The controller design for reusable launch vehicles is challenging due to enormous amounts of model parameter uncertainties and atmospheric disturbances. This paper first derives six-degree-of-freedom model of a reusable launch vehicle with atmospheric disturbances. Next, four kinds of atmospheric disturbances are introduced and wind models are established respectively. For attitude control of the reusable launch vehicle, a nonsingular terminal sliding mode controller is designed with stability guaranteed. Finally, simulation results show a satisfactory performance for the attitude tracking of the reusable launch vehicle with atmospheric disturbances.
SchiermanJWardDHullJet al.Integrated adaptive guidance and control for re-entry vehicles with flight-test results. J Guid Control Dyn2004; 27: 975–988.
2.
Schierman J and Hull J. In-flight entry trajectory optimization for reusable launch vehicles. In: AIAA guidance, navigation, and control conference and exhibit, 15–18 August 2005, pp.1–18. San Francisco, USA: AIAA.
3.
HansonJJonesR. Test results for entry guidance methods for space vehicles. J Guid Control Dyn2012; 27: 960–966.
4.
HodelSHallC. Variable-structure PID control to prevent integrator windup. IEEE Trans Ind Electron2001; 48: 442–451.
5.
GeorgieJValasekJ. Evaluation of longitudinal desired dynamics for dynamic-inversion controlled generic reentry vehicles. J Guid Control Dyn2012; 26: 811–819.
6.
Ito D, Ward D and Valasek J. Robust dynamic inversion controller design and analysis for the x-38. In: AIAA guidance, navigation, and control conference and exhibit, 6–9 August 2001, pp.1–11. Montreal, Canada: AIAA.
7.
JohnsonECaliseA. Limited authority adaptive flight control for reusable launch vehicles. J Guid Control Dyn2003; 26: 906–913.
8.
Lian B, Bang H and Hurtado J. Adaptive backstepping control based autopilot design for reentry vehicle. In: AIAA guidance, navigation, and control conference and exhibit, 16–19 August 2004, pp.1–10. Providence, USA: AIAA.
9.
FarrellJSharmaMPolycarpouM. Backstepping-based flight control with adaptive function approximation. J Guid Control Dyn2005; 28: 1089–1102.
10.
ZongQWangFTianB. Nonlinear adaptive filter backstepping flight control for reentry vehicle with input constraint and external disturbances. Proc IMechE, Part G: J Aerospace Engineering2013; 228: 889–907.
11.
DrakeDXinMBalakrishnanS. New nonlinear control technique for ascent phase of reusable launch vehicles. J Guid Control Dyn2004; 27: 930–937.
12.
Lam Q, Anderson B and Xin M. Preserving spacecraft attitude control accuracy using theta-d controller subject to reaction wheel failures. In: AIAA Infotech@aerospace, 20–22 April 2010, pp.1–19. Atlanta, USA: AIAA.
13.
Lam Q and Xin M. Robustness evaluation of theta-d technique for spacecraft attitude control subject to reaction wheel failures. In: AIAA guidance, navigation, and control conference, 2–5 August 2010, pp.1–17. Toronto, Canada: AIAA.
14.
Xin M and Balakrishnan S. State dependent Riccati equation based spacecraft attitude control. In: AIAA aerospace sciences meeting and exhibit. Reno, 14–17 January 2002, pp.1–7. USA: AIAA.
15.
Lam Q, Krishnamurthy P and Khorrami F. Enhancing flight control system performance using SDRE based controller as an augmentation layer. In: AIAA Guidance, navigation, and control conference, 10–13, August 2009, pp.1–14. Chicago, USA: AIAA.
16.
Zhu J, Banker B and Hall C. X-33 ascent flight control design by trajectory linearization – a singular perturbation approach. In: AIAA guidance, navigation, and control conference, 14–17 August 2000, pp.1–19. Denver, USA: AIAA.
17.
Zhu J. Well-defined series and parallel d-spectra for linear time-varying systems. In: American control conference, 29 June – 1 July 1994, pp.734–738. Ballmon, USA: IEEE.
18.
Bevacqua T, Best E, Huizenga A, et al. Improved trajectory linearization flight controller for reusable launch vehicles. In: AIAA Aerospace sciences meeting and exhibit, 5–8 January 2004, pp.1–12. Reno, USA: AIAA.
19.
ShaoXWangH. Sliding mode based trajectory linearization control for hypersonic reentry vehicle via extended disturbance observer. ISA Trans2014; 53: 1771–1786.
20.
ShaoXWangH. Active disturbance rejection based trajectory linearization control for hypersonic reentry vehicle with bounded uncertainties. ISA Trans2014; 54: 27–38.
21.
SmithEAdelfangI. A compendium of wind statistics and models for the NASA space shuttle and other aerospace vehicle programs. National Aeronautics and Space Administration, Marshall Space Flight Center, 1998.
22.
BuschekHCaliseA. Uncertainty modeling and fixed-order controller design for a hypersonic vehicle model. J Guid Control Dyn1997; 20: 42–48.
23.
DuYWuQJiangCet al.Adaptive recurrent-functional-link-network control for hypersonic vehicles with atmospheric disturbances. Sci China Inform Sci2011; 54: 482–497.
24.
MieleAWangTMelvinWet al.Gamma guidance schemes for flight in a windshear. J Guid Control Dyn1988; 11: 320–327.
25.
