Robust Control for the Suspension Cable System of the Unmanned Helicopter with Sensor Fault under Complex Environment

Mei, Rong

doi:https://doi.org/10.1155/2021/8869292

Complexity

On this page

Abstract Introduction Conclusion Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Special Issue

Unmanned Autonomous Systems in Complex Environments

View this Special Issue

Research Article | Open Access

Volume 2021 | Article ID 8869292 | https://doi.org/10.1155/2021/8869292

Robust Control for the Suspension Cable System of the Unmanned Helicopter with Sensor Fault under Complex Environment

Rong Mei¹

Academic Editor: Ning Wang

Received13 Sept 2020

Revised11 Nov 2020

Accepted26 Feb 2021

Published11 Mar 2021

Abstract

Aiming at the suspension cable system of an unmanned helicopter with sensor fault under complex environment, this paper studies the robust antiswing tolerant control scheme. To suppress the swing of the hanging load when the unmanned helicopter is in the forward flight state, a nonlinear line motion model is firstly established. Considering the sensor fault of the unmanned helicopter, a sensor fault estimator is developed. By using the fault estimator output, the robust antiswing tolerant controller is proposed using the backstepping technique and sliding mode control method. Under the designed robust antiswing tolerant controller, the desired tracking control performance can be obtained and the swing angle of the load is guaranteed small under the sensor fault. Furthermore, the closed-loop system stability is analyzed by using the Lyapunov technique. Simulation studies are given to show the efficiency of the designed robust antiswing control strategy.

1. Introduction

Due to the unique characteristics such as vertical takeoff, vertical landing, good maneuverability, high work capability in complex environments, and hovering low-speed flying, the helicopter has been widely used in different practical areas during the past several decades [1]. Specially, considering the superiorities of long flight distance, high altitude, strong robustness, and large load, the medium-scale helicopter receives great attention [2]. By using the ability of long flight distance and large load of medium-scale helicopter, we can carry out the external transport by using the suspension cable, which is one of the main applications of medium-scale helicopters in the military and civil application area [3]. Suspension flight can transport bulk goods, which does not need to consider the load capacity of helicopters and appearance of the goods. Compared with the helicopter free flying state, helicopter flight with additional load will increase the load gravity load and load disturbance. Thus, it is necessary to consider the influence of the hanging load on the system. The characteristics of the low-speed stability were analyzed for a helicopter with a sling load in [4]. In [5], the flight dynamics were established for the articulated rotor helicopter by considering an hanging load.

Because the working environment is complicated and dynamically changeable, it is a challengeable task to develop a good control law for a helicopter suspension cable system [6–8]; for example, the medium-scale helicopter can be used to monitor and suppress the forest fire. However, the complex and changeable forest environment will increase the probability of a crash for the medium-scale helicopter. To avoid human sacrifice in the work process, the suspension cable system of an unmanned helicopter is developed in recent years. In [9], to deliver airborne cargo precisely, an active control scheme was designed for an unmanned helicopter with a slung load. An antiswing controller was designed for the unmanned helicopter with slung load by nonlinear path tracking in [10]. In [11], an adaptation controller was developed for autonomous helicopter slung load operations. A nonlinear controller design was developed for a helicopter slung load system in [12]. In [13], an adaptation backstepping controller by using prescribed performance method was proposed for carrier used unmanned aerial vehicle. Furthermore, in order to improve the security and the economic efficiency, the efficient controller should be further designed for the suspension cable system of an unmanned helicopter with sensor fault.

