Optimal Robust Control Based on State-Dependent Differential Riccati Equation with Application on Ducted Fan Aircraft

Document Type : Original Article

Authors

Department of Electrical Engineering, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

Abstract

In this paper, optimal robust controllers are developed for tracking control of a ducted fan engine of a thrust-vectored aircraft in the presence of external disturbances. First, by applying a nonlinear regulator based on the state-dependent differential Riccati equation (SDDRE) approach, an optimal control law is designed that is not robust against external disturbances. The second design, a VSC (variable structure control) with an NTV (nonlinear time-varying) sliding sector, is proposed. The sliding sector is a subset of the state space which is obtained by the SDDRE. As the final design, to guarantee the system's robustness against external disturbances and achieve optimal performance, a robust optimal sliding mode controller based on SDDRE (ROSMC) is designed, which integrates the sliding mode control (SMC) theory with the SDDRE approach. For each design, the global asymptotic stability is proved using the Lyapunov stability theorem. Also, the SDDRE is solved by a change of variable and converting it to a differential Lyapunov equation (DLE). Numerical simulations are presented considering different types of external disturbances and several scenarios. Simulation results show that ROSMC has stronger robustness and demonstrates optimal performance compared to SDDRE and VSC designs.

Keywords

References

[1] B. Fazeli Asl, S. S. Moosapour, "Adaptive backstepping fast terminal sliding mode controller design for ducted fan engine of thrust-vectored aircraft," Aerospace Science and Technology, vol. 71, pp. 521-529, 2017.
[2] Fan, X. Changle, X. Bin, "Modelling, attitude controller design and flight experiments of a novel micro-ducted-fan aircraft", Advances in Mechanical Engineering, vol. 10, no. 3, pp. 1-16, 2018.
[3] Wang, C. Xiang, Y. Ma, and B. Xu, "Comprehensive nonlinear modeling and simulation analysis of a tandem ducted fan aircraft," in Guidance, Navigation and Control Conference (CGNCC), 2014 IEEE Chinese, pp. 255-261: IEEE, 2014.
[4] Chadli, S. Aouaouda, H.-R. Karimi, and P. Shi, "Robust fault tolerant tracking controller design for a VTOL aircraft," Journal of the Franklin Institute, vol. 350, no. 9, pp. 2627-2645, 2013.
[5] Cimen, "State-dependent Riccati equation (SDRE) control: A survey," IFAC Proceedings Volumes, vol. 41, no. 2, pp. 3761-3775, 2008.
[6] Pearson, "Approximation methods in optimal control I. Sub-optimal control," International Journal of Electronics, vol. 13, no. 5, pp. 453-469, 1962.
[7] Korayem, S. Nekoo, "Finite-time state-dependent Riccati equation for time-varying nonaffine systems: Rigid and flexible joint manipulator control," ISA transactions, vol. 54, pp. 125-144, 2015.
[8] Heydari and S. N. Balakrishnan, "Approximate closed-form solutions to finite-horizon optimal control of nonlinear systems," in American Control Conference (ACC), 2012, 2012, pp. 2657-2662: IEEE.
[9] Heydari, S. Balakrishnan, "Path planning using a novel finite horizon suboptimal controller", Journal of guidance, control, and dynamics, vol. 36, no. 4, pp. 1210-1214, 2013.
[10] G. Lin, M. Xin, "Impact Angle Guidance Using State-Dependent (Differential) Riccati Equation: Unified Applicability Analysis", Journal of Guidance, Control, and Dynamics, vol. 43, no. 11, pp. 2175-2182, 2020.
[11] Ashish, A.J. Sinclair, "Nonlinear control for spacecraft pursuit-evasion game using the state-dependent Riccati equation method", IEEE Transactions on Aerospace and Electronic Systems, vol. 53, no. 6, pp. 3032-3042, 2017.
