Abstract
This paper presents an adaptive dynamic surface control scheme for vertical takeoff and landing reusable launch vehicles (VTLVs) with unknown disturbances, model uncertainties, and an attitude constraint to achieve exact attitude tracking control in the aerodynamic descent phase. First, the six-degree-of-freedom dynamic model of the VTLV is established. Next, the unknown disturbances and model uncertainties in the VTLV model are considered as the total disturbances, which are estimated by employing an uncertainty and disturbance estimator to compensate the controller, thereby enhancing the control accuracy of the system. Moreover, a symmetric time-varying barrier Lyapunov function is utilized to cope with the attitude-constrained problem. Finally, the high tracking performance of the proposed adaptive dynamic surface controller is verified by numerical simulation results.
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The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
Yang, Y.: Study on roadmap of Chinese reusable launch vehicle. Missile Space Veh. 4, 1–4 (2006)
Wang, Z.G., Luo, S.B., Wu, J.J.: Recent progress on reusable launch vehicle, 1-2. National University of Defense Technology Press, Changsha (2004)
Cui, N.G., Wu, R., Wei, C.Z., et al.: Development and key technologies of vertical takeoff vertical landing reusable launch vehicle. Astronaut. Syst. Eng. Technol. 2(2), 27–42 (2018)
Song, Z.Y., Cai, Q.Y., Han, P.X., et al.: Review of guidance and control technologies of reusable launch vehicles. Acta Aeronautica et Aeronautica Sinica 42(11), 37–65 (2021)
Zhang, L., Wei, C., Wu, R., et al.: Fixed-time extended state observer based non-singular fast terminal sliding mode control for a VTVL reusable launch vehicle. Aerosp. Sci. Technol. 82, 70–79 (2018)
Wang, Z., Wu, Z., Du, Y.J.: Adaptive sliding mode backstepping control for entry reusable launch vehicles based on nonlinear disturbance observer. Proc. Inst. Mech. Eng. Part G J. Aerospace Eng. 230(1), 19–29 (2015)
Tian, B.L., Lu, H.C., Zuo, Z.Y., et al.: Multivariable uniform finite-time output feedback reentry attitude control for RLV with mismatched disturbance. J. Franklin Inst. 355(8), 3470–3487 (2018)
Wang, Z., Wu, Z., Du, Y.J.: Robust adaptive backstepping control for reentry reusable launch vehicles. Acta Astronaut. 126, 258–264 (2016)
Tian, B.L., Lu, H.C., Zuo, Z.Y., et al.: Adaptive prescribed performance attitude control for RLV with mismatched disturbance. Aerosp. Sci. Technol. 117, 106918 (2021)
Swaroop, D., Hedrick, J.K., Yip, P.P., et al.: Dynamic surface control for a class of nonlinear systems. IEEE Trans. Autom. Control 45(10), 1893–1899 (2000)
Hu, C.F., Gao, Z.F., Ren, Y.L., et al.: A robust adaptive nonlinear fault-tolerant controller via norm estimation for reusable launch vehicles. Acta Astronaut. 82, 685–695 (2016)
Zhou, L.L., Liu, L., Cheng, Z.T., et al.: Adaptive dynamic surface control using neural networks for hypersonic flight vehicle with input nonlinearities. Optimal Control Appl. Methods 41(6), 1904–1927 (2020)
Wang, L., Qi, R.Y., Peng, Z.Y.: Integrated design of adaptive fault-tolerant control for non-minimum phase hypersonic flight vehicle system with input saturation and state constraints. Proc. Inst. Mech. Eng. Part G J. Aerospace Eng. 236(11), 2281–2301 (2022)
Zhang, H.G., Han, J., Luo, C.M., et al.: Fault-tolerant control of a nonlinear system based on generalized fuzzy hyperbolic model and adaptive disturbance observer. IEEE Trans. Syst. Man Cybernet. Syst. 47(8), 2289–2300 (2016)
Piao, M.N., Wang, Y., Sun, M.W., et al.: Fixed-time-convergent generalized extended state observer based motor control subject to multiple disturbances. IEEE Trans. Ind. Inf. 17(12), 8066–8079 (2021)
Zhang, X.Y., Li, H., Zhu, B.: Improved UDE and LSO for a class of uncertain second-order nonlinear systems without velocity measurements. IEEE Trans. Instrum. Meas. 69(7), 4076–4092 (2020)
Zhong, Q.C., Rees, D.: Control of uncertain LTI systems based on an uncertainty and disturbance estimator. J. Dyn. Syst. Meas. Control 126(4), 905–910 (2004)
Kodhanda, A., Talole, S.E.: Performance analysis of UDE based controllers employing various filters 49(1), 83–88 (2016)
Ren, B., Zhong, Q.C., Dai, J.: Asymptotic reference tracking and disturbance rejection of UDE-based robust control. IEEE Trans. Ind. Electron. 64(4), 3166–3176 (2017)
Su, S., Lin, Y.: Robust output tracking control of a class of nonminimum phase systems and application to VTOL aircraft. Int. J. Control 84(11), 1858–1872 (2011)
Sun, L., Li, D., Zhong, Q.C.: Control of a class of industrial processes with time delay based on a modified uncertainty and disturbance estimator. IEEE Trans. Ind. Electron. 63(11), 7018–7028 (2016)