Sensor fault is an important fault of the practical systems due to the external circuit fault and mechanical fault of sensor and so on [14–18]. In general, there are four main types of sensor faults which include the complete failure fault, the fixed deviation fault, the drift deviation fault, and the precision reduction fault [19]. Now, there are many research results for the tolerant control problem of the various system with faults and unknown disturbance [20–27]. In [28], the local stabilization was studied for the Takagi–Sugeno (T-S) fuzzy discrete-time time-delay system in the presence of sensor fault. The sensor fault diagnosis technique and fault-tolerant control methods were developed for stochastic time-delayed control systems in [29]. In [30], the observer design method of the fault estimation was given for descriptor switched systems with sensor and actuator faults. The robust sensor fault estimator was studied for the continuous interconnected system in [31]. In [32], the tolerant control strategy was designed for an autonomous vehicle with proprioceptive sensors’ fault. A fault-tolerant control was developed for the linear system with sensor and actuator faults by using observer-based method in [33]. However, the fault-tolerant control methods need further development to improve their safety of various aircrafts with sensor fault.

In the past several years, various tolerant control schemes of the aircrafts with sensor fault have been studied [34]. In [35], the detection and recovery method was studied for the satellite attitude control system with sensor fault. Aiming at the hypersonic flight vehicle with multisensor faults, a nonlinear fault-tolerant control scheme was developed in [36]. In [37], an observer-based tolerant control scheme was designed for unmanned aerial vehicle with sensor faults. The reconstruction method was proposed for the aircraft with sensor fault under disturbances in [38]. In [39], the estimation method was studied for flight control systems with sensor fault based on the identification of aerodynamic parameters. In [40], a fuzzy adaptive tolerant control scheme was proposed for a quadrotor unmanned aerial vehicle with nonlinear sensor fault. However, the fault-tolerant control methods are rare for the suspension cable system of an unmanned helicopter with sensor fault which needs to be further studied.

Motivated by above analysis, the scheme of a robust antiswing control is studied for the suspension cable system of an unmanned helicopter with sensor fault to improve its reliability. The key innovations of this paper are stated as follows:(1)A design method of estimator is proposed to solve the estimation problem of sensor fault in suspension cable system of an unmanned helicopter.(2)The robust antiswing control law is developed for the suspension cable system of an unmanned helicopter by using sensor fault estimator, backstepping technology, and the desired tracking trajectory.(3)The closed-loop system stability of an unmanned helicopter with sensor faults is strictly analyzed under the robust antiswing control scheme.

The organization of this paper is described as follows. Section 2 gives the problem description, and the system model is introduced. The sensor fault estimator is proposed for the antiswing control in Section 3. Section 4 designs the robust antiswing control scheme based on sensor fault estimator. In Section 5, simulation results and analysis are given to show the effectiveness of the studied antiswing control scheme, and some conclusions are drawn in Section 6.

2. Problem Description

In this paper, the load uses a single-point hanging method to connect with the unmanned helicopter, which is the most widely used one because of compact and simple structure. To simplify the design of the controller, only the linear motion of the suspension cable system of the unmanned helicopter suspension system is considered, as shown in Figure 1 [3].

To establish the line motion model of the suspension cable system of an unmanned helicopter, we assume that the load swing amplitude at the initial time is zero; the unmanned helicopter sling is assumed to be massless, always straightened during flight, and will not come loose; the distance between the sling point and the unmanned helicopter particle is ignored; unmanned helicopter and hanging object are rigid bodies, without considering elastic deformation, and the load is regarded as a particle without considering the shape of the load. Ignore the influence of rotor airflow on unmanned helicopter and load movement and ignore the external disturbances, such as the wind, during the movement [3].

Under above assumptions, by using the Lagrange method, the nonlinear line motion model of the suspension cable system of an unmanned helicopter can be described as follows [3]:where is the lift of unmanned helicopter which is the control input. is the unmanned helicopter displacement, and is the swing angle of hanging load which are system outputs. is the unmanned helicopter mass, is the suspension load mass, is the gravity acceleration, and is the length of suspension cable.

Define and . Then, system (1) can be expressed aswhere denotes the helicopter displacement , is the swing angle of hanging load , is the forward flight speed of helicopter , denotes the angular velocity of the swing angle of hanging load , and is the lift . , , , and are given by

Define and . Assume that the system output is and . Then, we havewhere and .

