A quadrotor helicopter with uncertain actuator faults, such as loss of effectiveness and lockinplace, is studied in this paper. An adaptive fuzzy sliding mode controller based on direct selfrepairing control is designed for such nonlinear system to track the desired output signal, when any actuator of this quadrotor helicopter is loss of effectiveness or stuck at some place. Moreover, using the Lyapunov stability theory, the stability of the whole system and the convergence of the tracking error can be guaranteed. Finally, the availability of the proposed method is verified by simulation on 3DOF hover to ensure that the system performance under faulty conditions can be quickly recovered to its normal level. And this proposed method is also proved to be better than that of LQR through simulation.
Quadrotor helicopter is one kind of electric VTOL. Compared with the conventional rotor helicopter, quadrotor can generate more lift force and its structure is more compact. Especially, its four rotors can counteract the reaction torque mutually, so the propellers against reaction torque are not needed [
On the other hand, quadrotor, which is the underactuated system with 6DOF and 4 outputs, has the properties of multivariety, nonlinearity, strong coupling, and sensitivity to disturbance. Once it has some faults, it may lead to the loss of performance of flight, even loss of control. Thus, selfrepairing control is born.
Selfrepairing control, which utilizes the redundancy of the control system under normal working condition to improve the adaptability to the fault of the flight control system, can avoid catastrophes and make the faulty aircraft operate safely. Then, selfrepairing control consists of the direct one and the indirect one. Direct selfrepairing control does not need accurate system parameters, while system parameters and several control strategies are the necessity in indirect selfrepairing control.
As is known to all, attitude control is the key point of the whole flight control. In addition, the attitude and position of quadrotor helicopter have the direct coupling. Therefore, the research on attitude controller with the capability of selfrepairing from fault is imperative.
Recently, research on the flight control of mini quadrotor helicopter has got some achievements. For instance, Bouabdallah from EPFL has developed several control methods, such as PID, LQR, and Backstepping, based on OS4 [
However, the existing works on fault diagnosis and faulttolerant control of quadrotor helicopter are quite few at present. A Backstepping faulttolerant controller for quadrotor helicopter system based on the estimation of compound interference and partial FDI was proposed in [
The need for effective and realizable faulttolerant control for quadrotor helicopter with uncertain actuator faults motivates this research. In this paper, we develop an attitude system for quadrotor based on an adaptive fuzzy sliding mode tracking control to compensate the actuator fault such as loss of effectiveness and lockinplace. The main contributions of this paper are as follows.
The nonlinear model of quadrotor helicopter is put forward in detail, while the linear model ignoring the nonlinear factors such as gyroscopic effect is inaccurate when designing the faulttolerant control system.
An adaptive fuzzy sliding mode controller without fault identification is designed to track the desired output signal so that quadrotor can finish its mission safely even when any actuator of this quadrotor is loss of effectiveness or stuck at some place.
The rest of this paper is organized as follows. In Section
The attitude and position of quadrotor helicopter are operated by the rotor’s rotation rate, without the auto bank unit. The structure schematic is shown in Figure
The structure schematic of quadrotor helicopter.
Three attitude angles are controlled in these principles shown in Figure
The attitude control principle of quadrotor helicopter.
To limit the complexity of the dynamics modeling, the following assumptions are adopted [
The whole structure is rigid and symmetrical.
Thrust and drag forces are proportional to the square of propellers speed rotation.
The variable range of attitude angles is small (generally less than
Under these assumptions, using the NewtonEuler Equation, the dynamics equations are written in the following way:
There are some details about all terms in (
In (
Secondly,
Then,
In (
Secondly,
Next,
In conclusion, the dynamic model of quadrotor helicopter can be written as
To simplify the representations, we define
Due to the limit of the power of each electromotor, there exists a maximum rotation speed
In addition, the dynamic of the DCelectromotor which drives rotors is shown below:
Based on this analysis, let
According to report of research, the actuator of the helicopter can be easily damaged. In view of quadrotor helicopter, when the actuator fault occurs, the rotation speed of rotors will be abruptly changed so that the attitude system of quadrotor will vary rapidly or even lose control.
In this paper, we consider actuator faults including loss of effectiveness and lockinplace. When any actuator has failed, we can denote a general actuator fault model as [
Fault mode.
Fault parameter  State of system 


