actuator fault estimation and reconfiguration control for the quad rotor helicopter

International Journal of Advanced Robotic Systems Actuator Fault Estimation and Reconfiguration Control for the Quad-rotor Helicopter Regular Paper Fuyang Chen1,2*, Wen Lei1, Gang Tao3 a

International Journal of Advanced Robotic Systems

Actuator Fault Estimation and

Reconfiguration Control for the

Quad-rotor Helicopter

Regular Paper

Fuyang Chen1,2*, Wen Lei1, Gang Tao3 and Bin Jiang1,2

1 College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, China

2 Jiangsu Key Laboratory of Internet of Things and Control Technologies, Nanjing University of Aeronautics and Astronautics, China

3 Department of Electrical and Computer Engineering, University of Virginia, USA

*Corresponding author(s) E-mail: chenfuyang@nuaa.edu.cn

Received 03 April 2015; Accepted 09 January 2016

DOI: 10.5772/62224

© 2016 Author(s) Licensee InTech This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the

original work is properly cited

Abstract

In this paper, an improved reconfiguration control scheme

via an H∞ fault observer and adaptive control is studied for

the quad-rotor helicopter with actuator faults The bilinear

problem is eliminated by constructing fault compensation

and control law reconfiguration in the adaptive controller

Fault estimation is achieved by designing the fault observer

with an H∞ performance index, which is applied to evaluate

the ‘locking in place’ fault of the actuator in a quad-rotor

helicopter By drawing the H∞ performance index into the

adaptive fault observer, an asymptotically convergent

estimated error can be attained and the burden of the

adaptive controller is alleviated Some simulation and

experimental results confirm the availability of the recon‐

figuration control scheme

Keywords Actuator Fault, Reconfiguration Control,

Quad-rotor Helicopter, Fault Estimation

1 Introduction

The essential needs of surveillance, rescue, military and

security applications put unmanned aerial vehicles (UAV)

have been central to the concerns of researchers and engineers in the last decade than in any period since The quad-rotor helicopter, as a novel type of UAV aircraft, has become an attractive topic, given its new appearance, simple structure, low cost and special features [1-5] However, the possibility of system faults may be increased under some rugged flight conditions Meanwhile, the system behaviour can deteriorate when actuator, sensor or plant faults take place Many control approaches have been investigated for the quad-rotor helicopter, such as back-stepping control [6], sliding mode control [7], LQ control [8] and neural network control [9], to solve these problems Model-based fault detection and isolation (FDI) algorithms have been the subject of intensive investigation over the past two decades [10-14] Furthermore, many schemes considering actuator faults have been proposed in succes‐ sion, such as the observer-based method [15], the parity space method [16] and the multiple model-based method [17] Due to the increasing complexity of the products concerned and the demand for safer processes, more and more attention is being paid to the application of reconfi‐ guration control Considering the stability and good performance of the control system in faulty cases, the fault identification information is needed to realize the reconfi‐

guration of control law Thus, the complex changes of the

system dynamics can be handled rapidly The problems of

fault detection and estimation for non-linear dynamics are

considered by [18] An issue concerning observer-based

integrated robust fault estimation and accommodation of a

class of discrete-time uncertain non-linear systems is

studied by [19] [20] addresses the problem of fault detec‐

tion and diagnosis (FDD) for the quad-rotor helicopter with

actuator faults A sliding model observer-based fault

estimation method is presented by [21] for a class of

non-linear networked control systems with transfer delays [22]