In this paper, the forward speed is measured by airspeed head and the swing angle of hanging load is surveyed using an optical camera. We assume that accuracy losses of the airspeed head sensor and the optical camera sensor are considered in this study. The loss of accuracy of two sensors is given as follows [40]:where is the measured value of the airspeed head sensor and the optical camera sensor with fault and is the sensor fault occurring time.

The control design goal of this paper is to develop a robust antiswing control plan such that the system actual output can track the required one and the tracking error is convergent when the suspension cable system of the unmanned helicopter (3) suffers from the sensor fault.

To promote the design of the robust antiswing control scheme for the suspension cable system of the unmanned helicopter with sensor fault, some assumptions and lemmas are required.

Assumption 1. (see [40]). For the sensor fault , there exist corresponding inequality conditions , , and with .

Assumption 2. (see [2]). All states of the studied system are measurable and available. The desired system tracking signal and its derivative are always bounded. Furthermore, there exists an unknown positive constant which renders .

Lemma 1. (see [41]). For the any bounded initial conditions, if there is a positive and continuous Lyapunov function which satisfies and makes that , where are class functions and , are positive constants, then its solution is uniformly bounded.

Remark 1. In this paper, the sensor fault is considered for the suspension cable system of an unmanned helicopter. As well known, the sensor fault and its derivatives should be bounded in the practical system. If they are not bounded, the system controllability cannot be guaranteed. Thus, Assumption 1 is reasonable for the helicopter suspension cable system. On the other hand, to design the robust antiswing control law for the suspension cable system of an unmanned helicopter, all states are needed. Thus, we assume that all states are measurable and available. Furthermore, the desired system tracking signal and its derivative are also bounded. If they are not bounded, the tracking control goal of the suspension cable system of an unmanned helicopter with sensor fault cannot be realized. From above analysis, we can conclude that Assumption 2 is also reasonable.

3. Design of Sensor Fault Estimator

In this section, the design of sensor fault estimator will be given for the suspension cable system of the unmanned helicopter. Considering (4) and (5), we have

Since includes , can be written as . At the same time, . Thus, we obtain

Without loss of generality, we assume and its derivative are bounded. Then, with . Because the uncertain term is generated by the sensor fault, this assumption is reasonable. Under the sensor faults, the nonlinear line motion model (4) of the suspension cable system of an unmanned helicopter can be described as

Invoking (5), system (8) can be modified as

To estimate the unknown sensor fault of the suspension cable system of the unmanned helicopter, the sensor fault estimator can be designed as follows [41]:where and are the corresponding estimations of the sensor fault and the derivation of the sensor fault . and are the parameters of the studied sensor fault estimator which needs to be designed. The parameters and should satisfy and . and are the internal states of the fault estimator.

Define the estimation errors of the fault estimator as and . Then, considering (9) and (10), there yields

We define . Invoking (11) and (12), we obtainwhere , , , , and is designed as bounded function.

To investigate the convergence of the estimation error of the designed sensor fault estimator, the Lyapunov function is given as follows:where is a designed positive definite matrix.

Invoking (13) and Assumption 1, the time derivative of can be described as

From above process analysis, the following theorem can be obtained for the sensor fault estimator of suspension cable system of the unmanned helicopter.

Theorem 1. Consider the suspension cable system of the unmanned helicopter (4) with sensor faults satisfying Assumption 1, the nonlinear sensor estimator is designed as (10). If the designed function parameters and are chosen to render the following inequality valid:then the sensor fault estimation error is uniformly ultimately bounded.
In accordance with equations (15) and (16) and Lemma 1, we can make a conclusion that the sensor estimation error is uniformly ultimately bounded.

