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January  2021, 17(1): 447-465. doi: 10.3934/jimo.2019120

## Design of LPV fault-tolerant controller for hypersonic vehicle based on state observer

 1 College of Missile Engineering, Rocket Force University of Engineering, Xi'an Shaanxi 710025, China 2 School of Astronautics, Northwestern Polytechnical University, Xi'an Shaanxi 710072, China

* Corresponding author: Guangbin Cai

Received  March 2019 Revised  April 2019 Published  September 2019

Fund Project: This work was supported in part by the National Natural Science Foundation of China under grant number 61773387, and by China Postdoctoral Fund under grant numbers 2017T100770 and 2016M590971

Considering the parameter uncertainty and actuator failure of hypersonic vehicle during maneuvering, this paper proposes a state observer-based hypersonic vehicle fault-tolerant control (FTC) system design method. Because hypersonic vehicles are prone to failure during maneuvering, the state quantity cannot be measured. First, a state observer-based FTC control method is designed for the linear parameter-varying (LPV) model with parameter uncertainty and partial failure of the actuator. Then, the Lyapunov function is used to demonstrate the asymptotic stability of the closed-loop system. The performance index function proved that the system has robust stability under the disturbance condition. Subsequently, the linear matrix inequality (LMI) was used to solve the observer parameters and the corresponding gain matrix in the control system. The simulation results indicated that the designed controller can track the flight command signal stably and has strong robustness, which verified the effectiveness of the design controller.