Normal 

Loss of effectiveness 

Lockinplace 
Inspired from [
Thus, we design the control vector
To attain the control objective, we propose to use a proportional actuator structure as follows [
Using (
The direct adaptive fuzzy control based on sliding mode is proposed to actualize selfrepairing control in this paper. Adaptive fuzzy sliding mode control combines the advantages between adaptive fuzzy control and sliding mode control, which can not only adjust the adaptation law on line when uncertain function exists but also ensure the robustness of the considered nonlinear system.
The control block diagram is shown in Figure
The control block diagram for adaptive fuzzy sliding mode control.
We consider the output of this quadrotor helicopter attitude system as
Then, the dynamic equation of the output can be rewritten in the following form:
Our task is to design a robust adaptive fuzzy controller based on sliding mode. There is no couple between each output vector, so we can consider the sliding surface in the state error space as
The time derivative of (
If the functions
Effectively, when we select the control input as
Here we design a Lyapunov function as
Thus, we can conclude that
However, when the actuators of quadrotor helicopter have faults, the functions
To overcome this problem, we propose to use an adaptive fuzzy system to approximate this ideal control law. Moreover, the parameters of this fuzzy controller are updated by the error between the fuzzy controller and the desired one.
According to the approximation theorem [
Then the fuzzy approximation error is
In this paper, we assume that the fuzzy controller proposed satisfies the universal approximation property over the compact set
In the preview, we recall that the parameter vector
To design a suitable adaptation law, our goal is to minimize the approximation error between
Hence, the parameter estimate
The adaptive fuzzy control law
Firstly, the estimate error
Then, we substitute the proposed control law (
Then, another Lyapunov function is designed by the following form:
Obviously,
Substituting (
using the inequalities
Equation (
Using the fact that the control gain matrix is positive definite, so there exists a positive constant
Since the desired parameter vector
Then the inequality of
By quoting a theorem in [
In this paper, we take the 3DOF hover helicopter shown in Figure
3DOF hover experimental platform.
According to the user’s guide of Quanser Hover, the system parameters are given by
Furthermore, to illustrate the superiority of the method proposed, system dynamic performance under the adaptive fuzzy sliding mode control will be compared with that under the LQR method when these three cases occur: normal, the loss of effectiveness of actuators, and lockinplace fault.
The design procedure of LQR is shown below.
Firstly, the affine nonlinear model of quadrotor helicopter should be linearized. Next, we can select suitable weight matrices
Hence, the LQR controller is described by
In all simulation cases, the desired rolling angle, pitching angle, and yawing angle are selected to be square wave with the amplitude
Three fuzzy systems in the form of (
In addition, the time of simulation and step size are set to be 30 s and 0.001 s, respectively. The other design parameters used in this simulation are chosen as follows:
When no fault happened in this system, the simulation curves on adaptive fuzzy sliding mode controller and LQR controller are shown in Figure
The output response curves with no fault.
Rolling angle tracking curves
Pitching angle tracking curves
Yawing angle tracking curves
From Figure
We suppose that the system is subject to loss of effectiveness at 10 s in input
The output response curves with the loss of effectiveness in
Rolling angle tracking curves
Pitching angle tracking curves
Yawing angle tracking curves
Refer to Figure
Suppose that a lockinplace fault occurs in
The output response curves with the lockinplace in
Rolling angle tracking curves
Pitching angle tracking curves
Yawing angle tracking curves
We can obtain the same conclusion from Figure
Without the loss of generality, another case is set to indicate that adaptive fuzzy sliding mode controller still works and is better than LQR controller when the actuator fault occurs in other inputs.
We suppose that the system loses effectiveness at 10 s in input
The output response curves with the loss of effectiveness in
Rolling angle tracking curves
Pitching angle tracking curves
Yawing angle tracking curves
To sum up, when the actuator faults such as loss of effectiveness and lockinplace occur in the attitude system of quadrotor helicopter, under the adaptive fuzzy sliding mode controller, this system can still track the desired output signal very well and return to the normal performance very rapidly, which implies that the whole system has the certain capability of selfrepairing.
In this paper, firstly, we built the affine nonlinear model for the quadrotor helicopter attitude system, which is MIMO. With the consideration of unknown actuator faults such as loss of effectiveness and lockinplace, an adaptive fuzzy controller based on sliding mode has been proposed to realize the direct selfrepairing control for this attitude system. Through a series of simulations, it has verified the availability of the proposed method which can make the system recover from the actuator faults and has good tracking performance.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported by the National Nature Science Foundation of China under Grants 61273171 and 61304112, Natural Science Foundation of Jiangsu Province (BK20131364), the Fundamental Research Funds for the Central Universities (no. NE2014202), and the Foundation of Graduate Innovation Center in NUAA (kfjj130109).