proposes a fault-tolerant control scheme for non-linear

sampled data systems via an Euler approximate observer

But the convergence speed of the estimation algorithm is

also an important factor with respect to the assessment of

the adaptive observer The H ∞ performance index has a

relative fast approximation effect and the estimated error

is expected to converge on the actual fault exponentially

[23] presents an approach to the design of an H ∞ robust

observer-based fault detection scheme for diagnosing

incipient faults [24] addresses sensor fault detection and

isolation problems for linear time-invariant systems, where

the design conditions are derived with H ∞ performance

In this paper, an H ∞ performance index-based fault

observer is designed to compensate for the defect in the

adaptive control The structure of the adaptive controller is

redesigned to avoid the bilinear problem, where the fault

compensation algorithm is also considered The estimated

error of the proposed observer has proved asymptotically

convergent to zero In addition, the estimated error is

shown to be only related to the variance ratio of fault, initial

estimated error and the tracking index ratio, and not subject

to the amplitude of the actuator fault

The following part, Section 2, describes the quad-rotor

dynamics, while actuator fault models are presented and

formulated in Section 3 Section 4 illustrates the design of

the adaptive controller The proposed fault observer is

given in Section 5 in detail Some simulation and experi‐

mental results are shown in Section 6 Finally, conclusions

are drawn in Section 7

2 Quad-rotor Dynamics

The quad-rotor aircraft is controlled by the angular speeds

of four electric motors as shown in Figure 1 Each motor

produces a thrust and a torque, whose combination creates

the main thrust, the yaw torque, the pitch torque and the

roll torque acting on the quad-rotor [25] Conventional

helicopters modify the lift force by varying the collective

pitch Such aerial vehicles use a mechanical device known

as a swash-plate This system interconnects with servome‐

chanisms and blade pitch links in order to change the rotor

blades’ pitch angle in a cyclic manner, so as to obtain the

pitch and roll control torques of the vehicle In contrast, the

quad-rotor helicopter does not have a swash-plate, but has

constant pitch blades Therefore, in a quad-rotor, we can

only vary the angular speed of each one of the four rotors

to obtain the pitch roll control torques

Figure 1 Pitch, roll and yaw torques of the quad-rotor helicopter

The dynamical model of the quad-rotor helicopter is obtained by representing the aircraft as a solid body evolving in a three-dimensional space and subject to the main thrust and three torques: pitch, roll and yaw [26-28] The mathematical model described in this section relies on the following assumption:

Assumption 2.1: The rotations about the x and y axes are decoupled, while the three angles are close to zero when establishing the X , Y , Z model [29]

2.1 Modelling of the rotation

The thrust generated by each propeller can be modelled as

a first-order system described by:

s

w w

=

where u is the PWN input to the actuator, ω is the actuator bandwidth and K is a positive gain A state variable, v, is used to represent the actuator dynamics, which are defined as:

s

w w

=

Two propellers contribute to the motion in each axis The rotation around the centre of gravity is produced by the difference in the generated thrusts The roll/pitch angle θ

can be formulated using the following dynamics:

where

roll picth

are the rotational inertia of the device in roll and pitch axes.

L is the distance between the propeller and the centre of

gravity ΔF represents the difference between the forces

generated by the motors

The motion in the yaw axis is caused by the difference

between the torques exerted by the two clockwise and the

two counter-clockwise rotating propellers The dynamic

equation of the yaw axis can be described by:

y y

where τ = K y u K y is a positive gain, θ y is the yaw angle and

J y is the rotational inertia about the z axis

Δτ(=τ1+ τ2−τ3−τ4) is the resultant torque of the motors

2.2 X, Y, Z dynamics

The motion of the quad-rotor along the X and Y axes is

caused by the total thrust and changing roll/pitch angles,

while the motion in the vertical direction (along the Z axis)

is affected by all the propellers Dynamics of the (X , Y , Z)

can be written as:

4 sin( )

4 sin( )

4 cos( )cos( )

