0 2 4 6 8 10v(m

/s)

-2

0

2

0 2 4 6 8 10u(m

/s)



Fig. 7. Response attitude ( ), ,φ θ ψ and location in inertial frame (x, y, z) in

pre-flight simulation of longitudinal maneuver As seen in Fig. 4 to Fig. 7 , during the hover period, t = 0-2

s,all the states are zeros, which are the correct states that the helicopter should has in the hover condition. After the pitch down command is given to the pitch servo, t = 2-4 s, a pitching moment is generated, and pitches the helicopter down, see response ofθ . In response, the lower rotor is pitched down under the control of swash-plate (negative value in the response of αl from t = 2-4 s); while the upper rotor is

pitched up due to the effect of fly-bar (positive valuein the response of α f from t = 2-4 s). As a result, a positive

longitudinal force is generated to make the helicopter move forward. Therefore, a positive value of velocity (u), is obtained in the response from t = 2-4 s. The translation motion along the longitudinal is taken place; see the history of the helicopter in x response.

There is a coupling betweenthe pitch and roll channels due to the gyroscopic effect of rotor and fly-bar, see (35)and (36). As a pitch rate is resulted from the pitch command, a rolling moment is also generated. Therefore, a slight response is occurred in the response of roll rate (p).

The responses of the helicopter in the period of t = 4-6 s are contractive with the response in period of t = 2-4 s. Reduction in the translational velocity is occurred due to the effect of the pitch up action in the lower rotor (positive value in the response of αl from t = 2-4 s). The helicopter is pitched up

(positive value in the time response chart ofθ ). However, under the inertia from the previous pitch down action, the helicopter continues to move forward.

In the rest of the simulation, t = 6-10 s, the helicopter tries to recover its attitude to the vertical stand with zeros value in the response of Euler angles. At the end of the simulation, the helicopter reachesthe new position that is around 6 m away from the start point in the longitudinal direction. Reduction in the altitude is around 0.7 m referred to the initial altitude.

The simulation results inFig. 4 to Fig. 7proof that with the platform of the helicopter used in the simulation, the longitudinal maneuver can be performed under the control inputs as shown inFig. 3. Therefore, these control inputs will be used as the reference in preparation of the flight test on real helicopter test-bed.

The simulated observations obtained in the simulation of longitudinal maneuver are shown inFig. 8 to Fig. 10. These simulated data give a sample of the pattern of the flight test data that can be obtained in a longitudinal maneuver flight test.

Fig. 8. Simulated observation of velocity (V), altitude (h)

Fig. 9. Simulated observation of angular rate (p, q, r), translational acceleration (ax, ay, az) in longitudinal maneuver.

0.5

1

1.5

2

2.5

0 2 4 6 8 10

h(m

)

-2-10123

0 2 4 6 8 10V(m

/s)

-10

0

10

0 2 4 6 8 10r(d

eg/s

)

Time (s)

-30-15

0153045

0 2 4 6 8 10q(d

eg/

s)

-30-15

01530

0 2 4 6 8 10

p(d

eg/

s)

0.5

1.5

2.5

0 2 4 6 8 10

h(m

)

Time (s)

-1

0

1

0 2 4 6 8 10y(m

)

-202468

0 2 4 6 8 10

x(m

)

-2

0

2

0 2 4 6 8 10

ѱ

(de

g)

-5

0

5

0 2 4 6 8 10θ(d

eg)

-4

0

4

0 2 4 6 8 10∅(d

eg)



Fig. 10. Simulated observation of translational acceleration (ax, ay, az) in longitudinal maneuver.

In the next section, discussions on the flight test of the MAV helicopter and data processing will be introduced.

IV. DATA ACQUISITION AND DATA PROCESSING

A. Flight Test Instrumentations System

To capture the helicopter states and the control inputs of the rotor and servo, sensors have been selected and integrated. Based on DR&O of the sensory system, several sensors have been chosen with the main characteristic as shown inTABLE VI.

TABLE VI LIST OF SELECTED SENSOR

Sensor Name Performance

IMU 6dof v4 6 g for accelerometer, 500 deg/s for gyro

LV MaxSonar EZ4 sonar sensor 5 m

Shaft encoder 4000 RPM

PropStick USB MCU PWM readable

Digital Magnetic Compass Tilt compensated

GPS

The schematic diagram of the overall structure of sensory system is depicted in Fig. 11. [10].