Jiang Z and Ordonez R. Robust approach and landing trajectory generation for reusable launch vehicles in winds. In: IEEE International conference on control applications, 3–5 September 2008, pp.930–935. San Antonio, USA: IEEE.
26.
MulgundSStengelR. Optimal nonlinear estimation for aircraft flight control in wind shear. Automatica1996; 32: 3–13.
27.
Jing Y, Xu J, Dimirovski G, et al. Optimal nonlinear estimation for aircraft flight control in wind shear. In: American control conference, 10–12 June 2009, pp.3813–3818. St. Louis, USA: IEEE.
28.
Baldi P, Castaldi P, Mimmo N, et al. A new longitudinal flight path control with adaptive wind shear estimation and compensation. In: 50th IEEE conference on decision and control and European control conference, 12–15 December 2011, pp.6852–6857. Orlando, USA: IEEE.
29.
YoonSKimYParkS. Constrained adaptive backstepping controller design for aircraft landing in wind disturbance and actuator stuck. Int J Aeronaut Space Sci2012; 13: 74–89.
30.
JuangJGChengKC. Application of neural networks to disturbances encountered landing control. IEEE Trans Intell Transp Syst2006; 7: 582–588.
31.
Zhang G, Yang L, Zhang J, et al. Longitudinal attitude controller design for aircraft landing with disturbance using ADRC/LQR. In: IEEE international conference on automation science and engineering, 17–20 August 2013, pp.330–335. Madison, USA: IEEE.
32.
HallCShtesselY. Sliding mode disturbance observer-based control for a reusable launch vehicle. J Guid Control Dyn2006; 29: 1315–1328.
33.
Shtessel Y, McDuffie J and Jackson M. Sliding mode control of the x-33 vehicle in launch and re-entry modes. In: AIAA guidance, navigation, and control conference and exhibit, 12–14 August 1998, pp.1–11. Reston, USA: AIAA.
34.
ShtesselYHallCJacksonM. Reusable launch vehicle control in multiple time scale sliding modes. J Guid Control Dyn2000; 23: 1013–1020.
35.
Shtessel Y and Hall C. Multiple time scale sliding mode control of reusable launch vehicles in ascent and descent modes. In: American control conference, 25–27 June 2001, pp.4357–4362. Arlington, USA: IEEE.
DefoortMFloquetTKokosyAet al.A novel higher order sliding mode control scheme. Syst Control Lett2009; 58: 102–108.
41.
BartoliniGPisanoA. A survey of applications of second-order sliding mode control to mechanical systems. Int J Control2003; 76: 875–892.
42.
Bartolini G, Levant A, Pisano A, et al. 2-sliding mode with adaptation. In: Proceedings of the 7th IEEE Mediterranean conference on control and systems, 28–30 June 1999, pp.2421–2429. Haifa, Israel: IEEE.
43.
DamianoAGattoGMarongiuIet al.Second-order sliding-mode control of DC drives. IEEE Trans Ind Electron2004; 51: 364–373.
44.
TianBZongQWangJet al.Quasi-continuous high-order sliding mode controller design for reusable launch vehicles in reentry phase. Aerosp Sci Technol2013; 28: 198–207.
45.
TianBFanWZongQet al.Nonlinear robust control for reusable launch vehicles in reentry phase based on time-varying high order sliding mode. J Franklin Inst2013; 350: 1787–1807.
46.
TianBFanWZongQ. Integrated guidance and control for reusable launch vehicle in reentry phase. Nonlinear Dyn2015; 80: 397–412.
47.
TianBFanWSuRet al.Real-time trajectory and attitude coordination control for reusable launch vehicle in reentry phase. IEEE Trans Ind Electron2015; 62: 1639–1650.
48.
TianBYinLWangH. Finite-time reentry attitude control based on adaptive multivariable disturbance compensation. IEEE Trans Ind Electron2015; 62: 5889–5898.
49.
FengYYuXManZ. Non-singular terminal sliding mode control of rigid manipulators. Automatica2002; 38: 2159–2167.
50.
PolyakovA. Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control2012; 57: 2106–2110.
51.
TianBZuoZYanXet al.A fixed-time output feedback control scheme for double integrator systems. Automatica2017; 80: 17–24.
52.
TianBZuoZWangH. Leader-follower fixed-time consensus of multi-agent systems with high-order integrator dynamics. Int J Control2016. DOI: 10.1080/00207179.2016.1207101.
53.
YouMZongQTianBet al.Fixed-time reentry attitude control based on nonsingular terminal sliding mode. IMA J Math Control Inform2017. DOI: 10.1093/imamci/dnx010.
54.
JustusGCampbellWDoubledayKet al.New atmospheric turbulence model for shuttle applications. NASA Tm1990; 1–45.
55.
HornRJohnsonC. Topics in matrix analysis, Cambridge: Cambridge University Press, 1991.
56.
NiJLiuLLiuCet al.Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system. IEEE Trans Circuits Syst II Express Briefs2016; 64: 151–155.
57.
Sanchez-Torres JD and Loukianov AG. A fixed-time second order sliding mode observer for a class of nonlinear systems. In: International workshop on variable structure systems, 29 June–2 July 2014, pp.1–4. Nantes, France: IEEE.
58.
FengYYuXHanF. On nonsingular terminal sliding-mode control of nonlinear systems. Automatica2013; 49: 1715–1722.