=

=

-&&

&&

where (X , Y , Z) refer to the body-frame Cartesian coordi‐

nates, M is the total mass of the aircraft, r and p respectively

represent the roll and pitch angles, and g is the acceleration

of the gravity

3 Fault Formulation

3.1 System modelling

As shown in Section 2, the non-linear gyroscopic effect

resulting from the rigid body rotation in space and the

coupling of the attitude angles are both ignored to construct

a linear model of the quad-rotor aircraft We can then obtain

a linear control system in this normal form:

x t A x t B u t B d t

y t C x t

ï

ïî

&

(7)

where x p (t)∈ R n p represents the state vector, u p (t)∈ R m p is

the control input vector and y p (t)∈ R q p is the output vector

Here A p ∈ R n p ×n p , B p ∈ R n p ×m p , C p ∈ R q p ×n p d(t) denotes

bounded input disturbance and modelling error

3.2 Fault modelling

Actuator fault is a typical problem of the flight control system and can be divided into two categories according to the level of seriousness: complete failure and partial failure The former type includes locking in place (LIP), hard-over fault (HOF) and floating The latter implies the loss of effectiveness (LOE) in control capability The actuator fault for consideration in this paper can be presented as a second-order model as follows:

=

-&

where u1 describes the position of actuator of each propeller and u2 represents the rate of change of the actuator The coefficient of manoeuvrability, shown by σ i, is used to check whether the actuators can be controlled When σ i=1, it means there is a normal operation of the respective actuator If the LIP and HOF situations occur, then σ i=0 The coefficient of effectiveness is k i and k i ∈ ε, 1 under a LOE problem, where ε < <1, i =1, 2, ⋯m p The condition

k i =σ i=1 indicates there is no fault Moreover, λ 1i > >λ 2i,

λ 1i/λ 2i≥20, λ 1i> >1, λ 2i + β i> >1, i =1, 2, ⋯m p

Remark 3.1: The proposed reconfiguration control scheme

is bound up with the dynamic characteristics of the actuators and the coefficients σ i, k i in model (8) A group of adaptive fault observers can then be designed to estimate

σ i, k i online under different fault scenarios A block diagram

of the proposed control scheme is constructed in Figure 2

4 Adaptive Reconfigurable Control Design

When the dynamic process of the system has some un‐ known faults, the parameters of the reconfigurable control‐ ler are modified automatically to achieve a better response The following linear model of the quad-rotor helicopter with actuator faults is considered:

( )

p

B d t

y t C x t

s

-+

=

&

(9)

where

1 2

p p p

p p p

m m m

m m m

´

´

L

The actuator faults are described by the unknown matrices

Λ, σ and vector u(t) u¯ denotes the LIP position of the actuator

Equation (9) can then be regarded as the perturbation

equation of the system in the equilibrium state

Let f (t)=Λ(I −σ)u¯ + d(t), and we can get:

A linear reference model is selected as follows:

x t A x t B r t

y t C x t

ï

ïî

&

(12)

where x m (t)∈ R n m is the ideal state vector, r(t)∈ R m m is the

reference input vector and y m (t)∈ R q m is the output vector

Here A m ∈ R n m ×n m , B m ∈ R n m ×m m , C m ∈ R q m ×n m

A normal adaptive reconfigurable controller has the

following form [30]:

u t =K x t K r t+ +f t (13)

where K1∈ R m p ×n p and K2∈ R m p ×m m are the adaptive control

gain matrices and f^(t) is the fault compensation vector To

avoid the bilinear problem [31], the construction of the

controller is redesigned as:

ˆ

u t =K x t K r t K e t+ + + f t (14)

where K x ∈ R m p ×n m, K r ∈ R m p ×m m and K e ∈ R m p ×q p Let e = x p − x m

represent the state error vector and e y = y p − y m be the output

error vector, and we can obtain:

ˆ

e x x A x t B u t B f t

A x t B r t

B K B r t B f t f t

& & &

(15)

Consider the matching conditions of the model of referring and we can define:

*

*

*

f t f t

where K x*, K r, K e, f*(t) are attained when the entire matching is fulfilled A e is arbitrary stable system matrix The adaptive reconfigurable control law updates the gain matrices K x (t), K r (t), K e (t) and fault compensation vector

f^(t) online In this way, the state and output of the faulty system, which are guaranteed to be Lyapunov stable, track those of the reference model