Fig. 11. Schematic diagram of overall structure of sensory system

Due to the limitation of payload, only light sensor can be carried onboard of the helicopter. In detail, three navigation sensors are used: 1) 6DOF Inertial Measurement Unit from SparkFun Electronic[11], which provides the measurement of the airframe accelerations(ax, ay, az) and the angular rates(p, q, r) (measured range of 6g and 500deg/s, data rate: up to 200Hz); 2) Digital Magnetic Compass (DMC)with tilt compensated OS500-S from Ocean Server for sensing heading attitude, tilt angle in longitudinal and lateral direction (resolution: 0.10, data rate: 40Hz)[12]; 3) Sonar Range Finder sensor for measuring the helicopter altitude (range: 15cm – 6.5m)[13]. Besides that, two optical shaft encoders were also used to record the rotational speed of the rotor system.Two microcontrollers (MCU) were selected to collect and encode all the sensor reading into data packages[14]. A pair of Bluetooth modules was used to send the data to PC for storing and further processing[15].

Fig. 12 shows the full integration of the sensory system. The sonar range finder is located at the bottom of the system, below the IMU. The whole system is run at the frequency of 100 Hz. To damp the vibration caused by the rotation of the rotor system, silicon foam is used in the mounting of sensory system.

Fig. 12. Complete integration of sensory system

B. Flight Test Procedure and Flight Test Results

In this section, the flight test program to execute the longitudinal maneuver flight test will be discussed; fight test results will be introduced as well.

The flight test programs with detail of the procedure and flight test actions were planned to take care of the flight test. These flight test plans were prepared by following the simulation of pre-flight scenarios, see section III. To describe the test procedure, test action as well as to note the test event, a flight test card was used. A sample of flight test card recorded in flight test of longitudinal maneuver is shown in TABLE VII .

As described in the flight test card, the helicopter was kept at the hover condition in few second to achieve the steady state. During the hover period, Rotor RPM were kept constant and the control inputs for servos were given at zero value. A doublet with amplitude of 5 deg and pulse width of 2 s was given to the pitch servo to activate the motion in the longitudinal plane.

Microcontroller

Silicon absorber

IMU

DMC

Sonar sensor

-10.5

-10

-9.5

-9

0 2 4 6 8 10az(d

eg/

s)

Time (s)

-0.4

-0.2

0

0.2

0.4

0 2 4 6 8 10

ay(d

eg/

s)

-0.4

-0.2

0

0.2

0.4

0 2 4 6 8 10

ax(d

eg/

s)



TABLE VII

FLIGHT TEST CARD RECORDED IN LONGITUDINAL MANEUVER FLIGHT TEST

Test content:Longitudinal Maneuver of MAV Coaxial Helicopter

Test date: May 26, 2011 Place: Campus Center ITB

Helicopter specification:

- Mass : 0.8 kg - Rotor radius : 25 cm - Power supply : 11.1 V

Run Description Action Remark

# 1 Power the RC and helicopter test-based: • Switch on power

supply of RC; • Switch on power

supply of helicopter and sensory system.

− Start counter

time

− Start data

recording

# 2 Takeoff:

• Increase RPM of upper and lower rotor until hover condition is achieved.

− ttakeoff = 8th s − hover altitude: 1.8-2

m

# 3 Longitudinal Maneuver: • Keep RPM rotor

at constant values; • Give control input

in doublets type to servo system.

− t: 20th s − RPM-upper: 2000 − RPM-lower: 2143 − Hover altitude:

1.2-1.4 m − t-end_forward:

25th s − t_end_backward:

28th s − t-end: 30th s

− small vibration; − slightly reduction in

altitude before go forward;

− small input for roll servo was mistakenly given;

− slightly increase of RPM at the end of backward period to prevent touch down.

# 4 Landing: • Continuously

reduce rotor RPM to zeros values

− t-landing: 37th s

# 5 Repeat #1 #4÷ three times

The time history of the control inputs in the longitudinal maneuver flight test are shown inFig. 13 and Fig. 14.

Fig. 13. Control input of servo system in longitudinal maneuver

Fig. 14. Control input of rotor system in longitudinal maneuver

The measurement of angular rates about X-axis, Y-axis, Z-axis, accelerations along X-axis, Y-axis, Z-axis, and altitude are shown in Fig. 15 and Fig. 16.

