Proceedings of the 2011 IEEE Intemational Conference on Mechatronics

April 13-15, 2011, Istanbul, Turkey

From Integral Backstepping to Integral

Sliding Mode Attitude Stabilization of a

Quadrotor System: Real Time

Implementation on an Embedded Control

System Based on a dsPIC J.1C Sofiane Seghour #1, Mouloud Bouchoucha #2, Hafsa Osmani#3

# Laboratory Control & Command, EMP,

Bordj-El-Bahri, Algiers, 16111, Algeria

lsegsof@live.fr 2mouloud_bouchoucha@yahoo.fr

30smanihafsa@yahoo.fr

Abstract- this work aims to redesign an embedded control

system for an autonomous quadrotor. This embedded

control system is developed based on a DsPic

micro controller. A wireless communication between the

ground station and the system is insured via an Xbee

device and an inertial measurement unit is used for

attitude measurement. Two control algorithms are

implemented in real time on the embedded system for the

attitude stabilization; the Integral backstepping and the

integral sliding mode controllers. The results obtained

show good performance stabilization, demonstrates

superior angles tracking response as well as rejection to

the load disturbance.

Keywords-dsPIC, Dynamic Modeling, Embedded Control

system, IMU, Integral backstepping, integral sliding mode,

PWM, Quadrotor, UA V, �c.

I. INTRODUCTION

Unmanned Aerial Vehicles (UAVs) have been designed in the military field since more than one half century. The main objective was to replace human pilot in a painful tasks and when the environment became hostile where the security of pilots is not assured.

These firsts designed UAV's date from the Second World War; they have the dynamics and dimensions of plans and flew at very high altitudes [1].

Nowadays, researches in this field know a very big progress with the advance development of electronic and digital systems. This progress has given birth to low cost very small and accurate electronic components, a powerful calculators, and sensors. All these, aimed to product a small embedded, autonomous and intelligent systems, able to perform missions with more effectiveness and reliability.

Many universities and research's centre interest to the modeling, the control, and the design of quadrotor system [2]

978-1-61284-985-0/11/$26.00 ©2011 IEEE

[3]. The most part of these works use commercially platforms like UF04, HMX4 and Draganflyer and modify its embedded control systems by adding more sensors and calculators in order to give them more reliability and intelligence [4]. While others work deal with the design and control of new platforms, like the STARMAC project [5] and Mesicopter Project [6].

In this work, we use the Draganflyer four rotors helicopter of RCTOYS as a test bench, in order to replace its electronic part by another control system containing a control unit based on a dsPIC micro controller from Microchip [4]. However, instead of PIC025 power circuit, a speed controller card is realized based on a Mosfet IRLZ44NS to improve the motor control. It receives four P WM motor control signals from the control unit. An inertial measurement unit 3DM-GXl of MicroStrain is used as an attitude sensor. In addition, an internal speed motor controller is added in this work comparing with [4]. The controllers will be implemented in real time and tested on the quadrotor platform by using the developed embedded control system based on the dsPIC microcontroller.

In this paper two control algorithms are implemented in real time for the quadrotor system using the developed embedded system; the integral nonlinear backstepping and the integral sliding mode. The analysis of the system stability and asymptotic angular tracking performance is conducted through the Lyapunov theory. Finally, experimental results are presented to demonstrate that integral backstepping and integral sliding mode approach had achieved superior angular stabilization and tracking performance. However the integral sliding mode proves a more robust behavior and efficiency to compensate the load disturbance than the integral backstepping approach.

II. DEFINITION AND DYNAM ICAL MODEL

A Quadrotor is an aircraft that is propelled by four rotors. This model of rotary wing vehicles is very interesting since

154

the characteristic of taking- off and landing so the space of these manoeuvres is very limited while comparing with fixed­wing aircraft.

The motion of this vehicle is controlled by varying the rotating speed of the four rotors to change the thrust and torques produced by each one. The front and rear motors rotate counter clockwise, while the two other motors rotate clockwise in order to counter the yaw torque produced at the movement of the aircraft [7]. The main thrust derives from the sum of thrusts of each rotor; it creates the vertical motion of the platform. The pitch and roll torques are derived respectively from the differences (Fl - F3 ) and (F2 - F4) , while Fi is the thrust force of the rotor "i". The roll and pitch inclination create the translational motion along X and Y axis respectively.