Some error matrices and vectors are given as follows:

ˆ

K t K t K f t f t f t

-%

%

Substitute (16)~(20) into (15) and we can finally derive the state error equation:

Figure 3.1 Reconfiguration control scheme for quad-rotor helicopter

4 Adaptive reconfigurable control design

When the dynamic process of the system has some

unknown faults, the parameters of the

reconfigurable controller are modified

automatically to achieve a better response The

following linear model of the quad-rotor helicopter

with actuator faults is considered:

) )

)

) ( ) )

)

t x C t y

t d B

u I B t u B t x A t x

p p p p

p p

p p p

= +

− Λ + Λ +

ɺ

(9)

where

p p p

p p p

m m m

m m m

R diag

R k k k diag

×

×

∈

=

∈

= Λ

} , , , {

} , , , {

2 1

2 1

σ σ σ

⋯ (10)

The actuator faults are described by the unknown

matricesΛ, σ and vectoru(t) u denotes the LIP

position of the actuator

Equation (9) can then be regarded as the

perturbation equation of the system in the

equilibrium state

Letf t)=Λ(I−σ)u+dt), and we can get:

) ) )

) Ax t B ut B f t t

xɺp = p p + pΛ + p (11)

A linear reference model is selected as follows:







= +

= ), ( )

) ) )

t x C t y

t r B t x A t x

m m m

m m m m

ɺ (12) where n m

mt R

x )∈ is the ideal state vector,rt)∈Rm mis the reference input vector and q m

m t R

y )∈ is the output vector

Here m m m m q m n m

m m n m n n

∈

∈

A normal adaptive reconfigurable controller has the following form [30]:

) ˆ ) ) ) K1x t K2rt f t t

uc = p + + (13) where m p n p

R

∈

R

∈

2 are the adaptive control gain matrices and fˆ t) is the fault compensation vector To avoid the bilinear problem [31], the construction of the controller is redesigned as:

) ˆ ) ) ) ) K x t K rt Ke t f t t

uc = x m + r + y + (14) where m p n m

x R

∈ , m p m m

r R

∈ and m p q p

e R

∈ Let e=xp−xm represent the state error vector andey= yp− ymbe the output error vector, and we can obtain:

)]

( ) ˆ [ ) ) (

) ) (

) (

) )

) ) )

t f t f B t r B K B

t x K B A A e C K B A

t r B t x A

t f B t u B t x A x x e

p m r p

m x p m p p e p p

m m m

p p

p p m p

+ Λ +

− Λ +

Λ +

− + Λ +

=

−

−

+ Λ +

=

−

=ɺ ɺ ɺ

(15)

Consider the matching conditions of the model of referring and we can define:

Ap+BpΛKe*Cp=Ae (16)

Ap+BpΛKx*=Am (17)

BpΛKr*=Bm (18)

* ) ) 0

= +

Λf t f t (19) where *

x

K , * r

K , * e

K ,f* t)are attained when the entire matching is fulfilled A is arbitrary stable system e matrix The adaptive reconfigurable control law updates the gain matrices K (t )

x ,K (t )

r ,K (t )

e and fault compensation vector fˆ t)online In this way, the

Quad-rotor Helicopter

Fault Estimation

Reconfiguration Control

m

m

y

y

e

p

y f

fˆ u

c

u

r

−

−

∞

H Index Reference Model

Figure 2 Reconfiguration control scheme for quad-rotor helicopter

[ ( ) ( ) ˆ

r y

e A e B K x t K r t

K e t f t

&

The following adaptive control laws are designed:

1 T T( )

2 T T( )

3 T T( )

4

p

f= -G B Pe

where weighting vectors Γi (i =1, ⋯, 4) are diagonal to

positive definite matrices and P is a positive definite

symmetric solution to the equation:

