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PAPERS IN ENGLISH
AVIATION AND ROCKET-SPACE TECHNOLOGY
DESIGN A FAULT-TOLERANT CONTROLLER OF QUADROTOR USE SUPER SPIRAL SLIDE CONTROL MODE
Pham Van Quang
Master,
Air Defense - Air Force Academy, Vietnam, Hanoi E-mail: [email protected]
РАЗРАБОТКА ОТКАЗОУСТОЙЧИВОГО КОНТРОЛЛЕРА КВАДРОТОРА С ИСПОЛЬЗОВАНИЕМ РЕЖИМА УПРАВЛЕНИЯ СУПЕРСПИРАЛЬНЫМ СКОЛЬЖЕНИЕМ
Фам Ван Куанг
магистр, ПВО - ВВС Академия, Вьетнам, г. Ханой
ABSTRACT
This paper considers a fault-tolerant control method based on a super-twisting sliding mode controller to control the state and trajectory of a Quadrotor. The controller receives feedback signals including the failure signals of the rotors on the Quadrotor. The received error signals are sent to the controller input, from which the controller will distribute control actions to the rotors that are still in good working order to ensure that the Quadrotor follows the given trajectory. Simulation on Matlab-Simulink shows that the fault-tolerant control system using a super-twisting sliding mode controller can effectively reduce the impact of rotor faults on the system.
АННОТАЦИЯ
В данной статье рассмотрен отказоустойчивый метод управления на основе сверхвинтового скользящего регулятора для управления состоянием и траекторией Квадротора. Контроллер получает сигналы обратной связи, в том числе сигналы неработоспособности роторов Квадротора. Полученные сигналы ошибок поступают на вход контроллера, откуда контроллер будет распределять управляющие воздействия на еще исправно работающие несущие винты, чтобы обеспечить управляемость Квадротора по заданной траектории. Моделирование в Matlab-Simulink показывает, что отказоустойчивая система управления с использованием супервинтового контроллера скольжения может эффективно снизить влияние ошибок ротора на систему.
Keywords: quadrotor; control; fault-tolerant controller; state; trajectory.
Ключевые слова: квадротор; управление; отказоустойчивый контроллер; статус; траектория.
Introduction
A quadrotor has complex system dynamics with a variety of system states variables. That being said, the number of inputs available doesn't allow the quadrotor to have input redundancy. This makes it difficult for controlling an under actuated quadrotor. If situational discrepancy leads to the under performance of the propeller actuators, the quadrotor loses its control and fails to follow the desired trajectory. The under performance can be really risky leading to the crash landing of the quadrotor. Considering the high-cost sensors and the
load mounted on the quadrotor, crash landing can be a serious loss and dangerous for the surrounding environment. To overcome such situations, a fault tolerant controller has been designed to trigger appropriate control on the detection of faults among the propeller actuators. Among various control algorithms, Sliding Mode Control (SMC) has been observed to produce robust results on control of underactuated systems. Since SMC produces an undesirable high frequency chattering effect, an alternative has been provided to replace the nonlinear switching function. Super Twisting Sliding Mode Con-
Библиографическое описание: Pham V.Q. DESIGN A FAULT-TOLERANT CONTROLLER OF QUADROTOR USE SUPER SPIRAL SLIDE CONTROL MODE // Universum: технические науки : электрон. научн. журн. 2025. 1(130). URL:
https://7universum.com/ru/tech/archive/item/19142
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trol (STW SMC) is implemented to remove such undesirable high frequency chattering. On detection of the faults using state estimators, a control allocation algorithm is triggered. Based on appropriate loss of actuator effectiveness (LAE), control allocation is implemented and the quadrotor is made to follow the trajectory and land safely without any disturbances. The following will elaborate on the mathematical modelling and controller design to implement such a FTC for the Quadrotor.
The state feedback disadvantage of the basic sliding mode controller and the helical sliding mode controller will be overcome by the super-helical controller. In other words, the super-helical controller is the output feedback controller. The name super-helical here does not mean that the twist will be more, but only means that it is an output feedback controller. The content of the design method of this super-helical controller is as follows [1-3]:
Consider the problem of finding a controller u(x, t) so that every state trajectory of the system:
s = a(x, t) + b(x, t)u with two indeterminate functions:
(1)
ds
a(x, t) = — + LfS(x, t) and b(x, t) = Lhs(x, t)
where u is considered as a parameter of the two uncertain functions above, always approaching the origin s = s = 0 of the phase plane.