Fig. 15. Measured angular rates about X-axis, Y-axis, Z-axis (p, q, r),andmeasured acceleration along X-axis, Y-axis (ax, ay)obtained in longitudinal maneuver flight test

Fig. 16. Measuredazandaltitude obtained in longitudinal maneuver flight test

-10

-5

0

5

10

0 2 4 6 8 10a y (m

/s2 )

-10

-5

0

5

10

0 2 4 6 8 10a x (m

/s2 )

-20

-10

0

10

20

0 2 4 6 8 10q (d

eg/s

)

-20

-10

0

10

20

0 2 4 6 8 10p(d

eg/s

)

1800

1900

2000

2100

2200

Lowe

r R

otor

RP

M

2000

2100

2200

2300

Upp

er R

otor

RP

M

-8

-4

0

4

8

0 2 4 6 8 10

Time (s)

d lat (d

eg)

-8

-4

0

4

8

0 2 4 6 8 10d lon(d

eg)

0

1

2

3

0 2 4 6 8 10

h(m

)

Time(s)

5

10

15

0 2 4 6 8 10a z (m

/s2 )

-30

-15

0

15

30

0 2 4 6 8 10r(de

g/s)



C. Preliminary Flight Test Data Analysis

As shown inFig. 15 and Fig. 16, the measured data contained noise at high noise to signal ratio. From the notes taken in flight test card, these noises were probably come from the vibration of the airframe and rotor, the aerodynamic interference, and the effect of built-in gyro of the helicopter controller. This matter raises the requirement offiltering the measured data to get the appropriate data of the helicopter response.

Analyses on the spectra of typical flight test data show that the real response of the helicopter occurred at low frequency; while the noise occurred at both high and low frequency. Therefore, two kindsof filter were applied to handle the data filtering. A Butterworth low-pass filter was first used to cut-off noise at high frequency.

The data after the first filtering process still contained noise at low frequency, which is probably in the same frequency with the real signal. Hence, it is risky to apply low-pass filter to remove these noise. In other words, loss of real response can be happened. To deal with this issue, the second filtering process was carried out. This filtering process worked in frequency domain based on the characteristic of signal and noise. The flight test data were split into segments, for example, 1s length. Each of the data segments was transformed into frequency domain by the Discrete Fourier Transform (DFT). Analyses were then carriedout to understand the distribution of noise and signal in term of frequency and amplitude. The data obtained in hover phase was considered to contain the corrupted noise, which was assumed to be consistent in the flight test data. Based on these assumptions, the expected signal in the frequency domain can be obtained by subtracting the spectra of the data segment to the spectra of the corrupted noise. In final step, inverse of DFT was taken to get the signal in time domain[16].

The results on processing of the measured data obtained in the longitudinal maneuver flight test are shown in Fig. 17 to Fig. 22.

Fig. 17. Filtering of angular rates about Y-axis obtained in longitudinal maneuver by using Butterworth low-pass filter

Fig. 18. Filtering of angular rates about Y-axis in longitudinal maneuver by using spectral amplitude based filter.

Fig. 19. Filtering of measured acceleration alongX-axis obtained in longitudinal maneuver by using Butterworth low-pass filter

Fig. 20. Filtering of acceleration alongX-axis in longitudinal maneuver by using spectral amplitude based filter

Fig. 21. Filtering of measured acceleration along Z-axis obtained in longitudinal maneuver by using Butterworth low-pass filter

Fig. 22. Filtering of acceleration alongZ-axis in longitudinal maneuver by using spectral amplitude based filter

In Fig. 18, Fig. 20 and Fig. 22, the solid line represents the filtered data obtained by applying the Butterworth low-pass filter on measured data; the dot linerepresents the filtered data obtained by applying the spectral amplitude base filter on the output of Butterworth low-pass filter.

As shown in Fig. 17 to Fig. 22, by applying the Butterworth low-pass filter and the spectral amplitude based filter, the appropriate data can be obtained. In order to evaluate the quality of the filtered data, several tests have been carried out. The test contents consist of testing the altitude reading in comparing with notes taken during flight test, and test of IMU’s measured angular rates and accelerations by evaluating the integrated pitch angle, velocities and positionobtained from the integration of IMU’s measured data [18]. The test results show that the data obtained in flight test after the

5

10

15

0 2 4 6 8 10

a z(m

/s2 )

Time(s)

Measured dataButterworth low-pass filter

Filtering of Measured Acceleration obtained Longitudinal Maneuver Flight Test with Butterworth Low-pass Filter