T

where Q is also a positive definite symmetric matrix

Remark 4.1 The precision of the sensors (including angle

sensors and position sensors) in a quad-rotor helicopter is

relatively high Therefore, measurement of noises can be

ignored compared to the value of the actuator faults

Theorem 4.1 Under the adaptive reconfigurable controller

(14) and adaptive control laws (22)~(25), all signals in the

faulty flight control system can be bounded in a closed loop

Meanwhile:

t e t t e t t C e t

Proof:

A positive definite Lyapunov function can be chosen in the

following form:

2

Then the time-derivative of V is:

1

1

2

ˆ

1

2

e Qe tr K K B Pex t

e

=

&

&

&

% 0

T Qe <

(29)

Therefore, the value of V is degressive; that is:

By integrating (29), we can obtain this:

T

Remark 4.2 The global stability of the system can be

attained by (31) Hence:

5 Fault Observer Design

Fault estimation, conducted by adaptive observers, can obtain information about both the system state and faulty condition The estimating error is surely made convergent

to zero, while the convergence rate should be as high as possible The H ∞ tracking index has an exponential convergence rate of the estimating error and, in turn, the performance of the fault observer may be improved Some assumptions about system (11) are given as follows:

Assumption 5.1:

1. (A p , C p) is completely observable;

2 the rows of C p have full rank;

3.

f.(t) ≤ f0, where f0 is a known constant

The following observer is designed for the faulty system:

ˆ

x t A x t B u t K y t

y t B f t

&

(33)

ˆp( ) p pˆ ( )

f t =K y t y téë - ùû+K y t y téë - ùû

where x^ p (t) denotes the estimated state y^ p (t), y^.p (t)

respectively represent the estimated output and its deriv‐ ative f^(t) is the fault estimation and K p is gain matrix of the proposed observer K i and K v are the matrices to be designed with appropriate dimensions

The state estimation error and fault estimation error are defined as follows:

ˆ

f

Then:

ˆ

( )

p f

e t x t x t A K C e t

B e t

-+

&

(38)

ˆ

e t f t f t K C K C A

K C e t K C B e t f t

-& &

&

We can, therefore, construct the error system in this form:

( )

( ) ( )

( )

( ) ( )

x

x f x

f

e t

e t

f t

e t

A e t B f t

&

&

&

&

(40)

Remark 5.1 The stability of A ef relies on the proper selection

of K p, K i and K v, which are related to the accurate estima‐

tion of the system state and actuator faults

Theorem 5.1 For the error system (40), if P = P T>0,

Q =Q T>0 and K p, K i, K v exist, then the following matrix

equality is fulfilled:

1

0 0 0

T T

Q gI

(41)

in which case, the estimated error has the H ∞ tracking

performance index as:

2 ( )

( )

x

f

e t

where:

A =P A -K C + A -K C P I+ (43)

A =PB -éëQ K C +K C A´ -K C ùû (44)

A = -QK C B - K C B Q +I (45)

and e e x (t)

f (t)

2

=∫

0

t1

e x (t)

e f (t)

T e x (t)

e f (t) d t, f.(t)

2

=∫

0

t1

f.

T

(t) f.(t) d t

denotes the 2 matrix norm The H ∞ tracking index ratios γ >0 and I e, I s, I1 are unitary matrices with appropri‐ ate dimensions

Proof:

A positive Lyapunov function is chosen as:

1

T

V= êée tùú Péêe tùú

while its derivative along system (40) is:

1

( )

T

T x

ef f

e t

P B f t

e t

&

&

(47)

Define the following H ∞ tracking index

1

0

T t

e t e t

J= éêe tù éú êe tùú-gf t f t dt

then, according to (47), we can get

1

1

1

0

0

0

( ) ( )

( ) ( )

(0) ( ) ( ) ( )