4. Design of Robust Antiswing Control Plan Based on Sensor Fault Estimator

In this section, the fault-tolerant antiswing control law will be developed for the suspension cable system of the unmanned helicopter (4) with sensor faults based on the backstepping technique. The particular design steps are as follows. Step 1: considering and (9) yields To design the robust antiswing fault-tolerant control plan, we define where is a designed virtual control law. Substituting (18) into (17) yields The virtual control law can be proposed as where is a given parameter. Substituting (20) into (19), we have Choose the Lyapunov function in the form of Differentiating (22) and considering (21) yields Step 2: differentiating (18), we obtain

Considering (9), (24) can be described as

In this paper, the method of the dynamic surface control technique is introduced to acquire the derivatives of the virtual control law to handle the sensor fault in the first step. Consider the following first-order filter as follows [2]:where is a time constant.

By defining , we havewhere is the sufficiently smooth vector in regard to . It can be obtained that the smooth function is bounded on set with the maximum being [2].

In order to analyze the convergence of the first-order filter (24), the Lyapunov function candidate is given by

Differentiating (29) and invoking (27), we obtain

To handle , the sensor fault estimator (10) is used. Using the outputs of the sensor fault estimator and the first-order filter, the controller law is designed aswhere , , are designed parameter and .

Substituting (30) into (25), we obtain

Considering (27), (31) can be written as

Choose the Lyapunov function candidate as

Differentiating (33) and considering (31) yields

Considering , we have

The following theorem is given to summarize the design of the robust antiswing control scheme studied for the suspension cable system of an unmanned helicopter with sensor fault.

Theorem 2. For the studied suspension cable system of an unmanned helicopter with sensor fault, based on the nonlinear dynamic (4) satisfying Assumption 1 and Assumption 2, the nonlinear sensor fault estimator is designed as (10). By utilizing the designed sensor fault estimator, the robust antiswing control scheme is designed as (20), (26), and (30). Under the sensor fault estimator-based antiswing control of the suspension cable system of an unmanned helicopter, the closed-loop system is convergent and all signals are bounded.

Proof. In order to prove the stability of the whole system, the Lyapunov function is selected asDifferentiating (36) and considering (15), (23), and (35), we haveUsing the definition , we haveDefineThen, we haveFrom (40) and Lemma 1, we can conclude that when . Thus, the tracking control goal is realized for the suspension cable system of an unmanned helicopter with sensor fault. This concludes the proof.

5. Simulation Study

In the following, simulation results and analysis are given to illustrate the validity of the designed antiswing control of the suspension cable system of an unmanned helicopter based on the sensor fault estimator. The basic parameters of the suspension cable system of an unmanned helicopter are referred to [2] and are presented in Table 1.

In the given simulation analysis, the system initial conditions are given by . The desired trajectories of an unmanned helicopter are as follows:

Furthermore, the sensor fault vector is given by

The corresponding design parameters of the developed antiswing control of the suspension cable system of an unmanned helicopter based on the sensor fault estimator are chosen as , , and . The nonlinear sensor fault estimator is designed as (10). Based on the designed sensor fault estimator, the robust antiswing control scheme is developed as (20), (26), and (30). The simulation results are presented in Figures 2–7.

Figures 2 and 3 show the tracking control result of the suspension cable system of an unmanned helicopter with sensor fault by using the designed robust antiswing control plan which can verify the effectiveness of the developed antiswing control method. The tracking control errors are presented in Figures 4 and 5. They can be seen that the tracing errors of the suspension cable system of an unmanned helicopter with sensor fault are convergent and bounded. Then, Figures 6 and 7 show the effectiveness of the developed sensor fault estimator. We can note that the estimation results are good and meet the antiswing performance requirement by using the developed sensor fault estimator. Specially, we can see that the swing angle of the load is small in the flight process. Thus, the antiswing performance is achieved under the sensor fault.

On the basis of the given simulation results and analysis, we can draw a conclusion that the satisfactory antiswing control performance can be guaranteed for the suspension cable system of an unmanned helicopter based on the sensor fault estimator. Thus, the designed antiswing control scheme is valid for the suspension cable system of an unmanned helicopter.