-8

-4

0

4

8

0 2 4 6 8 10a x(m

/s2 )

Time(s)


Filtering of Measured Acceleration obtained Longitudinal Maneuver Flight Test with Butterworth Low-pass Filter

-20

-10

0

10

20

0 2 4 6 8 10q (d

eg/s

)

Time(s)

Filtering of Measured Pitch Rate obtained Longitudinal Maneuver Flight Test with Butterworth Low-pass Filter


-8

-4

0

4

8

12

0 2 4 6 8 10

q(d

eg/s

)

Time (s)

Butterworth low-pass filter

Spectra amplitude based filter

Filtering of Pitch Rate Data Obtained in Longitudinal Maneuver Flight Test

-2

-1

0

1

2

0 2 4 6 8 10a x(m

/s2 )

Time (s)

Butterworth low-pass filter

Spectra amplitude based filter

Filtering of Longitudinal Acceleration Data Obtained in Longitudinal Maneuver Flight Test

8.5

9

9.5

10

10.5

11

0 2 4 6 8 10a z(m

/s2 )

Time (s)

Butterworth low-pass filterSpectra amplitude based filter

Filtering of Vertical Acceleration Data Obtained in Longitudinal Maneuver Flight Test



filtered process are good; andthey can be used in further data analysis.

V. ESTIMATION OF PARAMETERS OF THE MICRO

COAXIAL HELICOPTER

This section introduces the estimation of parameters in the aerodynamic force and moment coefficient models in the longitudinal mathematical model using the obtained flight testdata. Two steps parameter estimation are used. In the first step, Extended Kalman Filter is used to estimate the states of the helicopter. The Total Least Square method will beapplied to estimate the parameter in the aerodynamic force and moment model.

A. Estimation of the Helicopter States

From the complete equations of motion of the micro coaxial helicopter derived in section II, the dynamic model in the longitudinal mode can beextracted as follows

sinxu a qw g θ= − −& (46)

coszw a qu g θ= + +& (47)

qθ =& (48)

sin cosh u wθ θ= −& (49)

, ,

l bl lon

f f f f

Kq

αα δτ τ

= − + −& (50)

,

ff

f f

qα

ατ

= − −& (51)

Due to the independence of the rotor and fly-bar flapping

angles( ),l fα α to the other states, (50) and (51)can be

separated to estimate the flapping angles of rotor and fly-bar

by using the control input of the pitch servo( )lonδ and the

measured pitch rate (q) obtained in longitudinal maneuver flight test.

The equations of motion (46)-(49) can be solved by using numerical integration if ax, az, and q are known, for example, from the measurement using the accelerometers as well as rate gyros. However, the measurements of the longitudinal and vertical accelerations are usually containing bias. The effect of these biases can be modeled as

xm x axa a λ= + (52)

zm z aza a λ= + (53)

where ,xm zma a are the measured values of the acceleration

along X-axis, Z-axis, ,x za a are the true value of acceleration,

and ,ax azλ λ are the biases.

Assume that the bias in longitudinal acceleration is small, and can be neglected. Substitution of (53) into (47) respectively, yields

cosz azmw a qu gλ θ= − + +& (54)

The parameter azλ is assumed constant in which the

derivative with time is zero. This parameter can be included into the state equations as follows

0azλ =& (55)

The state equations(46), (48), (49), (54), and (55)can be written in the state-space form of

( ), mx f x u=& (56)

where

− State vector : , , , ,T

azx u w hθ λ= ∆

− Input : , ,T

m xm zmu q a a=

If the altitude h can be measured, for example, using sonar range finder, then the observation may be written as

z h= (57)

In principle, the Extended Kalman Filter (EKF) can be applied to estimate the state in (56) as the inputs are known.

The results on estimation of states in the longitudinal maneuver by using EKF are shown in Fig. 23, Fig. 24 and Fig. 25.

Fig. 23. Estimation of velocity along X-axis, Z-axis, (u, w) and pitch angle

( )θ in longitudinal maneuver

-0.5

0

0.5

1

0 2 4 6 8 10

w(m

/s)

Time (s)

Estimation of Vertical Velocity Using Kalman Filter on Longitudinal Maneuver Flight Test Data

-0.5

0

0.5

1

1.5

2

0 2 4 6 8 10

u(m

/s)

Time (s)

Estimation of Longitudinal Velocity Using Kalman Filter on Longitudinal Maneuver Flight Test Data

-2

-1

0

1

2

0 2 4 6 8 10

θ(d

eg)

Time (s)

Estimation of Pitch Angle Using Kalman Filter on Longitudinal Maneuver Flight Test Data



Fig. 24. Estimation of bias in vertical acceleration in longitudinal maneuver

It can be seen in Fig. 24 that the estimation of the bias in the vertical acceleration is convergent with time. And, the value of the bias can be taken from the steady state. The biascan be

obtained as 20.05 /λ = −az m s . Hence, the true value of

acceleration about the Z-axis (az) can be obtained by using (53).