T t

t

T t

T T x

ef

e t e t

Vdt

e t e t

f t f t V dt

e t e t V

e t A P P A I P B

e t

f t

g

g

g

+

ò ò ò

& & &

&

& & &

&

1

0

( ) ( ) ( ) (0)

f

e t

e t dt

f t V

+

ò

&

(49)

if

1 1 1

0

T

T ef

A P P A I P B

in which case, the performance index (48) can be obtained

Let P1= P 0 0 Q = P1T>0 ; meanwhile,

1

0

ef

P B

Q

= ê ú

T

A P P A I

Definitions of A11, A12 and A22 can be seen in (43)~(45)

Finally, we derive the following:

(0)

T

e t e t

dt f t f t dt

e t e t

V

g

£

+

Formula (42), then, is fulfilled

Remark 5.2 According to the proposed method by [32], the

upper bound of the estimated error is shown as:

2

0 max 1 min 1 max 1

x

f

l

£

where λmin(P1), λmax(P1) are respectively the minimum and

maximum eigenvalues of matrix P1, while P1, Q1 both

satisfy:

T

Meanwhile, we know that the estimated error is only

associated with the variance ratio of fault, tracking index

ratio and the initial estimated error, and is unrelated to the

amplitude of fault according to Theorem 4.1

6 Simulations and Experiments

6.1 Quad-rotor model parameterization

According to the descriptions in Section 2, general models

of attitude and position can be constructed for the

quad-rotor helicopter In this paper, it is assumed that the

helicopter works near the equilibrium position and

coupling between attitude angles, while X , Y , Z dynamics

can be ignored, in which case linear models of the

quad-rotor helicopter can be attained Choose the angles’ state vector x1(t)= θ, θ y , θ., θ.y ∈ R4 and position state vector

x2(t)= X , Y , Z, X., Y., Z. ∈ R6 with the corresponding

y2(t)= X , Y , Z ∈ R3 The control input vector is

u(t)= u1, u2, u3, u4 ∈ R4 The linear state-space models can then be shown as:

x t A x t B u t

y t C x t

ï

ïî

&

(56)

x t A x t B u t G

y t C x t

ï

ïî

&

(57)

where

0 0 1 0

2

2

2

0 0 0 1 0 0

0 0 0 0 0 0

1

p

C

=

0 0

0 0 0 0 0

0

0 1 0 0 0 0

0

0 0 1 0 0 0

0

G g

é ù

ê ú

ê ú

ê ú

-ê ú The main parameters associated with the quad-rotor model are given in the following table [25]:

Symbol Value Unit

Table 1 Values of the model parameters

Remark 6.1 The above modelling process indicates that

Assumption 5.1 is tenable for the flight control system

Meanwhile, the value of fault is bounded as mentioned in

the following part

6.2 Numerical simulations

In the simulation, it is assumed that LIP takes place in the

front propeller, while the fault occurs at 3s The desired

attitude angles (i.e., pitch, roll and yaw) are [0°, 0.4°, 0.9°],

and the desired body-frame coordinates (i.e., X, Y and Z)

are [0 m, 0.4 m, 4.6 m] The fault can be presented as:

1

(1,1) 0, ( )

t s

s t

ï

ïî

Γ1=Γ2=Γ3=Γ4=diag 0.2, 0.4, 0.1, 0.1, γ =0.01

The gain matrices of the observer (33-35) for (56) are:

K i=

−56 −3.86

−10.002 −0.067

37.65 1.4

−0.007 −2.421

, K v=

−39.008 −76.45

−43.98 −0.543 7.753 45.97

−0.9 −43.36

The gain matrices of the observer (33-35) for (57) are:

K p=

−3.42 93.08 34.44 6.33 −2.84 −98.23

−33.987 4.785 −24.73 98.45 −36.38 0.0043 76.43 0.903 0.763

−0.735 −19.45 −63.41

Meanwhile,

K i=

64.32 43.56 0.0045 43.24 3.94 −0.946

−6.63 −35.32 3.274

−0.342 −49.25 4.264

, K v=

6.462 34.25 23.92 43.21 6.93 −0.234

−5.723 −31.87 5.823

−1.472 −3.92 −0.621

System response curves are respectively shown in Figure

3 and Figure 4, and the estimation curves of the fault can

be found in Figure 5 (simulation time: 10s, 20s)