[12] Pan, K. D. Kumar, G. Liu, and K. Furuta, "Design of variable structure control system with nonlinear time-varying sliding sector," IEEE Transactions on Automatic Control, vol. 54, no. 8, pp. 1981-1986, 2009.
[13] Xu, D. Zhou, and S. Sun, "Finite time sliding sector guidance law with acceleration saturation constraint," IET Control Theory & Applications, vol. 10, no. 7, pp. 789-799, 2016.
[14] Cucuzzella, G.P. Incremona, A. Ferrara, "Event-triggered variable structure control", International Journal of Control, vol. 93, no. 2, pp. 252-260, 2020.
[15] Hongmei, "Simulation Research on Ship Electric Propulsion Speed Regulation System Based on Variable Structure Control and FPGA", Microprocessors and Microsystems, In press, 2020.
[16] Tourajizadeh and S. Zare, "Robust and optimal control of shimmy vibration in aircraft nose landing gear," Aerospace Science and Technology, vol. 50, pp. 1-14, 2016.
[17] Pukdeboon and P. Kumam, "Robust optimal sliding mode control for spacecraft position and attitude maneuvers," Aerospace Science and Technology, vol. 43, pp. 329-342, 2015.
[18] -H. Zheng, J.-J. Xiong, and J.-L. Luo, "Second order sliding mode control for a quadrotor UAV," ISA transactions, vol. 53, no. 4, pp. 1350-1356, 2014.
[19] H. Korayem, S. R. Nekoo & M. H. Korayem, "Sliding mode control design based on the state-dependent Riccati equation: theoretical and experimental implementation", International Journal of Control, vol. 92, no. 9, pp. 2136-2149, 2017.
[20] H. Korayem, S.R. Nekoo, M. H. Korayem, "Optimal sliding mode control design based on the state-dependent Riccati equation for cooperative manipulators to increase dynamic load carrying capacity." Robotica, vol. 37, no. 2, pp. 321-337, 2019.
[21] Farkh, M. Ksouri, and F. Bouani. "Optimal Robust Control for Unstable Delay System," Comput. Syst. Sci. Eng., vol. 36, no. 2, pp. 307-321, 2021.
[22] Pujol-Vazquez, S. Mobayen, and L. Acho. "Robust control design to the furuta system under time delay measurement feedback and exogenous-based perturbation," Mathematics, vol. 8, no. 12, pp. 21-31, 2020.
[23] Gkizas, "Optimal robust control of a Cascaded DC–DC boost converter," Control Engineering Practice, vol. 107, 2021.
[24] Xu, Q. Wang, and Y. Li. "Adaptive Optimal Robust Control for Uncertain Nonlinear Systems Using Neural Network Approximation in Policy Iteration," Applied Sciences, vol. 11, no. 5, 2312, 2021.
[25] Kiamini, A. Jalilvand, and S. Mobayen, "LMI-based robust control of floating tension-leg platforms with uncertainties and time-delays in offshore wind turbines via TS fuzzy approach," Ocean Engineering vol. 154, pp. 367-374, 2018.
[26] Batmani, M. Davoodi, and N. Meskin, "Nonlinear suboptimal tracking controller design using state-dependent Riccati equation technique," IEEE Transactions on Control Systems Technology, vol. 25, no. 5, pp. 1833-1839, 2016.
[27] Batmani, and S. Khodakaramzadeh., "Nonlinear estimation and observer-based output feedback control," IET Control Theory & Applications, vol. 14, no. 17, pp. 2548-2555, 2020.
[28] Batmani, " Event-triggered Observer Design for Nonlinear Networked Control Systems," Tabriz Journal of Electrical Engineering, vol. 49, no. 1, pp. 71-77, 2019.
[29] Nazari, "State Dependent Riccati Equation based Model Reference Adaptive Control for Finite Duration Cancer Treatment by using a Mixed Therapy," Tabriz Journal Of Electrical Engineering, vol. 48, no. 1, pp. 369-380, 2018.
TABRIZ JOURNAL OF ELECTRICAL ENGINEERING
Volume 51, Issue 3 - Serial Number 97
November 2021
Pages 303-313

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