Fig. 25. Estimation of altitude in longitudinal maneuver

As shown in Fig. 25, the estimated altitude and measured altitude fit well in both trend and amplitude. The residual of the estimation is within 0.1 m.

Fig. 26. Estimation of rotor flapping of the lower and upper rotor

Fig. 26 depicts the estimation of the lower and upper rotors’ flapping angles by integrating (50), (51) with the control input

of the pitch servo ( )lonδ , and the measured angular velocity

about Y-axis (q) are obtained from the longitudinal maneuver flight test. Due to the existence of high noise to signalratio, the filtered value of q presented in sectionIV.C will be used, instead of the raw measured value. It can be seen that the flapping motion of lower rotor is in same phase with the

control input for pitch servo( )δlon , while the phase of

flapping motion of upper rotor is opposite to the pitch angle of the helicopter, see alsoFig. 13 andFig. 23.

B. Estimation of Aerodynamic Parameter in Longitudinal Mode of Micro Coaxial Helicopter

Recall the force and moment equations, these equations can be rewritten for the longitudinal mode as follows

sinu rv qw g X mθ= − − +& (58)

cos cosw qu pv g Z mθ φ= − + +& (59)

yyq M I=& (60)

In equations (58), (59) and(60), the aerodynamic force X, Z, and pitching moment Mcan be calculated from

1 4 22x XX ma R Cρπ ω= = (61)

1 4 22z ZZ ma R Cρπ ω= = (62)

1 5 22yy mM I q R Cρπ ω= =& (63)

Or

( )1 4 22X xC ma Rρπ ω= (64)

( )1 4 22Z zC ma Rρπ ω= (65)

( )1 5 22m yyC I q Rρπ ω= & (66)

where the force and moment coefficientsCX, CZ, and Cmcan be model as the regression of the helicopter states, i.e. the rotor

flapping angles( )u l,α α ,the angular rates about Y-axis (q), and

the control inputs, i.e. lonδ , Tu, Tl

0X X X X u X l X lon X u X lq T Tu l lon u lC C C q C C C C T C Tα α δα α δ= + + + + + + (67)

0Z Z Z Z u Z l Z lon Z u Z lq T Tu l lon u lC C C q C C C C T C Tα α δα α δ= + + + + + + (68)

0m m m m u m l m lon m u m lq T Tu l lon u lC C C q C C C C T C Tα α δα α δ= + + + + + + (69)

whereu

XCα

,l

XCα

, qXC ,

lonXC

δ,

uZC

α,

lZC

α,

qZClon

ZCδ

, , , ,qu l lon

m m m mC C C Cα α δ

, are the aerodynamic

coefficients and , , , , ,T T T T T Tu l u l u l

X X Z Z m mC C C C C C are the

propulsion coefficients. These parameters will be identified by using data obtained from flight test.

In the left side of (67), (68) and (69), the value of CX, CZ,

-0.2

-0.1

0

0.1

0.2

0 2 4 6 8 10

resi

dual

(m)

Time (s)

Difference Between Measured and Estimated Altitude using Extended Kalman Filter

-0.2

-0.1

0

0.1

0 2 4 6 8 10

λaz

(m/s

2 )

Time (s)

Estimation of Bias in Vertical Accleration Using Kalman Filter on Longitudinal Flight Test Data

-8

-4

0

4

8

0 2 4 6 8 10al(d

eg)

Time (s)

Estimation of Lower Rotor Flapping Using Kalman Filter on Longitudinal Maneuver Flight Test Data

-2

-1

0

1

2

0 2 4 6 8 10au(d

eg)

Time (s)

Estimation of Upper Rotor Flapping Using Kalman Filter on Longitudinal Maneuver Flight Test Data

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10

h(m

)

Time (s)

Estimation - Extended Kalman FilterMeasurement

Estimation of Altitude Using Kalman Filter on Longitudinal Maneuver Flight Test Data



Cm can be computed from the measurements of helicopter translational and rotational motion(ax, az, q), along with the geometric and mass/inertia propertied of the helicopter by using(64), (65) and(66). The time derivative of q is obtained by taking the 4 points Lagrange time derivative on the filtered value of angular rate about Y-axis.