Fig. 1 Quadrotor helicopter

The yaw torque is the sum of the reaction torques of each rotor produced by the shaft acceleration and the blade's drag Ml - M2 + M3 - M4 with Mi = kdWt and kd is the drag coefficient [4] [8].

The force Fi produced by the rotor "i" is proportional to the square of the angular speed, Fi = bwt with b the proportionality constant of the thrust force.

The dynamics of the quadrotor is described in the space by six degrees of freedom according to the fixed inertial frame related to the ground. This dynamics is related to the translational positions (x, y, z) and the attitude described by the Euler angles (rp, 8, t/J) . These six coordinates are the absolute position of the centre of masse. The Euler angles are defmed as follows:

• Roll angle rp:-'I!. < rp < 'I!.; 2 2 • Pitch angle 8:-'I!. < 8 < 'I!. ; 2 2 • Yaw angle t/J:-rr: < t/J < rr: ;

The rotation transformation matrix from the inertial fixed frame to the body fixed frame is given by:

_ rc{)c'!' C,!,SoS", -C�'!' c"'c�{): S"'S'l'j R- CoS'!' SoS�'I'+�� C�oS,!, ��

-S{) CoS", C{)C'" (1)

S and C represent the Sinus and Co-sinus functions respectively.

To derive the dynamic model of the quadrotor, the Newton Euler formalism will be used on both translation and rotation motions; therefore to obtain the following equations [4] [9] [11].

Where Ft is the thrust force given by

Ff ==R[O 0 tF; r

(2)

(3)

Fdt = kdt(: the drag force, and kdt = diag(kdtx' kdty, kdtz): the drag coefficient of translation.

Fg: the gravity force given by Fg = [0 0 mgF (4) m: the total masse of the quadrotor and g is the gravity

acceleration. I = diagUx,Iy,]z) : the inertia matrix, it is diagonal if we

suppose a symmetrical structure of the quadrotor. 1\ Denote the vector cross-product o : the angular speed expressed in the body fixed frame by:

o== l� �'" �()�'" t lo -S", c",c{) J (5)

T t: the moment created by the quadrotor according to the body fixed frame defined as:

Z'f== d(

F4-

F2) l d(

F

3-

F;) 1 MJ -M2 +M3 -M4

(6) d is the distance from the rotor center to the center of mass

of the quadrotor. T a : the aerodynamic friction torque, T g : the gyroscopic

torque. They are described as follows:

Ta ==kafO 4

Tg == LO 1\ JrW; i:::::l

(7)

(8) Where kat = diag(katx, katy, katz) : are the coefficients

of the aerodynamic friction and Wi is the angular speed of the rotor "i". Ir is the rotor inertia

In this work we mainly focus our interest to the attitude dynamics and we consider the reduced dynamical model as follows[9][11][12]:

l{··C )

2 -· ip = T 8t/J Iy - Iz - ktax<p - Irfl8 + dU2}

x jj = 2. {<ptjJ(Iz - Ix) - ktayf)2 - Jr"fi.<p + dU3} (9) ly

lfi = �{<p(J(Ix - Iy) - ktaztjJ2 + kdU3} z

With:

(10)

155

The rotors are driven by DC-motors with the well known equations [10]: {L di

= V - Ri + keWi dt IrWt = Ti - Qi

(11)

The reactive torque generated by the rotor i, in free air, due to rotor drag is given by [10] Qi = kdWl

III. EMBEDDED C ONTROL SYSTEM ARCHITECTURE

In this section we will describe the embedded control hardware ensuring the attitude stabilisation of the quadrotor; it is composed of four elements: the attitude sensor (IMU), the on board control unit, the speed controller and the wireless communication device. Each element will be detailed in the following sections.

A. Attitude sensor (IMU)

The attitude sensor used in our study is the 3DM-GX1 Inertial Measurement Unit from MicroStrain [4]. It contains three axes magnetometer, gyroscopes, accelerometers and one digital processor which performs the Kalman filter calculations and returns sensor orientations in several formats over a high speed serial link.

Fig. 2 IMU 3DM-GXl from MicroStrain

B. Onboard control unit

We have developed an embedded control board based on the microcontroller dsPIC30F601OA from Microchip.