If with two indeterminate functionsa (x, t) and b(x,t) of (1) there always exist positive constants q, C, G1, G2, Usuch that:
I<P(-)I + VIY(-)I<C,0<K1<Y(-)<K2 <p(-)
<qU,0<q <1
KO
Then the controller:
u = -X^\z1\sgn(z1) + with X > Oenough size, namely:
(2)
X >
2 (K1a+C)K2(l+q) K1a-C Ki(l-q)
and K^a> C
as
ukhi |u| > U a sgn(zl)khi |u| < U
(3)
will be a solution of the problem. In other words, controllers (2), (3) will return the state trajectory of (1 ) to the origin s = s = 0 after a finite period.
Another special feature of the above controller is that with (3) , the control signal value u always tends to move toward the bounded range [-U,U].
Materials and Methodology
Super Twist Slide Controller Design for Quadrotor
One of the main reasons for using a super-helical sliding mode controller to control a Quadrotor drone is that it is insensitive to unmodeled disturbances. Since it is a nonlinear controller, the modeling and control design will be more accurate than linear controllers.
The block diagram of the control system of the sliding mode controller is given below:
Figure 1. Block diagram using super-twist sliding mode controller
The slide surface is designed as follows:s = e + Xe Where:
e - is the error and X - is the tuning parameter. The sliding variables considered for controller design are:
S = 1,5k1/2s1/2 s i gn(s) + f 1,1k s i gn(s) (4)
To control the Quadrotor in the desired trajectory, the sliding variables must reach the sliding surface in a finite time and slide on the surface to approach the zero point. The input equations to control the state of the Quadrotor are calculated as follows:
Where:
A 'X
u*=-
15kl/2sl/2'
1,5KÏ 2sign(s<p) — J 1,1kl sign(s^) ug = ûg — 1,5kg/2 sg/2 sign(sg) — J 1,1k2 sign(sg) 1,5kg/2sgp/2sign(s}p) — f 1,1k3 sign(s^)
I — I 1 I
04>—j—- + 4>d — A(4>d — 4>)]'>ûg = Y
• ..L — L
+ ed—x(ed — e)
= ±[—H^ + td—XÙd—^î = 7^[g + zd—X(zd—z)]
(5)
(6)
i
I
y
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ф,в,ф - Euler angles (roll, pitch, yaw) in inertial frame of reference;
m, I - mass and frame length of the Quadrotor; Ix,Iy,Iz- moment of inertia along the respective axes;
д - acceleration of gravity; k; £ [0,1], i = 1,... ,3- thrust drag coef f icients;; z - altitude of the Quadrotor; фа,ва,фа,га- desired altitude, roll, pitch, yaw of the Quadrotor.
When one of the rotors loses partial or total rotational speed, the controller must be able to counteract that loss of speed and continue to control the Quadrotor to fly along the preset trajectory or control the Quadrotor to safety.
The control vector is represented as follows:
K = [k1k2k3k4] (7)
with ki £ [0,1], when ki = lit means all rotors are working properly.
The fault can be detected and the control effect vector ( K) value is obtained through an extended Kalman filter. Once the value of the control vector is received, the control allocation of the inputs is made accordingly to counteract the fault. Suppose that one rotor is operating at half its expected power (i.e., k = 0.5). The opposite rotor is made to activate only half of its current expected power. This ensures that the pitch and yaw torques are balanced, but ignores the steering torque in the other axis.
The control output after fault detection is given by system of equation (8).
T -
тф
Тф.
к 0 -1 к
— i
к к к
к 0 к
0 Ik 0 -
[kl k2 k3 k4]
(8)
Where
T- Thrust;
k, c- Thrust and drag coefficients;
Torques along the respective axes;
f1,f2,f3,f4- Thrustgiven by respective rotors. After fault detection, the control output is calculated according to the control allocation as follows.
When rotor number 1 fails: 1 11
- 0----
4 21 4c
1
0 1
0 1
0
1
4c 1
4 1
[4 21 (A -Î3-Î4+ f2kl\ (.