The curves in Figure 3 show that the desired flight per‐ formance can still be achieved under faulty conditions and that the convergent error goes to zero in a relatively short period of time The position responses in Figure 4 demon‐ strate good reconfigurable ability of the proposed scheme This implies that the quad-rotor helicopter can reach the predetermined position within 3s without any errors Figure 5 indicates that the proposed fault observer (where

γ =0.01) has perfectly estimated the capacity of the LIP fault Therefore, the designed control scheme has provided a direction for the flight control application

6.3 Experiments

The proposed method is also tested on the real-time simulation platform (called Qball-X4 of Quanser Company, see Figure 6) online [29]

The Quanser Qball-X4 is an innovative rotary wing vehicle platform suitable for a wide variety of UAV research applications The whole craft is enclosed within a protec‐

0 1 2 3 4 5

Time/sec

Pitch Roll Yaw

Figure 3 Attitude angles’ responses under the proposed scheme

tive carbon fibre cage, as seen in the Figure 6 The interface

with the Qball-X4 is MATLAB Simulink with QuaRC, while

the controllers can be developed in Simulink with QuaRC

on the host computer These models are then compiled into

the executables on the target quad-rotor helicopter In

experiments, LIP faults occur in the front propeller when artificially restricting the input voltage of a forward motor

to a fixed value This can be achieved by updating param‐ eters on the host computer The experimental results are provided in Figure 7 and Figure 8

-1 0 1 2 3 4

Time/sec

X-position Y-position Z-position

Figure 4 Position responses under the proposed scheme

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Time/sec

fault estimation actual fault

Figure 5 Estimation curves of actuator fault when γ =0.01.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Time/sec

fault estimation actual fault

achieved under faulty conditions and that the convergent error goes to zero in a relatively short period of time The position responses

in Figure 4 demonstrate good reconfigurable ability of the proposed scheme This implies that the quad-rotor helicopter can reach the

estimated the capacity of the LIP fault Therefore, the designed control scheme has provided a direction for the flight control application

6.3 Experiments

The proposed method is also tested on the real-time simulation platform (called Qball-X4 of Quanser Company, see Figure 6) online [29]

Figure 6 Quanser Qball-X4 The Quanser Qball-X4 is an innovative rotary wing vehicle platform suitable for a wide variety of UAV research applications The whole craft is enclosed within a protective carbon fibre cage, as seen in the Figure 6 The interface with the Qball-X4 is MATLAB Simulink with QuaRC, while the controllers can be developed in Simulink with QuaRC on the host computer These models are then compiled into the executables on the target quad-rotor helicopter In experiments, LIP faults occur in the front propeller when artificially restricting the input voltage of a forward motor to a fixed value

This can be achieved by updating parameters on the host computer The experimental results are provided in Figure 7 and Figure 8

Figure 6 Quanser Qball-X4

Some fluctuations in the experimental figures are unavoid‐

able considering the non-linear components in the vehicle

platform However, the trend of these curves can still keep

the flight trajectory steady and as desired on the Qball-X4

In addition, the fault estimation in Figure 8 can be approx‐

imately regarded as asymptotically convergent under the

proposed scheme For comparison, the adaption-based reconfiguration control method proposed by [33] is also tested on the platform (experiments on pitch angle and height) and contrastive curves are shown in Figure 9 Tracking errors need about 1~2s to converge to zero and have some obvious oscillations during the dynamic process

0

2

0 2 4

0 2 4 6 8

Time/sec

Figure 6.5 Tracking errors of attitude angles (°) of the Qball-X4

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Time/sec

fault estimation actual fault

Figure 6.6 Estimation curves of actuator fault tested on the Qball-X4

Some fluctuations in the experimental figures are

unavoidable considering the non-linear components

in the vehicle platform However, the trend of these

curves can still keep the flight trajectory steady and

as desired on the Qball-X4 In addition, the fault

regarded as asymptotically convergent under the

proposed scheme For comparison, the adaption-based reconfiguration control method proposed by [33] is also tested on the platform (experiments on pitch angle and height) and contrastive curves are shown in Figure 6.7