The first task of this unit is to acquire measurements from different sensors through its input/output ports and uses several modules of communication like UART module for the serial communication RS232, CAN, FC and SPI Buses. It runs at 10MHZ with 144Kbyte on chip flash program space and includes 8 PWM output channels, five 16 bits timers, output -compare module and input -capture module [4].

The second task of this unit is to run control algorithms for the stabilisation of the platform and generate PWM control signals to control its four rotors.

C. Speed controller

To be able to stabilize in plate the quadrotor, we must independently control the speed of the four propellers, and thus of the four D.C. motors. However, controlling motors starting from the microcontroller directly is impossible

because the current drawn by a motor is quite higher than the current admitted by a pin of a micro controller, who is of 25mA. Hence, a speed controller card based on the IR1Z44N Mosfet is realized. We have chosen the Mosfet IR1Z44N. The IRFZ44 in a D2 pack has very small resistance and high power dissipation, which makes them ideal for H-Bride situation. This design adds many more components to current design with four Mosfet and a driver per motor. This interface receives the PWM control signals from a micro controller at a

of 200Hz.

D. Hall Effect Sensor

The rotors speeds are obtained from Hall Effect sensors in combination with little magnets. Two magnets are mounted under the main rotor gear. The magnets pass above the sensor as the gear rotates. The normally high (+5V), output signal pulses switch to low (OV), as each magnet passes above.

Fig. 5 Hall Effect Sensor

The angular speed is then obtained by measuring the time

T Period (s) between two falling edges, it's the time for one rotor revolution in seconds (Fig. 6). Finally the angular speed for one rotor is given by:

w = 21[/ (rad/s) Tperiod

Fig. 6 Hall Effect Sensor Timing Diagram

E. Wireless communication device

To perform wireless communication with a remote computer, we have used two XBee Modems from Maxstream. This wireless device contains an intelligent electronic which allows to perform both a simple point to point communication and a real multi points transmission network.

Data transmission is very simple and seems as a serial transmission along a virtual serial link.

156

Fig. 7 Wireless Serial adaptation board with XBee device.

The quadrotor system with embedded control system, speed controller card and sensors is presented in figure (Fig.8):

Fig.8 The quadrotor with the embedded electronic and sensors

IV. CONTROL LAWS DESIGN

For real time implementation of control algorithms for the attitude stabilization of the quadrotor system, the test-bench in Fig.8 is used. The standard RS232 interface is used to ensure the communication between an embedded control system based on a dsPic30F6010A J.Lc and a PC which is considered as an earth station. The PC earth station is used for tuning the controller parameters, to generate a Euler angles desired trajectory, and to show the output of input control of the qaudrotor (torque input control, motors speeds, Euler angles output). The microcontroller allows the sensors signal acquisition and the control algorithm calculus. Let us point up that the whole algorithm runs at a predefmed sampling time, generated by a timer's interruption. A motor driving circuit using Mosfet has been designed, tested and built. The algorithms of control develop into two parts, an internal loop to control the propellers speed and an external loop to stabilize the attitude of the quadrotor.

A. Rotor Torques Design

To design the rotor torques, the desired rotor velocity Wdi must be determined, the desired rotor speed may then be obtained from (10), and our objective is the control speeds of the four propellers by using the torques Ti ' i = 1,2,3,4 as a control inputs.

We defme the rotor speed error as: IDi = Wi - Wdi Whose time derivative is: w, = w, - W'd, Using model equation in [11] and the above equation we

have:

Irw, = Ti - Qi - IrWdi Therefore, a control law may be developed [10] from the

above equation as follows:

Ti = Qi + IrWdi - KiIDi (12) where Ki ,i = {I, 2, 3, 4} are a controllers parameters.

Applying the above controller one obtains:

w, = - tIDi ( 13)

which shows the exponential convergence of Wito wdi.The physical quadrotor under consideration is powered by four voltage controlled permanent magnet DC motors. Assuming negligible armature inductance: Vi = RIa + keWmi

The equation for the motor torque is given as follows

Tm = kcla The rotor torque '[i can be related to the motor torque '[mb

using the gear ratio N as follows; Tmi = � Similarly, the rotor speed Wi can be related to the motor

speed Wmi using the gear ratio N to give; Wmi = NWj

So we have: Vi=R2+Nkewi (14) Nkc

Assuming no losses, the electrical input power must be equal to the mechanical output power [10] and can be written

v, 1: . as Vila = Tmiwmi � -' = ke =...!!!!. = kc

cum; fa

B. Control Design

The main objective of the control algorithms developed in this paper is to stabilize the attitude of the quadrotor aircraft. The attitude stabilization objective has been achieved using two approaches knows as Integral Backstepping control method, and Integral sliding-mode control method. The benefit within the use of the integral term in both approaches is to improve the tracking errors.