In the right side of (67), (68) and (69), the measured angular

rate (q), the measured control input for pitch servo ( )lonδ , and

the measured rotor control input in term of thrust (Tu, Tl) are obtained from the flight test of longitudinal maneuver. The

flapping angles of the upper and lower rotors( ),u lα α are

estimated from the flight test data as described in section V.A.

By knowing the values of CX, CZ, Cm, and the values of the independent variables , , , , ,u l lon u lq T Tα α δ , the parameters in

(67), (68), (69)can be estimated using regression method such as Least Squares (LS) method [19], or Total Least Squares method (TLS)[20]. A study by H. Muhammadet al. (2012)[21]on estimation of aerodynamic parameter of Micro Aerial Vehicle helicopter using TLS method showed that TLS could give consistent estimation of the parameters in presence of noise in measured data. Therefore, TLS method will be used to estimate the parameters of aerodynamic model.

By applying the Total Least Square method on the filtered flight test data, results on estimation of parameters of the force and moment model CX, CZ, and Cm in the longitudinal maneuver can be obtained as shown inTABLE VIII.

TABLE VIII

ESTIMATION RESULTS OF PARAMETERS OF AERODYNAMIC FORCE AND

MOMENT MODEL IN LONGITUDINAL MODE

Parameters Value Standard

Deviation

Parameters Value Standard

Deviation

0XC 0.0134

0.0042 lon

ZCδ

-0.1802 0.0108

uXC

α -0.0655

0.0149

TlZC

0.0004 0.0009

lXC

α 0.3900

0.0218

TuZC

-0.0057 0.0007

qXC

0.0569

0.0039

0mC

0.0189 0.0068

lonXC

δ -0.3569

0.0201

umC

α

0.2370 0.0241

TlXC

0.0041

0.0016

lmC

α

-0.6448 0.0354

TuXC

-0.0063

0.0012

qmC

-0.0833 0.0063

0ZC

0.0495

0.0022 Lon

mCδ

0.5995 0.0326

uZC

α

0.0124

0.008 Tl

mC

-0.0066 0.0026

lZC

α 0.2034

0.0117

TumC

0.0009 0.002

qZC

0.0285

0.0021

The estimation of CX, CZ,and Cmcan be achieved by using

TLS estimation. The verifications of these aerodynamic coefficientsare shown in Fig. 27, Fig. 28, and Fig. 29.

As shown in Fig. 27, the estimated CX was obtained by applying Total Least Square method on the flight test data; while the measured coefficient was directly computed from the measurement of helicopter translation; along with the geometric, mass and inertia properties of the helicopter using (64). It can be seen that by taking into account the information of noise in the measurement, estimated CX obtained from TLS method follows well the trend of the measured CX.

In term of magnitude, the estimated and measured value of CX are in the same order, except some periods in which transition of control input were made, i.e. at t = 2, t = 4, t = 8s, see also lonδ in Fig. 13. It indicates that linear model of

longitudinal aerodynamic force has successful been built.

Fig. 27. Comparison between estimated and measured valued of CX, and the corresponding difference.

As shown in Fig. 28, the estimated CZ fits the measured CZ at good rate in trend. The amplitude of the estimated value and measured value is in the same order. Therefore, it can be conclude that the vertical aerodynamic force coefficient CZ has been modeled with appropriate parameters.

Fig. 28. Comparison between estimated and measured valued of CZ, and the corresponding difference.

-4.E-03

-2.E-03

0.E+00

2.E-03

4.E-03

0 2 4 6 8 10Res

idua

l [-

]

Time (s)

Difference Between Measured and Estimated Vertical Aerodynamic Force Coefficient

2.3E-02

2.4E-02

2.5E-02

2.6E-02

2.7E-02

2.8E-02

0 2 4 6 8 10

CZ

[-]

Time (s)

Measured data Estimated - TLS

Estimation of Vertical Aerodynamic Force Coefficient by using Total Least Square

-4.E-03

-2.E-03

0.E+00

2.E-03

4.E-03

0 2 4 6 8 10

Res

idua

l [-

]

Time (s)