6. Conclusion

The robust antiswing control scheme has been proposed for the suspension cable system of an unmanned helicopter with sensor fault. In order to tackle the sensor fault, a sensor fault estimator has been designed to estimate it. By using the output of sensor fault estimator, the robust tolerant control scheme has been developed to maintain the desired tracking control performance during the flight progress. In accordance with the designed antiswing controller, the system can track the desired trajectory and the whole system stability is guaranteed by using the Lyapunov method. Simulation results have been presented to show the efficiency of the studied antiswing control law for the suspension cable system of an unmanned helicopter with sensor fault. In the future work, the finite time sensor fault estimator can be designed for the suspension cable system of an unmanned helicopter.

Data Availability

The data used to support the findings of this study are available upon request to the corresponding author.

Conflicts of Interest

The author declares that there are no conflicts of interest.

Acknowledgments

This work was partially supported by the National Natural Science Foundation of China (Grant no. 61803207) and Qinglan Project in Jiangsu Province.

References

K. Dalamagkidis, K. P. Valavanis, and L. A. Piegl, “Nonlinear model predictive control with neural network optimization for autonomous autorotation of small unmanned helicopters,” IEEE Transactions on Control Systems Technology, vol. 19, no. 4, pp. 818–831, 2010.
View at: Publisher Site | Google Scholar
K. Yan, M. Chen, Q. Wu, and K. Lu, “Robust attitude fault-tolerant control for unmanned autonomous helicopter with flapping dynamics and actuator faults,” Transactions of the Institute of Measurement and Control, vol. 41, no. 5, pp. 1266–1277, 2019.
View at: Publisher Site | Google Scholar
H. N. Wang, Decreasing Oscillations of Aerial Cranes, Beijing Institute of Technology, Beijing, China, 2015.
B. Nagabhushan, “Low-speed stability characteristics of a helicopter with a sling load,” Vertica, vol. 9, no. 4, pp. 345–361, 1985.
View at: Google Scholar
D. Fusato, G. Guglieri, and R. Celi, “Flight dynamics of an articulated rotor helicopter with an external slung load,” Journal of the American Helicopter Society, vol. 46, no. 1, pp. 3–13, 2001.
View at: Publisher Site | Google Scholar
M. Chen, Y. Ren, and J. Y. Liu, “Anti-disturbance control for a suspension cable system of helicopter subject to input nonlinearities,” IEEE Systems, Man, and Cybernetics: Systems, vol. 48, no. 12, pp. 2292–2304, 2017.
View at: Google Scholar
F. Omar, F. Karray, O. Basir et al., “Autonomous overhead crane system a fuzzy logic controller,” Journal of Vibration and Control, vol. 10, no. 6, pp. 1255–1270, 2004.
View at: Publisher Site | Google Scholar
K. Yomchinda and K. Thanan, “Development of dynamic inversion based outer-loop anti-swing control law for a helicopter slung-load system,” AIAA Journal, vol. 10, no. 6, pp. 205–209, 2015.
View at: Google Scholar
K. Kang, J. V. R. Prasad, and E. Johnson, “Active control of a UAV helicopter with a slung load for precision airborne cargo delivery,” Unmanned Systems, vol. 04, no. 03, pp. 213–226, 2016.
View at: Publisher Site | Google Scholar
S. El-Ferik, A. H. Syed, H. M. Omar, and M. A. Deriche, “Anti-swing nonlinear path tracking controller for helicopter slung load system,” Ifac Proceedings Volumes, vol. 46, no. 30, pp. 134–141, 2013.
View at: Publisher Site | Google Scholar
M. Bisgaard, A. la Cour-Harbo, and J. Dimon Bendtsen, “Adaptive control system for autonomous helicopter slung load operations,” Control Engineering Practice, vol. 18, no. 7, pp. 800–811, 2010.
