actuator fault estimation and reconfiguration control for the quad rotor helicopter

International Journal of Advanced Robotic Systems ARTICLE Actuator Fault Estimation and Reconfiguration Control for the Quad-rotor Helicopter Regular Paper Fuyang Chen1,2*, Wen Lei1, Gang Tao3 and Bin Jiang1,2 College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, China Jiangsu Key Laboratory of Internet of Things and Control Technologies, Nanjing University of Aeronautics and Astronautics, China 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, Quadrotor Helicopter, Fault Estimation 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 backstepping 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‐ Int J Adv Robot Syst, 2016, 13:33 | doi: 10.5772/62224 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 nonlinear 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 Section illustrates the design of the adaptive controller The proposed fault observer is given in Section in detail Some simulation and experi‐ mental results are shown in Section Finally, conclusions are drawn in Section only vary the angular speed of each one of the four rotors to obtain the pitch roll control torques Figure 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: F=K Int J Adv Robot Syst, 2016, 13:33 | doi: 10.5772/62224 u (1) 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: v= Quad-rotor Dynamics The quad-rotor aircraft is controlled by the angular speeds of four electric motors as shown in Figure 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 w s+w w u s+w (2) 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: Jq&& = DFL (3) J = Jroll = J picth (4) where 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: J yq&&y = Dt is the rotational 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 secondorder model as follows: (5) where τ = K y u K y is a positive gain, θy is the yaw angle and Jy 3.2 Fault modelling inertia about the z axis Δτ( = τ1 + τ2 − τ3 − τ4) is the resultant torque of the motors u& 1i = u2 i u& i = - éël2 i + ( - s i ) b i ùû u2 i + s i l1i ( kiuci - u1i ) (8) 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 σi , is used to check 2.2 X, Y, Z dynamics whether the actuators can be controlled When σi = 1, it 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: means there is a normal operation of the respective actuator If the LIP and HOF situations occur, then σi = The coefficient of effectiveness is ki and ki ∈ ε, under a LOE problem, where ε < < 1, i = 1, 2, ⋯ mp The condition ki = σi = indicates there is no fault Moreover, λ1i > > λ2i , λ1i / λ2i ≥ 20, λ1i > > 1, λ2i + βi > > 1, i = 1, 2, ⋯ mp && = F sin( p) MX && = -4 F sin(r ) MY (6) && = F cos(r )cos( p) - Mg MZ Remark 3.1: The proposed reconfiguration control scheme is bound up with the dynamic characteristics of the actuators and the coefficients σi , ki in model (8) A group of adaptive fault observers can then be designed to estimate 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 Fault Formulation 3.1 System modelling σi , ki online under different fault scenarios A block diagram of the proposed control scheme is constructed in Figure 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: 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: np L = diag{ k1 , k2 , L , kmp } Ỵ R represents the state vector, up (t) ∈ R mp is the control input vector and yp (t) ∈ R is the output vector Ap ∈ R np ×np , Bp ∈ R np ×mp , Cp ∈ R qp ×np (9) y p (t ) = C p x p (t ) (7) qp Here + Bp d(t ) where ìï x& p (t ) = Ap xp (t ) + Bpup (t ) + Bpd(t ) í ïỵ y p (t ) = C p xp (t ) where xp (t) ∈ R x& p (t ) = Ap xp (t ) + Bp Lu(t ) + Bp L( I - s )u d(t) denotes bounded input