1) Integral Backstepping control approach The Backstepping approach is a recursive algorithm for the

control laws synthesis. This technique offers a systematic Lyapunov choice to design a nonlinear control system and to stability demonstration. If we consider the reduced model of the quadrotor orientation, the system can be written in the

state space as: K = f CK, J!) such that Q is the input vector and

Kthe state vector defined by [9] [11] [12]:

K = [Xl X2 X3 X4 Xs X6] = [tp <p (J iJ 1jJ tjJ] The state model is then given by [8] [10] [11].

Xl =X2

X2 = alx4x6 +a2ili4+bIU2

X3 = X4

X4 =a3x2x6 +a4ili2 +b2U3

Xs = X6

X6 = aSx4x2 +b3U4

Let us consider the following nonlinear system: f x, = Xi+l . . • - " C ) + U

; t = 1,2,3 & ] = 2,3,4 X,+l - Ji Xi, Xi+l Bi j

(15)

(16)

The most common way to include integral action in Backstepping is to use parameter adaptation. Another method is to augment the plant dynamics with the integral state

�, = Xid - Xi [13]. The resulting system is still in strict feedback form; however, the vector relative degree is increased to 3 and two steps of Backstepping is therefore necessary.

157

Step 1: The subsystem is considered {�I � :jd - Xj XI - Xj+l

Where Xi+l is a virtual control, we defInite a new state Zj such as:Zj = Xjd - Xi> and we introduce the fIrst Lyapunov

function: Vi (x) = � z/ + � �/ 2 2 Its time derivative is: Vi ex) = Zj(Sj - Xj+1 + X;d ) If we apply the Lyapunov theorem, i.e. by imposing

Vi ex) � 0 condition, the stabilization of Zi and Si can be obtained by introducing a new virtual control input Xi+1 where:

Xi+1 = X;d + Si + aizi with ai > 0 Step 2: Let us make the change of variable according to

cP = Xi+1 - X;d - Si - ajzj (17) We consider the subsystem

{ �I = Zj Zj = -Sj - ajzj - cP

cb = Fj(Sj,zj,CP) + BjUj with Uj as a real control.

We defme the second Lyapunov function as: V2 (x) =

Vi (x) + �cp2 2

Its time derivative is:

V2 ex) = -ajzj2 + CPCJi(Xj, Xj+l) + BjUj +(at - 2)zj - X;d + ajSj + alz2 )

In a similar way to the preceding step, one can deduce the input control Uj which returns the function of Lyapunov

V2 (x) � 0 so, we obtain: Uj = Bj -1 ( -Ii. (Xj, Xj+1) + (2 + ajaj+1)zj + aj+l Sj -

(aj + aj+1 )(Xj+l-Xld ) + X;d) with aj, aj+l > 0

and the resulting tracking control laws are:

Uz = b1 -1 (a1 X4 X6 + azx� + a3iix4 + (2 + a1az)Zl )

+aZ(l - (a1 + az)xz

U3 = b2 -1 (-a4 Xz X6 + asxt - a6ihz + (2 + a3a4)Zz )

+a4(2 - (a3 + a4)x4

U4 = b3 -1 (a7 X2X4 + asxt + (2 + aSa6)Z3 + a6(3 )

-(as + a6)x6 with: :

• aj > 0 V i = {1, ... ,6} • Zj = Xjd - Xj , i = 1,3,5 • �I = Zj ,i = 1,3,5; • X;d = X;d = 0

2) Integral sliding-mode control approach In this section we use Backstepping and Lyapunov redesign

to introduce sliding mode control, a popular technique for robust control under the matching condition. The fIrst step in this design is similar to the one for the backstepping approach, except for the second step were Sj (Surface) is used instead of

cP for more clearance [14]: Sj = Xj+l - x;d - Sj - ajzj We consider the augmented Lyapunov function:

