Switched linear parameter-varying tracking control for quadrotors with large attitude angles and time-varying inertia. (English) Zbl 1472.93128
Summary: This paper is concerned with large-angle attitude tracking control for quadrotors in the presence of time-varying inertia and external disturbances using a switched linear parameter-varying (LPV) system method. The attitude system of the quadrotor is divided into two parts, that is, the outer attitude-angle loop and inner angular-velocity loop. A feedback linearization controller is designed in the outer loop to generate the desired angular velocities. In the inner loop, the nonlinear quadrotor dynamics with time-varying inertia is approximated by a switched LPV system that consists of a series of LPV models. The persistent dwell time (PDT) switching logic is adopted to describe the fast and slow switches coexist among these LPV models. Then, both the continuous-time state-feedback and dynamic output-feedback controllers are designed, which ensure the globally uniformly asymptotically stability and \(\mathcal{L}_2 - \mathcal{L}_\infty\) external disturbance attenuation performance of the attitude tracking error system. Finally, the effectiveness of the proposed tracking control method of quadrotors is validated with an example.
MSC:
| 93C85 | Automated systems (robots, etc.) in control theory |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93C05 | Linear systems in control theory |
Keywords:
\(\mathcal{L}_2 - \mathcal{L}_\infty\) performance; persistent dwell time; quadrotor; switched linear parameter-varying systemsReferences:
| [1] | CarrilloLRG, ColungaGRF, SanahujaG, LozanoR. Quad rotorcraft switching control: an application for the task of path following. IEEE Trans Control Syst Technol. 2014;22(4):1255‐1267. https://doi.org/10.1109/TCST.2013.2284790. · doi:10.1109/TCST.2013.2284790 |
| [2] | QinL, HeX, YanR, DengR, ZhouD. Distributed sensor fault diagnosis for a formation of multi‐vehicle systems. J Franklin Inst. 2019;356(2):791‐818. https://doi.org/10.1016/j.jfranklin.2017.11.020. · Zbl 1406.93217 · doi:10.1016/j.jfranklin.2017.11.020 |
| [3] | ZhouZ, WangH, WangY, XueX, ZhangM. Distributed formation control for multiple quadrotor UAVs under Markovian switching topologies with partially unknown transition rates. J Franklin Inst. 2019;356(11):5706‐5728. https://doi.org/10.1016/j.jfranklin.2018.11.051. · Zbl 1415.93038 · doi:10.1016/j.jfranklin.2018.11.051 |
| [4] | FuC, HongW, LuH, ZhangL, GuoX, TianY. Adaptive robust backstepping attitude control for a multi‐rotor unmanned aerial vehicle with time‐varying output constraints. Aerosp Sci Technol. 2018;78:593‐603. https://doi.org/10.1016/j.ast.2018.05.021. · doi:10.1016/j.ast.2018.05.021 |
| [5] | JaliliS, RezaieB, RahmaniZ. A novel hybrid model predictive control design with application to a quadrotor helicopter. Opt Control Appl Methods. 2018;39:1301‐1322. https://doi.org/10.1002/oca.2411. · Zbl 1398.93190 · doi:10.1002/oca.2411 |
| [6] | FangX, LiuF, DingZ. Robust control of unmanned helicopters with high‐order mismatched disturbances via disturbance‐compensation‐gain construction approach. J Franklin Inst. 2018;355(15):7158‐7177. https://doi.org/10.1016/j.jfranklin.2018.08.015. · Zbl 1398.93239 · doi:10.1016/j.jfranklin.2018.08.015 |
| [7] | HowJP, BehihkeB, FrankA, DaleD, VianJ. Real‐time indoor autonomous vehicle test environment. IEEE Control Syst Mag. 2008;28(2):51‐64. https://doi.org/10.1109/MCS.2007.914691. · Zbl 1395.93393 · doi:10.1109/MCS.2007.914691 |
| [8] | PoundsPEI, BersakDR, DollarAM. Stability of small-scale UAV helicopters and quadrotors with added payload mass under PID control. Auton Robot. 2012;33:129‐142. https://doi.org/10.1007/s10514‐012‐9280‐5. · doi:10.1007/s10514‐012‐9280‐5 |
| [9] | ChenM, HuzmezanM. A combined MPBC/2DOF H_∞ controller for a quadrotor UAV. Paper presented at: Proceedings of the AIAA Guidance, Navigation, and Control Conference and Exhibit; 2003:11‐14; Austin, Texas. https://doi.org/10.2514/6.2003‐5520 · doi:10.2514/6.2003‐5520 |