disturbance and modelling error mp ´ mp s = diag{s , s , L ,s mp } Ỵ R mp ´ mp (10) The actuator faults are described by the unknown matrices Λ, σ and vector u(t) u¯ denotes the LIP position of the actuator Fuyang Chen, Wen Lei, Gang Tao and Bin Jiang: Actuator Fault Estimation and Reconfiguration Control for the Quad-rotor Helicopter xm Reference Model ym ey − f u Quad-rotor Helicopter yp r − H ∞ Index fˆ Fault Estimation uc Reconfiguration Control Figure 3.1 Reconfiguration control scheme for quad-rotor helicopter Figure Reconfiguration control scheme for quad-rotor helicopter Adaptive reconfigurable control design Equation (9) can then be regarded as the perturbation When the dynamic of thestate system has some equation of the system in theprocess equilibrium unknown faults, the parameters Let f (t) = Λ(I − σ)u¯ + d(t), and controller we can get: are reconfigurable of the modified automatically to achieve a better response The following linear model of the quad-rotor helicopter x& p (t ) = Ap xp (t ) + Bp Lu(t ) + Bp f (t ) (11) with actuator faults is considered: xɺ p (t ) = Ap x p (t ) + B p Λu (t ) + B p Λ( I − σ )u (9) + B p d (t ) A linear reference model is selected as follows: y p (t ) = C p x p (t ) - AKm2x∈m (Rtm)p-×mmBmare r(t ) the adaptive where K1 ∈ R m p ×n p and ˆ ) ( ) xmfault (t ) = ( Again + B L K C e + A A control matrices and isp LK the f m(t )+ B p p e p p x m ×m x {k(t,)k+,B r(t ) ïì x& m (t )Λ==A m m m diag ⋯ , km } ∈ R í ( ) ( ), y t C x t = ïỵ m m ×m m m σ = diag {σ , σ , ⋯ , σ } ∈ R p compensation+ vector ( Bp LKr To )r(t )the [ Lfˆ (t ) +problem - Bavoid + Bpbilinear f (t )] m [31], the construction of the controller is redesigned as: Consider of referring uc (t ) = K xthe xm (tmatching ) + K r r (t ) +conditions K e e y (t ) + fˆ (tof ) the model(14) m ×n and we K can∈ define: where , Kr ∈ Rm R x p p (12) (10) p mp The actuator faults are described by the unknown n Λ , σ and vector u (t ) u denotes mmthe LIP matrices where xm(t) ∈ R m is the ideal state vector, r(t) ∈ R is the position of the actuator q reference Equation input vector and y (t) ∈ R m is the output vector (9) canm then be regarded as the perturbation equation of the n ×n n ×m q ×n system in the Here Am ∈equilibrium R m m, Bm ∈ R m m, Cm ∈ R m m state Let f (t ) = Λ( I − σ )u + d (t ) , and we can get: A normal adaptive reconfigurable controller has the (11) xɺ p (t ) = Ap x p (t ) + B p Λu (t ) + B p f (t ) following form [30]: A linear reference model is selected as follows:  xɺ m (t ) = Am xm (t ) + Bm r (t ) (12) ˆ uc (t ) = K1xyp (t(t))+= K (13) C2mrx(mt ()t+ ), f (t )  m where xm (t ) ∈ R nm is the ideal state vector, r (t ) ∈ R mm is the mreference inputm ×m vector and ym (t ) ∈ R qm is the p ×np and K ∈ R p m are the adaptive control output vector ^ gain matrices and f (t) is the fault compensation vector To Here Am ∈ R nm ×nm , Bm ∈ R nm ×mm , Cm ∈ R qm ×nm where K ∈ R avoid the bilinear problem [31], the construction of the controller is redesigned as: uc (t ) = K x xm (t ) + Kr r(t ) + K e e y (t ) + fˆ (t ) , Kr ∈ R mp ×mm (14) and K e ∈ R mp ×qp and K e ∈ R m p ×q p can obtain: eɺ = xɺ p − xɺm = Ap x p (t ) + B p Λu (t ) + B p f (t ) LK * = Am p r (tx) − AmA xmp(t+) −BB m (15) (16) (17) = ( Ap + B p ΛK eC p )e + ( Ap − Am + B p ΛK x ) xm (t ) + ( B p ΛK r − Bm )r (t )*+ B p [Λfˆ (t ) + f (t )] Bp LKr = Bm Consider the matching conditions of the model of referring and we can define: * (16) Ap +LB f *p(ΛtK ) +e Cfp(=t )A=e Ap + B p ΛK x* = Am (17) B ΛK * = B (18) (18) (19) * m p * r where K x*, K r*, K e , f (t) are attained when the entire (19) Λf * (t ) + A f (t )is= arbitrary stable system matrix matching is fulfilled e * * * * where