Vi (x) = �Z.2 + �S.2 + �J:.2 2 I 2 I 2 '> 1

The chosen law for the attractive surface is the time derivative of Si satisfying (SiSl � 0) [14]:

51 = -kjsiBn(Sa - kj+1Sj In the other hand we have:

51 = Ii. (Xj, Xj+1) + BjUj - X;d - Zj - aj( -Sj - alzj - Sj) 51 = Ii. (Xj, Xj+1) + Bj Uj - X;d - Zj + aj(Xj+l - X;d )

As for the Backstepping approach, the control Uj is

extracted as follow : Uj = Bj -1 ( -Ii. (Xj, Xj+1) + X;d + Zj - aj (Xj+1 - X;d )

-kjsiBn(Sj) - kj+1Sj) And the resulting control laws are given by:

U2 = b1-1{(a1x4x6 + a2x� + a3iix4 + Zl - a1(x2 - Xid)

-k1sign(sl) - k2 Stl U3 = b2 -

1{ -a4x2x6 + asxt - a6iix2+z3 - a2(x4 - Xid) (19) -k1sign(sl) - k2 Stl

U4 = b3 -1{a7xZx4 + asxt+z3 - a3(x6 - X;d)

-kssign(s3) - k6s3 } With:

• aj > 0 V i = {1,3,5} • kj > 0 V i = {1, . . ,6} • Zj = Xjd - Xj , i = 1,3,5 • �I = Zj ,i = 1,3,5; • Sj = Xj+1 - X;d - Sj - ajzj Vi = {1,3,5} • X;d = 0

V. REAL TIME IMPLEMENTATION

In order to validate the control law developed in the previous section, we implemented the controller on the embedded control unit, the sampling period is 30ms. We carried out several experiments to stabilize the orientation of vehicle. The altitude was then fIxed by the operator. We have implemented the Integral Backstepping controllers on the real system, the controllers Parameters were tuned by trial and error, until obtaining a better responses performance of the system.

In the fIrst experiment, the Integral backstepping controller is used to stabilize the system and maintain the roll, pitch and yaw angles in zero. The desired thrust U1 and gain ki used for the motor torques control design were kept at UJ. =2 .6, Kj = 0.004. The Parameters of controllers are taken: al =

8.56, a2 = 11.6, a3 = 8.96, a4 = 9.03, as = 3.92, a6 = 2.96. The results show the aircraft angles (fIg.9), control inputs and speed propeller rotation for each rotor (fIg. 10). 15 10,-,-'-:'-,-..,.--,.--,-,-- -,-..,-,

110 -: - � -: � - :- � - � -: - � - j' oH;:::"'::;>'L;=��-=?' .q'�' '9 6b I I I I I I I I I 6b I I I I I I I I I ! 5 �-10 - 1- t-- I-;-- t- - 1- t- - I- ;--

I I I ..s:::l I I I I I I I I I

Fig.9

B -20 -1-+.-1--.+-1- -1-+. -1--.+-p: I I I I I I I I I

2 3 4 5 6 7 8 9 10 -300 1 2 3 4 5 6 7 8 9 10 Time (s�gr-) -,-.,--;r-r-.----.-..,.--,-,--,Time (sec) ]' 30 -: - � -: - � -:- � -:- � - � t �: � � 0�\T������

-100 1 2 3 4 5 6 7 8 9 10 Time (sec)

outputs angles stabilization (Integral Backstepping approach)

158

I I I , ,

I I E I , , , , , , 2S I I I I 1 I I I S 0.5

1 A 1- I - 1- I - 'I -I I

lit I I I I I I I I � 0 ' T,tp ,.;on "A, .... I V" I I I T I I I :: -0.5 -I - I- -+ - I- -+ - - -I 1- -+ -g I I I I I I I I I

1234 5 6 7

Time (sec) 8 9 10 8 -10 I 2 3 4 5 6 7 8 9 10

Time (sec)

I I I I I I

I I

: : I �l� :: -I I I I I I I �:=:r��:::;��� 'E I I I I I I I T I -, r l -r r .� -0.05 ! r ! - r l- r - - I - 1- � I I I I I I I I I I I I I e +- -1- -+ - I- --l -J �IO � -� � -� � -� -7

-� -� -1 0 J I 2 3 4 � � 7 � � 10 Time (sec) Time (sec)

Fig.10 Control inputs and speeds propellers (Integral Backstepping approach)

In the second experiment, after having stabilized the quadrotor in horizontal plane, we added a mass of 50mg as a disturbance on one of the end of the roll axis.