View at: Publisher Site | Google Scholar
K. Thanapalan, “Nonlinear controller design for a helicopter with an external slung load system,” Systems Science & Control Engineering, vol. 5, no. 1, pp. 97–107, 2017.
View at: Publisher Site | Google Scholar
Z. Yang, S. H. Wang, B. Chang, and W. H. Wu, “Adaptive constrained backstepping controller with prescribed performance methodology for carrier-based UAV,” Aerospace Science and Technology, vol. 5, no. 7, pp. 90–92, 2019.
View at: Google Scholar
G. Peng, C. Yang, W. He, and C. L. P. Chen, “Force sensorless admittance control with neural learning for robots with actuator saturation,” IEEE Transactions on Industrial Electronics, vol. 67, no. 4, pp. 3138–3148, 2020.
View at: Publisher Site | Google Scholar
Z. Gao and D. W. C. Ho, “State/noise estimator for descriptor systems with application to sensor fault diagnosis,” IEEE Transactions on Signal Processing, vol. 54, no. 4, pp. 1316–1326, 2006.
View at: Google Scholar
C. Yang, D. Huang, W. He, and L. Cheng, “Neural control of robot manipulators with trajectory tracking constraints and input saturation,” IEEE Transactions on Neural Networks and Learning Systems, pp. 1–12, 2020.
View at: Publisher Site | Google Scholar
M. Chen, P. Shi, and C. C. Lim, “Adaptive neural fault-tolerant control of a 3-DOF model helicopter system,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 46, no. 2, pp. 260–270, 2015.
View at: Google Scholar
G. Tao, S. Chen, and S. M. Joshi, “An adaptive control scheme for systems with unknown actuator failures,” Automatica, vol. 38, no. 6, pp. 1027–1034, 2002.
View at: Publisher Site | Google Scholar
X. Wei, M. Verhaegen, and T. V. Engelen, “Sensor fault detection and isolation for wind turbines based on subspace identification and Kalman filter techniques,” International Journal of Adaptive Control & Signal Processing, vol. 24, no. 8, pp. 687–707, 2010.
View at: Google Scholar
C. Yang, C. Chen, W. He, R. Cui, and Z. Li, “Robot learning system based on adaptive neural control and dynamic movement primitives,” IEEE Transactions on Neural Networks and Learning Systems, vol. 30, no. 3, pp. 777–787, 2019.
View at: Publisher Site | Google Scholar
M. Chen, S.-Y. Shao, and B. Jiang, “Adaptive neural control of uncertain nonlinear systems using disturbance observer,” IEEE Transactions on Cybernetics, vol. 47, no. 10, pp. 3110–3123, 2017.
View at: Publisher Site | Google Scholar
C. Yang, X. Wang, L. Cheng, and H. Ma, “Neural-Learning-based telerobot control with guaranteed performance,” IEEE Transactions on Cybernetics, vol. 47, no. 10, pp. 3148–3159, 2017.
View at: Publisher Site | Google Scholar
M. Chen, B. B. Ren, and Q. X. Wu, “Anti-disturbance control of hypersonic flight vehicles with input saturation using disturbance observer,” Science China Information Science, vol. 58, no. 1, pp. 1–13, 2015.
View at: Publisher Site | Google Scholar
H. Lin, T. Zhang, Z. Chen, H. Song, and C. Yang, “Adaptive fuzzy Gaussian mixture models for shape approximation in robot grasping,” International Journal of Fuzzy Systems, vol. 21, no. 4, pp. 1026–1037, 2019.
View at: Publisher Site | Google Scholar
H. Huang, C. Yang, and C. L. P. Chen, “Optimal robot-environment interaction under broad fuzzy neural adaptive control,” IEEE Transactions on Cybernetics, pp. 1–12, 2020.
View at: Publisher Site | Google Scholar
M. Chen and J. Yu, “Adaptive dynamic surface control of NSVs with input saturation using a disturbance observer,” Chinese Journal Of Aeronautics, vol. 28, no. 3, pp. 853–864, 2015.
View at: Publisher Site | Google Scholar