(fi—A-kA ( f- A )
fl +Аз +Î4+ f2kl>
Î1+Î2-Î3-Î4 A fl+f2+f3+f4 )
When rotor number 3 fails:
fl + f2 - f3 - f4 k3
0
1 21
0 1 21
1
~Tl 0 1 21
0
1
~4c 1
4c 1
~4c 1
f3 - f4 k3
Îl+CÎ2+Î3+Î4k3\
When rotor number 2 fails: 1 11
- 0----
4 21 4c
1
~Yl 0 1
0 1
0
1
4c 1
4 1
[4 21
ÎÎ2 -Î3-Î4+ flk2\ f. ( Cl+C2-C3-C4 )(
(-Î2 - flk2\ \ C-C )
4c ]
Î2+f3+Î4+kk2\
fl+Î2-Î3-Î4 A fl+f2+Î3+Î4 )
When rotor number 4 fails:
0
1 21
0 1 21
fl+f2-f4-f3k
fl + f2 - f3 - f4 fl + f2 + f3 + f4
1
~Ti 0 1
0
1
~4c 1
4c 1
~4c 1
f4 - f3 k4
1 (T=T)
fl +Cf2 + f4 + f^
fl + f2 - f3 - f4 fl + f2 + f3 + f4
Simulation results
Quadrotor parameters used in the simulation process [ 4-8 ]: Yaw moment: m = 0.445(kg); Moment of inertia along x;y;z axes are respectively: Ix = 0.0027 (kgm2); Iy = 0.0029 (kgm2); Iz = 0.0053 (kgm2).
Simulation results are shown in Figure 3-7:
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10
5 О
0.2 О -0.2
0.05 О
Thrust (N) vs T¡me(s)
10 20 30 40 50 60 ТО 80 SO 10О
Rolling l/P(N m) vs T¡me(s)
in n í л Ii 1
О 10 20 30 40 50 60 70 80 SO 10О
Pitching l/P(N m) vs Time(s)
I 'l
0.2 i
О -0.2 '
10
20
30 40 50 60 70
Yawing l/P(N m) vs Time(s)
80
90
10 20 30 40
Figure 2. Control parameters
Figure 3. Quadrotor coordinates
100
90 100
Figure 4. Quadrotor state corners
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Figure 5. Error
y axis x axis
Figure 6. Quadrotor motion trajectory used Super Twist Slide Controller
Conclusion
By applying the super-twist slip control method and using the Quadrotor mathematical model, a control law for a fault-tolerant control system based on the super-
twist slip control principle was designed and evaluated with single-rotor faults. Based on the simulation results, the system maintains acceptable performance with partial rotor faults with higher controller gains.
References:
1. Z. Liu, L. Wang, Y. Song, Q. Dang, and B. Ma, ''Fault diagnosis and accommodation for multi-actuator faults of a fixed-wing unmanned aerial vehicle,'' Meas. Sci. Technol., vol. 33, no. 7, Apr. 2022, Art. no. 075903.
2. Lichao Cui, Yulian Jiang, Xudong Zhang. Sliding mode control of unmanned aerial vehicle based on finite-time disturbance observer. Journal of Physics: Conference Series 2216 (2022) 012038.
UNIVERSUM:
ТЕХНИЧЕСКИЕ НАУКИ_январь. 2025 г.
3. HJ Jayakrishnan. Position and Attitude control of a Quadrotor UAV using Super Twisting Sliding Mode. 4 th IFAC Conference on Advances in Control and Optimization of Dynamical Systems ACODS 2016 Tiruchirappalli, India, 1-5 February 2016.
4. Nguyen Doan Phuoc. Basic and advanced sliding control. Science and Technology Publishing House, 2014.
5. Nicholas Ferry. Quadcopter Plant Model and Control System Development With MATLAB/Simulink Implementation. Rochester, New York. December 2017.
6. HJ Jayakrishnan. Position and Attitude control of a Quadrotor UAV using Super Twisting Sliding Mode. In Robotics and Automation, 2016. ICRA 2016. Proceedings of the 2016 IEEE International Conference on, 284-289. IEEE.
7. Bouabdallah, S. and Siegwart, R. (2005). Backstepping and sliding-mode techniques applied to an indoor micro quadrotor. In Robotics and Automation, 2005. ICRA 2005. Proceedings of the 2005 IEEE International Conference on 2247-2252. IEEE.
8. Benallegue, A., Mokhtari, A., and Fridman, L. (2006). Feedback linearization and high order sliding mode observer for a quadrotor uav. In Variable Structural Systems, 2006. VSS'06. International Workshop on, 365-372. doi: 10.1109/VSS.2006.1644545.
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