E 0.5

�5,----_--_-_--, 1 10 S 5 -

� Ob::f-'------J-----'U"'-'-'-"--'/i -so \10 /5 20

Time (sec)

Fig. 11 Roll response with disturbance

b � 180 I I I ......... 160 --- 1----1----1---

1l 140 - ---,----,---� 120r ---:----;----,---

S -' - -' -, ,

= 100 _ ---, ---,----,---j !:--�---;';:------O':----;!20' ! 800 5 io is 20 ] " -10

8 10 15

Time (sec) Time (sec)

Fig. 12 Control inputs and propellers speeds (integral Backstepping approach)

We make the same for pitch angle; we added a mass of 50mg as disturbance.

-;;;-10 [

� O f-L-'l'...-"r---'----;:t';;Mck-tr.....-:! � ..c::-IO B p:;

-200L----'c--�ILO

--iI5�--='

20 Time (sec) Fig. 13 Pitch response with disturbance

e - � .... 180

b ' ,;,.. " -S 05 - - -I'"..l':' 'Jt);j � - - 1l 160

.� . �. L" : �9/II't�I#II'YI� � 140

" O��"': : f-� 11120 ] I I � 8 -0.50 5 10 15 20 g. 100

0 15

Time (sec) Jt Time (sec) 20

Fig. 14 Control input and propellers speeds (Pitch disturbance)

In the fourth experience, the closed-loops were tested for a

cycloid reference with tf = 10ms , Di = Xdi (tf ) - Xdi (0) and Xdl (tf) = Xd2 (tt) = +8, Xd3 (tt) = +20.

( ) _ {Xdi (0) + 2Di [2TC!.. - sin (2TC !..)] if 0 :5 t :5 tf Xdi t - TC tf tf

Xdi (tf) if t > tf

and then for a sinusoidal reference with Xdi (t) =

Xdi (O)sin C; t) , Xdl (0) = Xd2 (0) = 8 , Xd3 (0) = 20 and

T=36 ms, The Parameters of controllers: (11 = 9.6 , (12 =

13.8, (13 = 8.3, (14 = 13, (15 = 4.16, (16 = 2.9. 15

10 20 30 40 SO 60 70 80 Time (sec)

90 100 110 120

l[ :.--'-.-.--.-�-r-' l[ ::lr-.,-.-,-,---,--.-.-, � 0 � 0

� -20 l -20

� � -40

0 10 20 30 40 50 60 70 5 10 15 20 25 30 35

Time (sec) Time(sec) Fig. 15 Desired Angles (Red) and real Angles outputs (Blue)

Then, we have implemented the sliding mode. The experimental conditions were similar to those applied for the Integral backstepping controller. We tried to maintain the same initial states for the three angles and we obtained stabilization in less than 3 seconds. The desired thrust U1 and gain Kiused for the motor torques control design were kept at U]=2.6N, Ki = 0.004.The controllers parameters are taken: (11 = 8 , kl = 10 , k2 = 6, (13 = 8 , k3 = 10 , k4 = 4.6 , (15 = 4.15, ks = 1.52,k6 = 1.36.

The following graphs show the obtained performances: '"' 15 ;='----'--T, -., -'-', -', -.-.---, � 101 r � r r r r � r r I 1105 -,-r -,-r -I-r-I-T-I- 1 0 I I I I I I

-; - I- ---l- +- -- + -- + -- '.;;;.,1 -10 -1-1- -1-1- -1-1- -1-1- --'..,;...' I I I I I I � 0 , I � _20p-I--l-I---l-I---l-I---l-51 : : : I : :: . . � - 0 I 2 3 4 5 6 7 9 10 -300 1 2 3 4 5 6 7 8 9 10 Time(sec) Time (sec) 15.-,-,-,-,-,-,-,-,-,-,

I I I I

I I I I - 50 I 2 3 4 5 6 7 8 9 10 Time(sec) Fig.16 Output angles stabilization (integral sliding mode controller)

'E' � 0.5 -+ - 1- -+ -1- + -1- +- -4-1-, , , I I I , , , 'E' � 0.5 0 � 0

j -0-�0!:-1C-:2�3�4"---!5"---!6,.---;!;7,.---;!;8�9--;" Time (sec)

,i 10 ) -0.5 -

- 10 2 3 Time (sec) 4 E g

� 160 I I I I I I I I I

1l 140 -t c:'i�:t:t;;���� .i -0 02 1 :- � : � :- �

) -0.040 � �-: � : -� 7 8 � : : � : � : 10 Time (sec) � Time (sec)

Fig.17 Control inputs and speeds propellers (integral sliding mode approach)

159

In the robustness test to external load disturbance and for more convenience, we have maintained the same work conditions; a mass of 50 Mg is fixed on the end of the roll axis.