Difference Between Measured and Estimated Longitudinal Force Coefficient

-4.E-03

-2.E-03

0.E+00

2.E-03

4.E-03

0 2 4 6 8 10

CX

[-]

Time (s)

Estimation of Longitudinal Aerodynamic Force Coefficient byusing Total Least Square




Fig. 29 shows the comparison of the estimated and measured pitching moment coefficient in longitudinal maneuver. The estimated value is obtained from TLS method; while the measured valued is obtained from measured data by using (66). In general, the estimated and the measured pitching moment fits well together both in trend and amplitude. Slight difference between these two quantities is occurred at period around 4 s due to the rough change in giving control input to

pitch servo, as expressed in time history of lonδ in Fig. 13.

Fig. 29. Comparison between estimated and measured valued of Cm, and the corresponding difference.

In brief, the estimation of the parameters in the model of

aerodynamic force and moment coefficients in the longitudinal maneuver flight has successfully been conducted by applying the Kalman Filter and the Total Least Square method on the flight test data of longitudinal maneuver.

VI. CONCLUSIONS AND FUTURE WORKS

A. Conclusions The mathematical model of micro coaxial helicopter has

successfully been obtained by combiningthe analytical approach and the system identification approach.

The analytical mathematical model of the helicopter has derived from physical approach with the consideration of rotor and fly-bar dynamics. Pre-flight simulation was successfully built to simulate the flight test scenarios.

In term of flight test, a sensory system has been evaluated and integrated to capture data for estimating of parameters identification based on flight test data. Flight tests with different scenarios have been carried out in certain procedure to acquire flight test data. Preliminary and advanced process of flight test data were done to extract signal from noise data, as well as to suppress the corrupted noise in the data.

Adequate parameters in the linearized model of force and moment coefficients in the longitudinal maneuverhave been obtained by applyingthe Extended Kalman Filter and the Total Least Square method on the flight test data. The verification

showed that the estimated force and moment coefficientsCX, CZ, and Cm fit well the trend of the corresponding measured quantities. These estimated force and moment coefficient are in same order of magnitude compared to the measured forces and moment.

B. Future Works

Above remarks on the achievement of present work show that the development of mathematical model of a micro coaxial helicopter can be done by following the procedure presented in this current work. Toward the refinement of mathematical model of the micro coaxial helicopter and application of this mathematical model into control system development, several works should be fulfilled as follows.

In term of system improvement, works should be focused on reducing the vibration on the helicopter and improving the working condition of sensory system. The structures and the skid of the helicopter, for example, should be rebuilt to avoid of vibration interferences. Installation of absorber to minimize the effect of vibration to sensor reading quantity is also a minor solution need to be considered.

In the aspect of estimating of parameters and sub-mathematical model, there some works needed to be considered. More flight tests should be done to validate the identified dynamic model, repeating flight test run (execution) in certain number is necessary to ensure the consistent of parameters. In term of flight scenarios, the flight test should cover more flight regime to expand the valid range of the linear model, towards the coverage of entire flight envelop of typical micro coaxial helicopter. The flight test should be carried out by a skilled pilot to execute the flight test plan with high efficiency.

As soon as the validation of the mathematical model is obtained, more works can be concentrated on development of autonomous control system to allow the helicopter control itself in an indoor mission. Semi-autonomous control in combined with way-point following technique and vision aid is also a challenge set to be the target in long term plan.

ACKNOWLEDGMENT

The authors gratefully acknowledge Department of

Aeronautics and Astronautics, Faculty of Mechanical and Aerospace Engineering, Institut Teknologi Bandung and Department of Aeronautics and Astronautics, School of Engineering,The University of Tokyo for offering good condition to complete the research.

REFERENCES

[1] A. Dzul, T. Hamel and R. Lozano, “Modeling and nonlinear control for

a coaxial helicopter”, in Proc.Systems, Man and Cybernetics, 2002 IEEE International Conference, Hammamet, Tunisia, October 2002.

-4.0E-03

-2.0E-03

0.0E+00

2.0E-03

4.0E-03

0 2 4 6 8 10

resi

dual

[-]

Time (s)

Difference Between Measured and EstimatedPitching Moment Coefficient

-8.0E-03

-4.0E-03

0.0E+00

4.0E-03

8.0E-03

0 2 4 6 8 10

Cm

[-]

Time (s)


Estimation of Pitching Moment Coefficient by using Total Least Square



[2] L. Chen and P. McKerrow, “Modeling the Lama coaxial helicopter”, inProc.The Australasian Conference on Robotics and Automation, ACRA'07, Brisbane, December 2007.