Citation: Guangbin CAI, Yang Zhao, Wanzhen Quan, Xiusheng Zhang. Design of LPV fault-tolerant controller for hypersonic vehicle based on state observer. Journal of Industrial & Management Optimization, 2021, 17 (1) : 447-465. doi: 10.3934/jimo.2019120
##### References:
 [1] G. B. Cai, G. R. Duan and C. H. Hu, A velocity-based LPV modeling and control framework for an airbreathing hypersonic vehicle, International Journal of Innovative Computing Information and Control, 7 (2011), 2269-2281.   Google Scholar [2] M. Corless and J. Tu, State and input estimation for a class of uncertain systems, Automatica J. IFAC, 34 (1998), 757-764.  doi: 10.1016/S0005-1098(98)00013-2.  Google Scholar [3] P. Gahinet and P. Apkarian, A linear matrix inequality approach to $H_\infty$ control, International Journal of Robust and Nonlinear Control, 4 (1994), 421-448.  doi: 10.1002/rnc.4590040403.  Google Scholar [4] Z. F. Gao, T. Cao and J. X. Lin, Sliding mode fault tolerant tracking control for a flexible hypersonic vehicle with actuator faults, ICIC Express Letters Part B, Appli-Cations: An International Journal of Research and Surveys, 6 (2015), 1797-1804.   Google Scholar [5] Z. F. Gao, B. Jiang, P. Shi, J. Y. Liu and Y. F. Xu, Passive fault-tolerant control design for near-space hypersonic vehicle dynamical system, Circuits, Systems, and Signal Processing, 31 (2012), 565-581.  doi: 10.1007/s00034-011-9385-7.  Google Scholar [6] Z. F. Gao, J. X. Lin and T. Cao, Robust fault tolerant tracking control design for a linearized hypersonic vehicle with sensor fault, International Journal of Control Automation and Systems, 13 (2015), 672-679.  doi: 10.1007/s12555-014-0169-2.  Google Scholar [7] S. Gao and J. S. Mei, Fault tolerant control of actuator faults for input nonlinear systems, Information and Control, 44 (2015), 463-468.   Google Scholar [8] X. Guan, J. Zhao and Y. He, Track technology of hypersonic aircraft in near space, Journal of Ordnance Equipment Engineering, 32 (2011), 4-6.   Google Scholar [9] J. J. He, R. Y. Qi and B. Jiang, Adaptive output feedback fault-tolerant control design for hypersonic flight vehicles, Journal of the Franklin Institute, 352 (2015), 1811-1835.  doi: 10.1016/j.jfranklin.2015.01.016.  Google Scholar [10] L. Huang, Z. S. Duan and J. Y. Yang, Challenges of control science in near space hypersonic aircrafts, Control Theory and Applications, 28 (2011), 1496-1505.   Google Scholar [11] B. Fidan, M. Mirmirani and P. Ioannou, Flight dynamics and control of air-breathing hypersonic vehicles: Review and new directions, 12th AIAA International Space Planes and Hypersonic Systems and technologies, (2003). doi: 10.2514/6.2003-7081.  Google Scholar [12] B. Li, X. Qian, J. Sun, K. L. Teo and C. J. Yu, A model of distributionally robust two-stage stochastic convex programming with linear recourse, Applied Mathematical Modelling, 58 (2018), 86-97.  doi: 10.1016/j.apm.2017.11.039.  Google Scholar [13] B. Li and Y. Rong, Joint transceiver optimization for wireless information and energy transfer in non-regenerative MIMO relay systems, IEEE Transactions on Vehicular Technology, 67 (2018), 8348-8362.   Google Scholar [14] B. Li, Y. Rong, J. Sun and K. L. Teo, A distributionally robust linear receiver design for multi-access space-time block coded MIMO systems, Journal of Industrial and Management Optimization, 16 (2017), 464-474.  doi: 10.1109/TWC.2016.2625246.  Google Scholar [15] B. Li, J. Sun, H. L. Xu and M. Zhang, A class of two-stage distributionally robust stochastic games, Journal of Industrial and Management Optimization, 15 (2019), 387-400.   Google Scholar [16] A. Marcos and S. Bennani, LPV modeling, analysis and design in space systems: Rationale, objectives and limitations, AIAA Guidance, Navigation, and Control Conference, (2009). doi: 10.2514/6.2009-5633.  Google Scholar [17] J. T. Parker, A. Serrani, Y. Stephen, A. B. Michael and B. D. David, Control-oriented modeling of an air-breathing hypersonic vehicle, Journal of Guidance Control and Dynamics, 30 (2007), 856-869.  doi: 10.2514/1.27830.  Google Scholar [18] C. Peng, X. M. Wang and R. Xie, Fault-tolerant control for hypersonic vehicle with system uncertainty, Journal of Beijing University of Aeronautics and Astronautics, 42 (2016), 1414-1421.   Google Scholar [19] R. Y. Qi, Y. H. Huang and B. Jiang, Adaptive backstepping control for a hypersonic vehicle with uncertain parameters and actuator faults, Proceedings of the Institution of Mechanical Engineers, Part Ⅰ: Journal of Systems and Control Engineering, 227 (2013), 51-61.  doi: 10.1177/0959651812450134.  Google Scholar [20] D. O. Sigthorsson, Control-Oriented Modeling and Output Feedback Control of Hypersonic Air-Breathing Vehicles, Ph.D thesis, The Ohio State University, 2008. Google Scholar [21] H. B. Sun, S. H. Li and C. Y. Sun, Robust adaptive integral-sliding-mode fault-tolerant control for air-breathing hypersonic vehicles, Proceedings of the Institution of Mechanical Engineers, Part Ⅰ: Journal of Systems and Control Engineering, 226 (2012), 1344-1355.   Google Scholar [22] C. Y. Sun, C. X. Mu and Y. Yu, Some control problems for near space hypersonic vehicles, Acta Automatica Sinica, 39 (2013), 1901-1913.  doi: 10.3724/SP.J.1004.2013.01901.  Google Scholar [23] J. G. Sun, S. M. Song and G. Q. Wu, Fault-tolerant track control of hypersonic vehicle based on fast terminal sliding mode, Journal of Spacecraft and Rockets, 54 (2017), 1304-1316.  doi: 10.2514/1.A33890.  Google Scholar [24] Z. D. Wang, G. L. Wei and G. Feng, Reliable control for discrete-time piecewise linear systems with infinite distributed delays, Automatica J. IFAC, 45 (2009), 2991-2994.  doi: 10.1016/j.automatica.2009.09.012.  Google Scholar [25] Y. Wang, Y. Zhang and C. Bai, Review of guidance and control approaches for air-breathing hypersonic vehicle, Journal of Ordnance Equipment Engineering, 38 (2017), 72-76.   Google Scholar [26] Y. F. Xu, B. Jiang and Z. F. Gao, Fault tolerant tracking control for near space hypersonic vehicle via neural network, 3rd Systems and Control in Aeronautics and Astronautics (ISSCAA) International Symposium, (2010), 637–642. doi: 10.1109/ISSCAA.2010.5633189.  Google Scholar [27] F. Yang, K. L. Teo, R. Loxton, V. Rehbock, B. Li, C. J. Yu and L. Jennings, Visual MISER: An efficient user-friendly visual program for solving optimal control problems, Journal of Industrial and Management Optimization, 12 (2016), 781-810.  doi: 10.3934/jimo.2016.12.781.  Google Scholar [28] Q. C. Yang, Q. Zong and Q. Dong, Reentry control and performance evaluation method for hypersonic vehicle, Information and Control, 46 (2017), 33-40.   Google Scholar [29] C. F. Zhang, Q. Zong and Q. Dong, A survey of models and control problems of hypersonic vehicles, Information and Control, 46 (2017), 90-102.   Google Scholar [30] H. X. Zhang, Z. F. Gong, G. B. Cai and R. Song, Reentry tracking control of hypersonic vehicle with complicated constraints, Journal of Ordnance Equipment Engineering, 40 (2019), 1-6.   Google Scholar