'E'

Il I I I j

I'�LS:��J o 5 10 IS 20 Time (sec) Fig. 18 Roll response with disturbance

---"--- ....:. --- '----, , , � 05

.i _o :I-c- ; .. ,o.L-"" -"""''''''"twI'''¥MI'''I''I � ] - 10�� =lloO � 5 . 10 15 20 0 10 IS TIme (sec) Time (sec)

Fig. 19 Control inputs and propellers speeds (Roll disturbance)

20

The same for axis of Pitch, we added a mass of 50mg as disturbance.

1 : ,imt--�'1""'-'¥1 � ] -5 ll:; -100 5 10 IS 20 Time (sec)

Fig. 20 Pitch response with disturbance

: � � - '- - - 1

, � 15 20 25 30 J 1O<j':-0 ---::1'::-5 ---='::----='::---='. Time (sec) Time(sec)

Fig. 21 Control inputs and propellers speeds (Pitch disturbance)

The last experience, the closed-loops were tested for a

cycloid reference with tf = 10ms ,Di = Xdi (tf) - Xdi (0)

and Xdl (tt) = Xd2 (tt) = +s, Xd3 (tt) = +20. {Xdi(O) + 2Di [211"� - sin (211"�)] if 0 :5 t :5 tf Xdi (t) = 11" tf tf Xdi (tf ) if t > tf

and then for a sinusoidal reference with Xdi (t) =

Xdi (O)sin C; t) , Xdl (0) = Xd2 (0) = 8 , Xd3 (0) = 20 and

T=36 mS, The Parameters of controllers: U1 = 7.76 , kl =

10.56 , k2 = 6.4, U3 = 8.1 ,k3 = l1.35,k4 = 5.51,us = 4.16 , ks = 1.92,k6 = 1.92. A. Comparative study:

The experimental results presented below, show that the two controllers arrives to stabilize the quadrotor attitude, with a response time lower than 3 second for the Roll and Pitch and less than 5 second for Yaw, with slight superiority in the integral sliding mode controllers comparing with integral bacstepping controllers. The small oscillation around zero is due to a small amplitude of measurement of the angles generated by the inertial sensors.

In robustness tests; and in presence of an external disturbance, the results shows that the integral sliding-mode controller presents a better behavior than that in the integral Backstepping controller, as we can observe, the error of angle

at the time when we added the mass on the Roll axis or pitch axis one using the integral sliding-mode (about 5 degrees on Roll and 8 degrees on Pitch) is lower than that when the integral backstepping is used (about 10 degrees on Roll and 14 degrees on Pitch). While the time necessary to return to the equilibrium state is about 7 seconds when the integral sliding­mode is used and about 10 seconds one using integral backstepping.

I 20

& ·10 .200 20 120

,

-400 10 20 30 40 50 60 70 -400 5 10 IS 20 25 30 35 40 Time(sec) Time (sec)

Fig. 22 Desired Angles (Red) and real Angles outputs (Blue)

VI. CONCLUSIONS

This paper presents the design of an embedded control system for the attitude stabilisation of quadrotor VA V. An embedded control unit has been developed to acquire measurements from several sensors and performs control law algorithms to stabilize the attitude of the platform. In our case, an IMV 3DM-GXl is used as an attitude sensor. The rotation speed of the propeller for each rotor is obtained from Hall Effect sensors in combination with little magnets. Two control algorithms are implemented in real time using the embedded control system for the attitude stabilization of the quadrotor helicopter; the integral backstepping algorithm and the integral sliding mode algorithm. The experimental results obtained demonstrate good performance stabilization and tracking for both controllers with slight superiority of the sliding mode controller. However one notices a more robustness and efficiency for the integral sliding mode controller to the external disturbances rejection.

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