C. Yang, G. Peng, L. Cheng, J. Na, and Z. Li, “Force sensorless admittance control for teleoperation of uncertain robot manipulator using neural networks,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, pp. 1–11, 2019.
View at: Publisher Site | Google Scholar
Y. Wu and J. Dong, “Local stabilization for discrete-time T-S fuzzy time-delay systems with sensor fault,” Fuzzy Sets and Systems, vol. 374, no. 11, pp. 115–137, 2019.
View at: Publisher Site | Google Scholar
H. Wang and L. Yao, “Sensor fault diagnosis and fault-tolerant control for stochastic distribution time‐delayed control systems,” International Journal of Adaptive Control and Signal Processing, vol. 33, no. 9, pp. 1395–1406, 2019.
View at: Publisher Site | Google Scholar
L. Chen, Y. Zhao, S. Fu, M. Liu, and J. Qiu, “Fault estimation observer design for descriptor switched systems with actuator and sensor failures,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 66, no. 2, pp. 810–819, 2019.
View at: Publisher Site | Google Scholar
J. Xia, B. Jiang, and K. Zhang, “Robust asymptotic estimation of sensor faults for continuous-time interconnected systems,” International Journal of Control, Automation and Systems, vol. 17, no. 12, pp. 3170–3178, 2019.
View at: Publisher Site | Google Scholar
B. Mohamed, C. Ahmed, B. Moussa et al., ““Proprioceptive sensors’ fault tolerant control strategy was designed for an autonomous vehicle,” Sensors, vol. 18, no. 6, p. 1893, 2018.
View at: Google Scholar
T. H. Lee, C. P. Lim, S. Nahavandi et al., “Observer-based fault-tolerant control for linear systems with sensor and actuator faults,” IEEE Systems Journal, vol. 13, no. 2, pp. 1981–1990, 2019.
View at: Google Scholar
M. Taimoor and L. Aijun, “Lyapunov theory based adaptive neural observers design for aircraft sensors fault detection and isolation,” Journal of Intelligent & Robotic Systems, vol. 98, no. 3, pp. 311–323, 2019.
View at: Publisher Site | Google Scholar
S. S. Nasrolahi and F. Abdollahi, “Sensor fault detection and recovery in satellite attitude control,” Acta Astronautica, vol. 145, no. 4, pp. 275–283, 2018.
View at: Publisher Site | Google Scholar
F. Chen, J. Niu, and G. Jiang, “Nonlinear fault-tolerant control for hypersonic flight vehicle with multi-sensor faults,” IEEE Access, vol. 6, Article ID 25436, p. 25427, 2018.
View at: Publisher Site | Google Scholar
Z. Liu, D. Theilliol, L. Yang, Y. He, and J. Han, “Observer-based linear parameter varying control design with unmeasurable varying parameters under sensor faults for quad-tilt rotor unmanned aerial vehicle,” Aerospace Science and Technology, vol. 92, no. 9, pp. 696–713, 2019.
View at: Publisher Site | Google Scholar
P. Lu, E.-J. van Kampen, C. de Visser, and Q. Chu, “Nonlinear aircraft sensor fault reconstruction in the presence of disturbances validated by real flight data,” Control Engineering Practice, vol. 49, pp. 112–128, 2016.
View at: Publisher Site | Google Scholar
J. C. Wang and X. H. Qi, “Sensor fault estimation method for flight control systems based on aerodynamic parameter identification,” Binggong Xuebao/Acta Armamentarii, vol. 36, no. 1, pp. 103–110, 2015.
View at: Google Scholar
C. Hu, L. Cao, X. Zhou, B. Sun, and N. Wang, “Fuzzy adaptive nonlinear sensor‐fault tolerant control for a quadrotor unmanned aerial vehicle,” Asian Journal of Control, vol. 22, no. 3, pp. 1163–1176, 2020.
View at: Publisher Site | Google Scholar
M. Chen, “Robust tracking control for self-balancing mobile robots using disturbance observer,” IEEE/CAA Journal of Automatica Sinica, vol. 4, no. 3, pp. 458–465, 2017.
View at: Publisher Site | Google Scholar

Copyright

Copyright © 2021 Rong Mei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation

Download other formats

Order printed copies

Views

247

Downloads

869

Citations