show all references

##### References:
 [1] G. B. Cai, G. R. Duan and C. H. Hu, A velocity-based LPV modeling and control framework for an airbreathing hypersonic vehicle, International Journal of Innovative Computing Information and Control, 7 (2011), 2269-2281.   Google Scholar [2] M. Corless and J. Tu, State and input estimation for a class of uncertain systems, Automatica J. IFAC, 34 (1998), 757-764.  doi: 10.1016/S0005-1098(98)00013-2.  Google Scholar [3] P. Gahinet and P. Apkarian, A linear matrix inequality approach to $H_\infty$ control, International Journal of Robust and Nonlinear Control, 4 (1994), 421-448.  doi: 10.1002/rnc.4590040403.  Google Scholar [4] Z. F. Gao, T. Cao and J. X. Lin, Sliding mode fault tolerant tracking control for a flexible hypersonic vehicle with actuator faults, ICIC Express Letters Part B, Appli-Cations: An International Journal of Research and Surveys, 6 (2015), 1797-1804.   Google Scholar [5] Z. F. Gao, B. Jiang, P. Shi, J. Y. Liu and Y. F. Xu, Passive fault-tolerant control design for near-space hypersonic vehicle dynamical system, Circuits, Systems, and Signal Processing, 31 (2012), 565-581.  doi: 10.1007/s00034-011-9385-7.  Google Scholar [6] Z. F. Gao, J. X. Lin and T. Cao, Robust fault tolerant tracking control design for a linearized hypersonic vehicle with sensor fault, International Journal of Control Automation and Systems, 13 (2015), 672-679.  doi: 10.1007/s12555-014-0169-2.  Google Scholar [7] S. Gao and J. S. Mei, Fault tolerant control of actuator faults for input nonlinear systems, Information and Control, 44 (2015), 463-468.   Google Scholar [8] X. Guan, J. Zhao and Y. He, Track technology of hypersonic aircraft in near space, Journal of Ordnance Equipment Engineering, 32 (2011), 4-6.   Google Scholar [9] J. J. He, R. Y. Qi and B. Jiang, Adaptive output feedback fault-tolerant control design for hypersonic flight vehicles, Journal of the Franklin Institute, 352 (2015), 1811-1835.  doi: 10.1016/j.jfranklin.2015.01.016.  Google Scholar [10] L. Huang, Z. S. Duan and J. Y. Yang, Challenges of control science in near space hypersonic aircrafts, Control Theory and Applications, 28 (2011), 1496-1505.   Google Scholar [11] B. Fidan, M. Mirmirani and P. Ioannou, Flight dynamics and control of air-breathing hypersonic vehicles: Review and new directions, 12th AIAA International Space Planes and Hypersonic Systems and technologies, (2003). doi: 10.2514/6.2003-7081.  Google Scholar [12] B. Li, X. Qian, J. Sun, K. L. Teo and C. J. Yu, A model of distributionally robust two-stage stochastic convex programming with linear recourse, Applied Mathematical Modelling, 58 (2018), 86-97.  doi: 10.1016/j.apm.2017.11.039.  Google Scholar [13] B. Li and Y. Rong, Joint transceiver optimization for wireless information and energy transfer in non-regenerative MIMO relay systems, IEEE Transactions on Vehicular Technology, 67 (2018), 8348-8362.   Google Scholar [14] B. Li, Y. Rong, J. Sun and K. L. Teo, A distributionally robust linear receiver design for multi-access space-time block coded MIMO systems, Journal of Industrial and Management Optimization, 16 (2017), 464-474.  doi: 10.1109/TWC.2016.2625246.  Google Scholar [15] B. Li, J. Sun, H. L. Xu and M. Zhang, A class of two-stage distributionally robust stochastic games, Journal of Industrial and Management Optimization, 15 (2019), 387-400.   Google Scholar [16] A. Marcos and S. Bennani, LPV modeling, analysis and design in space systems: Rationale, objectives and limitations, AIAA Guidance, Navigation, and Control Conference, (2009). doi: 10.2514/6.2009-5633.  