Figure 7 Tracking errors of attitude angles (°) of the Qball-X4

0 2 4

0 2 4

0 2 4 6 8

Time/sec

Figure 6.5 Tracking errors of attitude angles (°) of the Qball-X4

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Time/sec

fault estimation actual fault

Figure 6.6 Estimation curves of actuator fault tested on the Qball-X4

Some fluctuations in the experimental figures are

unavoidable considering the non-linear components

in the vehicle platform However, the trend of these

curves can still keep the flight trajectory steady and

as desired on the Qball-X4 In addition, the fault

regarded as asymptotically convergent under the

proposed scheme For comparison, the adaption-based reconfiguration control method proposed by [33] is also tested on the platform (experiments on pitch angle and height) and contrastive curves are shown in Figure 6.7

Figure 8 Estimation curves of actuator fault tested on the Qball-X4

-10 0

10

-10 0 10

Time/sec

Reference[29]

Proposed

Figure 6.7 Tracking errors of pitch angle(°) and height(m) under different methods

Tracking errors need about 1~2s to converge to zero

and have some obvious oscillations during the

dynamic process under the method designed by

[33] This causes the trembling of the quad-rotor

helicopter in flight, which is sometimes

unacceptable Under the proposed scheme,

however, fast tracking responses can keep the

helicopter more secure and reposeful

7 Conclusions

This paper has provided an improved

reconfiguration control scheme for a quad-rotor

helicopter with an actuator fault by applying the

fault observer with an H performance index and

adaptive control The control law with fault

compensation has been considered in order to deal

with the LIP faults of the actuator in the quad-rotor

The proposed fault observer offers more

identification information to enable precise

reconfigurable ability and compensates for the

defect of direct adaptive control The observer is

enhanced by utilizing the H performance index,

while exponential convergence of the estimated

error is attained The proposed reconfigurable

scheme, then, shows a good capacity for

compensating and estimating the actuator faults

Future work will focus on the multiple faults or

compound failures in the quad-rotor helicopter

8 Acknowledgments

The project was supported by the Aeronautics

Science Foundation of China (2014ZC52033) and the

National Natural Science Foundation of China (61533009, 61374130, 61473146), which is a project funded by the Priority Academic Programme Development of Jiangsu’s Higher Education Institutions

9.References

[1] Dierks, T., and Jagannathan, S (2010) Output feedback control of a quadrotor UAV using neural networks IEEE Transactions on Neural Networks, 21(1), 50-66

[2] Sadeghzadeh, I., Mehta, A., and Zhang, Y (2011, August) Fault/damage tolerant control

of a quadrotor helicopter UAV using model reference adaptive control and gain-scheduled PID In: AIAA Guidance, Navigation, and Control Conference

[3] Liu, H., Lu, G., and Zhong, Y (2013) Robust LQR Attitude Control of a 3-DOF Laboratory Helicopter for Aggressive Maneuvers IEEE Transactions on Industrial Electronics, 60(10), 4627-4636

[4] Kim, G B., Nguyen, T K., Budiyono, A., Park, J K., Yoon, K J., and Shin, J (2013) Design and Development of a Class of Rotorcraft-based UAV International Journal of Advanced Robotic Systems, 10

[5] Cabecinhas, D., Cunha, R., and Silvestre, C (2014) A nonlinear quadrotor trajectory tracking controller with disturbance rejection Control Engineering Practice, 26, 1-10

[6] Honglei, A., Jie, L., Jian, W., Jianwen, W., and Hongxu, M (2013) Backstepping-Based

Figure 9 Tracking errors of pitch angle(°) and height(m) under different methods

10 Int J Adv Robot Syst, 2016, 13:33 | doi: 10.5772/62224