K x , K r , K e , f (t ) are attained when the entire The adaptive reconfigurable control law updates the gain matching Kis (t) fulfilled is arbitrary system vector Ae (t) , K r (t), K and faultstable compensation matrices x e ^ matrix The Inadaptive reconfigurable lawthe faulty f (t) online this way, the state and control output of updates the gainare matrices K rbe (t ) ,Lyapunov K x (t ) ,to K e (t ) and fault system, which guaranteed stable, track compensation vector fˆmodel (t ) online In this way, the those of the reference Some error matrices and vectors are given as follows: K% e (t ) = K e (t ) - K e* , f% (t ) = fˆ (t ) - f * (t ) K% (t ) = K (t ) - K * , K% (t ) = K (t ) - K * x x r r (20) r Let e = xp − xm represent the state error vector and ey = yp − ym be the output error vector, and we can obtain: p × mm +B LK e Cerror = Ae vector, and we and e y = y p − ym be Athe output p p p x mp ×nm m * p p where K x ∈ R (15) Let e = x p − xm represent the state error vector where A normal adaptive reconfigurable controller has the following form [30]: e& =ucx&(tp) -= x&Km1 x=p (tA (13) ) +p xKp2(rt()t+ ) +BfpˆL (t u ) (t ) + Bp f (t ) Int J Adv Robot Syst, 2016, 13:33 | doi: 10.5772/62224 Substitute (16)~(20) into (15) and we can finally derive the state error equation: Therefore, the value of V is degressive; that is: e& = Ae e + Bp L[K% x xm (t ) + K% r r(t ) (21) + K% r e y (t ) + fˆ (t )] £ V (t ) £ V (0), V (t ) ẻ LƠ The following adaptive control laws are designed: K& x = -G1BTp PexTm (t ) By integrating (29), we can obtain this: (22) ¥ K& r = -G BTp Per T (t ) (23) K& e = -G BTp PeeTy (t ) (24) & fˆ = -G BTp Pe (25) where weighting vectors Γi (i = 1, ⋯ , 4) are diagonal to positive definite matrices and P is a positive definite symmetric solution to the equation: AeT P + PAe = -Q (26) 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: lim e(t ) = 0,lim e y (t ) = lim C p e(t ) = t đƠ t đƠ t đƠ (27) Proof: A positive definite Lyapunov function can be chosen in the following form: V = [eT Pe + tr( K% Tx G1-1LK% x ) + tr( K% rT G -21LK% r ) + tr( K% eT G -31LK% e ) + f% T G -41Lf% ] (28) Then the time-derivative of V is: & & V& = eT Pe& + tr( K% Tx G1-1LK% x ) + tr( K% rT G -21LK% r ) & & + tr( K% eT G -31LK% e ) + f% T G -41Lf% & = - eT Qe + tr[K% Tx G1-1L( K% x + G1BTp PexTm (t )) & & + K% rT G -21L( K% r + G BTp Per T (t )) + K% eT G -31L( K% e & + G BTp PeeTy (t )] + f% T G -41 ( fˆ + G BTp Pe ) = - eT Qe < (30) ¥ & = V (0) - V (¥) and I e , I s , I are unitary matrices with appropri‐ ate dimensions Proof: (39) A positive Lyapunov function is chosen as: T é e x (t ) ù é e x (t ) ù V =ê ú P1 ê ú e ( t ) êë e f (t ) ûú ëê f ûú We can, therefore, construct the error system in this form: A p - K pC p Bp ù é e&x (t ) ù é ú ê ú=ê & ëê e f (t ) ûú êë -[ KiC p + K vC p ( Ap - K pC p )] - K vC p Bp úû é e x (t ) ù é0 ù ·ê ú + ê ú f& (t ) êë e f (t ) úû ë I û é e x (t ) ù = Aef ê ú + Bef f& (t ) ëê e f (t ) ûú (46) while its derivative along system (40) is: T é e x (t ) ù é e x (t ) ù T V& = ê ú [ Aef P1 + P1 Aef ] ê ú êë e f (t ) úû êë e f (t ) úû (40) T é e x (t ) ù + 2ê ú P1Bef f& (t ) ëê e f (t ) ûú Remark 5.1 The stability of Aef relies on the proper selection (47) Define the following H ∞ tracking index of K p , K i and K v , which are related to the accurate estima‐ tion of the system state and actuator faults T t1 é e x (t ) ù é e x (t ) ù T J=ò ê ú ê ú - g f& (t ) f& (t ) dt ( ) ( ) e t e t ê f ûú êë f ûú ë Theorem 5.1 For the error system (40), if P = P T > 0, Q = Q T > and K p , K i , K v exist, then the following matrix equality is fulfilled: é A11 ê T ê A12 ê ë then, according to (47), we can get A12 A22 -QT ù ú -Q ú < -g I1 úû (41) t1 J=ò t1 performance index as: t1 t ³ are chosen 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: − 56 − 3.86 − 39.008 − 76.45 − 10.002 − 0.067 − 43.98 − 0.543 , Kv = Ki = 37.65 1.4 7.753 45.97 − 0.007 − 2.421 − 0.9 − 43.36 Int J Adv Robot Syst, 2016, 13:33 | doi: 10.5772/62224 as: 34.44 − 98.23 − 24.73 0.0043 0.763 − 63.41 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 and Figure 4, and the estimation curves of the fault can be found in Figure (simulation time: 10s, 20s) The curves in Figure 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 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 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‐ Position Responses X-position Y-position Z-position -1 Time/sec 10 4.5 Figure Position responses under the proposed scheme 3.5 fault estimation actual fault 4.5 f(t) 42.5 3.5 fault estimation actual fault 1.5 f(t) 2.5 0.5 0 1.5 10 Time/sec 12 14 16 18 20 Figure Estimation curves of actuator fault when γ = 0.01 The curves in Figure show that the desired flight performance 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 Figure0.5 demonstrate 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 indicates that the proposed fault observer (where γ = 0.01 ) has perfectly estimated the Therefore, the designed control scheme a direction for18 the flight20 control application capacity 2of the LIP fault 10 12 has provided 14 16 6.3 Experiments Time/sec The proposed method is alsoγtested = 0.01.on the real-time simulation platform (called Qball-X4 of Quanser Company, see Figure Estimation curves of actuator fault when Figure 6) online [29] Figure Quanser Qball-X4 Figure Quanser Qball-X4 The Quanser Qball-X4 is an innovative rotary wing vehicle platform suitable for a wide variety of UAV research applications Theinwhole craft is enclosed a protectiveexperiments, carbon fibre cage,LIP as seen in theoccur Figurein The with tive carbon fibre cage, as seen the Figure Thewithin interface faults theinterface front propeller when the Qball-X4 is MATLAB Simulink with QuaRC, while the controllers can be developed in Simulink with QuaRC on the with the Qball-X4 host is MATLAB Simulink with QuaRC, while artificially restricting the input voltage of a forward motor computer These models are then compiled into the executables on the target quad-rotor helicopter In experiments, the controllers canLIPbefaults developed infront Simulink to a fixed value This be motor achieved by value updating param‐ occur in the propellerwith whenQuaRC artificially restricting the input voltage of a can forward to a fixed This can be achieved by are updating the host computer The experimental results are The provided in Figure results are on the host computer These models thenparameters compiledoninto eters on the host computer experimental and Figure the executables on the target quad-rotor helicopter In provided in Figure and Figure Fuyang Chen, Wen Lei, Gang Tao and Bin Jiang: Actuator Fault Estimation and Reconfiguration Control for the Quad-rotor Helicopter 4 Yaw Yaw 2 0 0 1 2 33 44 55 66 77 88 9 10 10 1 2 33 44 55 66 77 88 10 10 1 2 33 44 55 Time/sec Time/sec 66 77 88 9 10 10 Pitch Pitch 4 2 0 0 8 6 Roll Roll 4 2 0 0 Figure Tracking errors of attitude angles (°) of6.5 the Tracking Qball-X4 Figure errorsofofattitude attitudeangles angles(°) (°) of of the the Qball-X4 Qball-X4 Figure 6.5 Tracking errors 4.5 4.5 4 3.5 3.5 fault estimation fault estimation actual fault actual fault f(t) f(t) 2.5 2.5 2 1.5 1.5 1 0.5 0.5 0 0 10 Time/sec 10 Time/sec 12 12 14 14 16 16 18 18 20 20 Figure Estimation curves of actuator fault tested on the Qball-X4 Figure 6.6 Estimation curves of actuator fault tested on the Qball-X4 Figure 6.6 Estimation curves of actuator fault tested on the Qball-X4 10 Pitch( 。 ) Some fluctuations in the experimental figures are Some fluctuations in the experimental are unavoidable considering the non-linear figures components unavoidable considering the non-linear components in the vehicle platform However, the trend of these curves can still keep the flight trajectory steady and in the vehicle platform However, the trend of these as desired the the Qball-X4 In addition, the and fault -10 flight trajectory curves can stillonkeep steady 6.6 In canaddition, be approximately as estimation desired on intheFigure Qball-X4 the fault regarded in as asymptotically under the estimation Figure 106.6 canconvergent be approximately Reference[29] proposed scheme For comparison, the adaptionProposed proposed scheme Forcontrol comparison, adaptionbased reconfiguration methodthe proposed by based control method proposedon by [33] isreconfiguration also tested on the platform (experiments pitch and height) contrastive curves are [33] is angle also tested on theand platform (experiments on shown in Figure 6.7 pitch angle and height) and contrastive curves are 10 shown in Figure 6.7 Height(m) regarded as asymptotically convergent under the -10 Time/sec Figure Tracking errors of pitch angle(°) height(m) underof different methods Figure 6.7 and Tracking errors pitch angle(°) 10 Tracking errors about 1~2sfigures to converge to zero Some fluctuations in theneed experimental are unavoid‐ and have some obvious oscillations during the able considering the non-linear components in the vehicle dynamic process under the method designed by platform However, the trend of these curves can still keep [33] This causes the trembling of the quad-rotor the flight trajectory steady and as desired on the Qball-X4 helicopter flight, in which sometimes In addition, the faultin estimation Figure is can be approx‐ unacceptable Under the proposed scheme, imately regarded as asymptotically convergent under the however, fast tracking responses can keep the helicopter more secure and reposeful Int J Adv Robot Syst, 2016, 13:33 | doi: 10.5772/62224 Conclusions This paper has provided an improved 10 and height(m) under different methods National Foundationtheofadaption-based China proposed Natural scheme Science For comparison, (61533009, 61374130, 61473146), which is a project reconfiguration control method proposed by [33] is also funded Priority(experiments Academic on Programme tested onbythethe platform pitch angle and Development of Jiangsu’s Higher height) and contrastive curves are shownEducation in Figure Institutions Tracking errors need about 1~2s to converge to zero and have some obvious oscillations during the dynamic process 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 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 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 ∞ perform‐ ance 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 Acknowledgements 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 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 quad‐ rotor 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 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Gang Tao and Bin Jiang: Actuator Fault Estimation and Reconfiguration Control for the Quad- rotor Helicopter xm Reference Model ym ey − f u Quad- rotor Helicopter yp r − H ∞ Index fˆ Fault Estimation. .. Lozano, R (2014) Fault Estimation for a Quad- Rotor Fuyang Chen, Wen Lei, Gang Tao and Bin Jiang: Actuator Fault Estimation and Reconfiguration Control for the Quad- rotor Helicopter 11 [21] [22]... ∞ perform‐ ance 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