Google Scholar [17] J. T. Parker, A. Serrani, Y. Stephen, A. B. Michael and B. D. David, Control-oriented modeling of an air-breathing hypersonic vehicle, Journal of Guidance Control and Dynamics, 30 (2007), 856-869.  doi: 10.2514/1.27830.  Google Scholar [18] C. Peng, X. M. Wang and R. Xie, Fault-tolerant control for hypersonic vehicle with system uncertainty, Journal of Beijing University of Aeronautics and Astronautics, 42 (2016), 1414-1421.   Google Scholar [19] R. Y. Qi, Y. H. Huang and B. Jiang, Adaptive backstepping control for a hypersonic vehicle with uncertain parameters and actuator faults, Proceedings of the Institution of Mechanical Engineers, Part Ⅰ: Journal of Systems and Control Engineering, 227 (2013), 51-61.  doi: 10.1177/0959651812450134.  Google Scholar [20] D. O. Sigthorsson, Control-Oriented Modeling and Output Feedback Control of Hypersonic Air-Breathing Vehicles, Ph.D thesis, The Ohio State University, 2008. Google Scholar [21] H. B. Sun, S. H. Li and C. Y. Sun, Robust adaptive integral-sliding-mode fault-tolerant control for air-breathing hypersonic vehicles, Proceedings of the Institution of Mechanical Engineers, Part Ⅰ: Journal of Systems and Control Engineering, 226 (2012), 1344-1355.   Google Scholar [22] C. Y. Sun, C. X. Mu and Y. Yu, Some control problems for near space hypersonic vehicles, Acta Automatica Sinica, 39 (2013), 1901-1913.  doi: 10.3724/SP.J.1004.2013.01901.  Google Scholar [23] J. G. Sun, S. M. Song and G. Q. Wu, Fault-tolerant track control of hypersonic vehicle based on fast terminal sliding mode, Journal of Spacecraft and Rockets, 54 (2017), 1304-1316.  doi: 10.2514/1.A33890.  Google Scholar [24] Z. D. Wang, G. L. Wei and G. Feng, Reliable control for discrete-time piecewise linear systems with infinite distributed delays, Automatica J. IFAC, 45 (2009), 2991-2994.  doi: 10.1016/j.automatica.2009.09.012.  Google Scholar [25] Y. Wang, Y. Zhang and C. Bai, Review of guidance and control approaches for air-breathing hypersonic vehicle, Journal of Ordnance Equipment Engineering, 38 (2017), 72-76.   Google Scholar [26] Y. F. Xu, B. Jiang and Z. F. Gao, Fault tolerant tracking control for near space hypersonic vehicle via neural network, 3rd Systems and Control in Aeronautics and Astronautics (ISSCAA) International Symposium, (2010), 637–642. doi: 10.1109/ISSCAA.2010.5633189.  Google Scholar [27] F. Yang, K. L. Teo, R. Loxton, V. Rehbock, B. Li, C. J. Yu and L. Jennings, Visual MISER: An efficient user-friendly visual program for solving optimal control problems, Journal of Industrial and Management Optimization, 12 (2016), 781-810.  doi: 10.3934/jimo.2016.12.781.  Google Scholar [28] Q. C. Yang, Q. Zong and Q. Dong, Reentry control and performance evaluation method for hypersonic vehicle, Information and Control, 46 (2017), 33-40.   Google Scholar [29] C. F. Zhang, Q. Zong and Q. Dong, A survey of models and control problems of hypersonic vehicles, Information and Control, 46 (2017), 90-102.   Google Scholar [30] H. X. Zhang, Z. F. Gong, G. B. Cai and R. Song, Reentry tracking control of hypersonic vehicle with complicated constraints, Journal of Ordnance Equipment Engineering, 40 (2019), 1-6.   Google Scholar
Curve of flight path angle under actuator fault
Structure diagram of control system
Velocity curve under actuator fault
Flight path angle curve under actuator fault
Attack angle curve under actuator fault
Altitude curve under actuator fault
Velocity tracking performance
Flight path angle tracking performance
Attack angle tracking performance
Altitude tracking performance
Control surface deflection angle curve
Diffuser area ratio curve
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