[3] W. Wang, K. Nonami, M. Hirata, O. Miyazawa, “Autonomous control for micro flying and small wireless helicopter X.R.B”, in Proc. IEEE International Conference on Intelligent Robots and Systems, Beijing, China,October2006,pp. 2906 – 2911.

[4] D. M. Schafroth. Aerodynamics, Modeling, and Control of an Autonomous Micro Helicopter. Ph.D. dissertation, ETH ZURICH, Netherland, 2010.

[5] S. Bouabdallah, C. Bermes, D. Schafroth, R. Siegwart, “Modeling and system identification of the muFly micro helicopter”, Journal of Intel Robot System, 2010, pp. 27 – 47.

[6] A. Budiyono, K.J. Yoon, F. D. Daniel, “Integrated identification modeling of rotorcraft based unmanned aerial vehicle”, in Proc.17th Mediterranean Conference on Control and Automation, Thessaloniki, Greece, June 2009, pp. 898-903.

[7] C. Bermer, S. Bouabdallah, D. Schafroth, R. Siegwart, “Design of the autonomous micro helicopter mFly”, Journal of Mechatronics, vol. 21, no. 5, August 2011, pp. 765-775.

[8] J. Shin, D. Fujiwara, K. Nonami and K. Hazawa, “Model-based optimal attitude and positioning control of small-scale unmanned helicopter”, Robotica,Vol. 23, pp. 51 – 63.

[9] J.A. Mulder, W.H.J. J Staveren, J. C. Vaart, E. Weerdt, Flight Dynamics: Lecture Notes. Delft University of Technology, The Netherlands, 2006.

[10] H. P. Thien, Taufiq Mulyanto, Hari Muhammad, and Shinji Suzuki, “Estimation of UAV’s attittude by using multi-sensors integration”, in Proc. The 30th IASTED International Conference on Modeling, Identification and Control (AsiaMIC 2010), Phuket, Thailand, October 2010, pp. 174-180.

[11] SparkFun Electronics, (2008), IMU 6 degree of freedom v4 datasheet, http://www.sparkfun.com, last visited: June 2010.

[12] Ocean Server Technology Inc., (2009), Digital Compass User Guide.http://www.ocean-server.com/, last visited: June 2010.

[13] Max Botix Inc., (2007), LV – Max Sonar EZ – 4 datasheet. http://www.maxbotix.com/, last visited: June2010.

[14] Parallax Inc., (2009), Propeller P8X32A datasheet, 2-4. http://www.parallax.com/,last visited: July 2010.

[15] SparkFun Electronics, (2011), Bluetooth DIP Module, Roving Network, http://www.sparkfun.com/products/10144, last visited: April 2011.

[16] N. W.D. Evans, J. S. Mason, W. M. Liu and B. Fauve, “On the fundamental limitations of spectral subtraction: an assessment by automatic speed recognition”, in Proc. The 2005 European Signal Processing Conference, 2005, pp. 2-5.

[17] H.P. Thien, T. Mulyanto and H. Muhammad, “Modeling and identification of longitudinal dynamic model of micro coaxial helicopter”, in Proc. The 4th Regional Conference on Mechanical and Aerospace Technology, Ho Chi Minh City, Vietnam, January 2012.

[18] H.P. Thien, System Modeling and Identification of Coaxial Rotor Micro Aerial Vehicle, Ph.D. dissertation, Institut Teknologi Bandung, to be published.

[19] V. Klein, E. A. Morelli, Aircraft System Identification: Theory and Practice. American Institute of Aeronautics and Astronautics, Inc., 2006, pp. 181.

[20] M. Laban, K. Masui,“Total Least Square estimation of aerodynamics model parameters from flight data”,Journal of Aircraft, Vol. 30, no. 1, 1992,pp. 150-152.

[21] H. Muhammad, H.P.Thien & T. Mulyanto,“Estimationof aerodynamic parameter of micro aerial vehicle using total least square”, inProc. The 4th Regional Conference on Mechanical and Aerospace Technology, Ho Chi Minh City, Vietnam, January2012.

Date post:	22-May-2018
Category:	Documents
Upload:	phammien
View:	217 times
Download:	1 times

Mathematical Modeling and Experimental Identification … · International Journal of Basic &...

Documents