Ma, J.T., Wen, H., Jin, D.P.: PDE model-based boundary control of a spacecraft with double flexible appendages under prescribed performance. Adv. Space Res. 65(1), 586–597 (2020)
Ni, J., Ahn, C.K., Liu, L.: Prescribed performance fixed-time recurrent neural network control for uncertain nonlinear systems. Neurocomputing 363, 351–365 (2019)
Ilchmann, A., Ryan, E.P., Townsend, P.: Tracking with prescribed transient behavior for nonlinear systems of known relative degree. SIAM J. Control. Optim. 46(1), 210–230 (2007)
Bu, X.W.: Air-breathing hypersonic vehicles funnel control using neural approximation of non-affine dynamics. IEEE/ASME Trans. Mechatron. 23(5), 2099–2108 (2018)
Gu, X.Y., Guo, J.G., Guo, Z.Y., et al.: Performance improvement-oriented reentry attitude control for reusable launch vehicles with overload constraint. ISA Trans. 128, 386–396 (2022)
Xu, S.H., Guan, Y.Z., Wei, C.Z., et al.: Reinforcement-learning-based tracking control with fixed-time prescribed performance for reusable launch vehicle under input constraints. Appl. Sci. 12(15), 7436 (2022)
Xu, S.H., Guan, Y.Z., Bai, Y.L., et al.: Practical predefined-time barrier function-based adaptive sliding mode control for reusable launch vehicle. Acta Astronaut. 204, 376–388 (2023)
Wang, M.Z., Wei, C.Z., Pu, J.L., et al.: Predefined-time nonsingular attitude control for vertical-takeoff horizontal-landing reusable launch vehicle. Appl. Sci. 12(19), 10153 (2022)
Shao, X.D., Hu, Q.L., Shi, Y., et al.: Predefined-time nonsingular attitude control for vertical-takeoff horizontal-landing reusable launch vehicle. IEEE Trans. Control Syst. Technol. 28(2), 10153 (2018)
Wang, Z.W., Liang, B., Sun, Y.C., et al.: Adaptive fault-tolerant prescribed-time control for teleoperation systems with position error constraints. IEEE Trans. Ind. Inf. 16(7), 4889–4899 (2019)
Tee, K.P., Ge, S.S., Tay, E.H.: Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica 45(4), 918–927 (2009)
Yuan, Y., Wang, Z., Guo, L., et al.: Barrier Lyapunov functions-based adaptive fault tolerant control for flexible hypersonic flight vehicles with full state constraints. IEEE Trans. Syst. Man Cybernet. Syst. 50(9), 3391–3400 (2018)
Wu, Z.H., Lu, J.C., Zhou, Q., et al.: Modified adaptive neural dynamic surface control for morphing aircraft with input and output constraints. Nonlinear Dyn. 87(4), 2367–2383 (2017)
Cui, N.G., Wu, R., Wei, C.Z., et al.: Double-order power fixed-time convergence sliding mode control method for launch vehicle vertical returning. J. Harbin Inst. Technol. 52(4), 15–24 (2020)
Liang, X.H., Wang, Q., Hu, C.H., et al.: Fixed-time observer based fault tolerant attitude control for reusable launch vehicle with actuator faults. Aerosp. Sci. Technol. 107, 106314 (2020)
Zhao, Z., He, W., Ge, S.S.: Adaptive neural network control of a fully actuated marine surface vessel with multiple output constraints. IEEE Trans. Control Syst. Technol. 22(4), 1536–1543 (2014)
Ren, B., Ge, S.S., Tee, K.P., et al.: Adaptive neural control for output feedback nonlinear systems using a barrier Lyapunov function. IEEE Trans. Neural Netw. 21(8), 1339–1345 (2010)
Xu, B.: Robust adaptive neural control of flexible hypersonic flight vehicle with dead-zone input nonlinearity. Nonlinear Dyn. 80(3), 1509–1520 (2015)
Ge, S.S., Wang, C.: Adaptive neural control of uncertain MIMO nonlinear systems. IEEE Trans. Neural Netw. 15(3), 674–692 (2004)
Tian, B.L., Fan, W.R., Zong, Q.: Integrated guidance and control for reusable launch vehicle in reentry phase. Nonlinear Dyn. 80(1–2), 397–412 (2015)
Tian, B.L., Fan, W.R., Su, R.: Real-time trajectory and attitude coordination control for reusable launch vehicle in reentry phase. IEEE Trans. Ind. Electron. 62(3), 1639–1650 (2014)
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The authors would like to express their sincere thanks to anonymous reviewers for their helpful suggestions for improving the technique note.
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All authors contributed to the study conception and design. Overarching research goals and aims were formulated by WL and SS. The modeling analysis and the design of the control methodology were performed by RM and WL. The theory analysis and simulation verification were completed by RM and SS. The first draft of the manuscript was written by RM and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. SS is responsible for ensuring that the descriptions are accurate and agreed by all authors.
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Mo, R., Li, W. & Su, S. UDE-based adaptive dynamic surface control for attitude-constrained reusable launch vehicle. Nonlinear Dyn 112, 5365–5378 (2024). https://doi.org/10.1007/s11071-023-09233-9
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DOI: https://doi.org/10.1007/s11071-023-09233-9