| [10] | BasriMAM, HusainAR, DanapalasingamKA. Enhanced backstepping controller design with application to autonomous quadrotor unmanned aerial vehicle. J Intell Robot Syst. 2015;79(2):295‐321. https://doi.org/10.1007/s10846‐014‐0072‐3. · doi:10.1007/s10846‐014‐0072‐3 |
| [11] | TianB, CuiJ, LuH, ZuoZ, ZongQ. Adaptive finite‐time attitude tracking of quadrotors with experiments and comparisons. IEEE Trans Ind Electron. 2019;66(12):9428‐9438. https://doi.org/10.1109/TIE.2019.2892698. · doi:10.1109/TIE.2019.2892698 |
| [12] | WangH, YeX, TianY, ZhengG, ChristovN. Model-free based terminal SMC of quadrotor attitude and position. IEEE Trans Aerosp Electron Syst. 2016;52(5):2519‐2528. https://doi.org/10.1109/TAES.2016.150303. · doi:10.1109/TAES.2016.150303 |
| [13] | HouZ, LuP, TuZ. Nonsingular terminal sliding mode control for a quadrotor UAV with a total rotor failure. Aerosp Sci Technol. 2020;98:105716. https://doi.org/10.1016/j.ast.2020.105716. · doi:10.1016/j.ast.2020.105716 |
| [14] | WangL, SuJ. Switching control of attitude tracking on a quadrotor UAV for large‐angle rotational maneuvers. Paper presented at: Proceedings of IEEE International Conference on Robotics and Automation; 2014:2907‐2912; Hong Kong, China. https://doi.org/10.1109/ICRA.2014.6907277 · doi:10.1109/ICRA.2014.6907277 |
| [15] | MellingerD, MichaelN, KumarV. Trajectory generation and control for precise aggressive maneuvers with quadrotors. Int J Robot Res. 2012;31(5):664‐674. https://doi.org/10.1177/0278364911434236. · doi:10.1177/0278364911434236 |
| [16] | AlexisK, NikolakopoulosG, TzesA. Switching model predictive attitude control for a quadrotor helicopter subject to atmospheric disturbances. Control Eng Pract. 2011;19(10):1195‐1207. https://doi.org/10.1016/j.conengprac.2011.06.010. · doi:10.1016/j.conengprac.2011.06.010 |
| [17] | ZhuY, ZhengWX, ZhouD. Quasi‐synchronization of discrete‐time Lur’e‐type switched systems with parameter mismatches and relaxed PDT constraints. IEEE Trans Cybern. 2020;50(5):2026‐2037. https://doi.org/10.1109/TCYB.2019.2930945. · doi:10.1109/TCYB.2019.2930945 |
| [18] | CastilloA, SanzR, GarciaP, QiuW, WangH, XuC. Disturbance observer‐based quadrotor attitude tracking control for aggressive maneuvers. Control Eng Pract. 2019;82:14‐23. https://doi.org/10.1016/j.conengprac.2018.09.016. · doi:10.1016/j.conengprac.2018.09.016 |
| [19] | WuL, QiT, FengZ. Average dwell time approach to \(\mathcal{L}_2 - \mathcal{L}_{\operatorname{\infty}}\) control of switched delay systems via dynamic output feedback. IET Control Theory Appl. 2009;3(10):1425‐1436. https://doi.org/10.1049/iet‐cta.2008.0315. · doi:10.1049/iet‐cta.2008.0315 |
| [20] | LiX, HouL. l_2−l_∞ control for sampled‐data systems with packet dropout: switched system method. Int J Control Autom Syst. 2019;17(11):2746‐2753. https://doi.org/10.1007/s12555‐018‐0867‐2. · doi:10.1007/s12555‐018‐0867‐2 |
| [21] | LanXJ, WangYJ, LiuL. Dynamic decoupling tracking control for the polytopic LPV model of hypersonic vehicle. Sci China Inf Sci. 2015;58(9):1‐14. https://doi.org/10.1007/s11432‐015‐5339‐1. · doi:10.1007/s11432‐015‐5339‐1 |
| [22] | PereiraRL, KienitzKH, LeandroMAC. Optimal guaranteed cost control for discrete‐time LPV systems with bounded rates of variation. Opt Control Appl Methods. 2018;39:1989‐1998. https://doi.org/10.1002/oca.2463. · Zbl 1405.49014 · doi:10.1002/oca.2463 |
| [23] | WuF, YangXH, PackardA, BeckerG. Induced \(\mathcal{L}_2\)‐norm control for LPV systems with bounded parameter variation rates. Int J Robust Nonlinear Control. 1996;6:983‐998. https://doi.org/10.1002/(SICI)1099‐1239(199611)6:9/10<983::AID‐RNC263>3.0.CO;2‐C. · Zbl 0863.93074 · doi:10.1002/(SICI)1099‐1239(199611)6:9/10<983::AID‐RNC263>3.0.CO;2‐C |
| [24] | TrapielloC, PuigV, MorcegoB. Position‐heading quadrotor control using LPV techniques. IET Control Theory Appl. 2019;13(6):783‐794. https://doi.org/10.1049/iet‐cta.2018.6147. · doi:10.1049/iet‐cta.2018.6147 |
| [25] | HasseniS, AbdouL. Integral Backstepping/LFT‐LPV H_∞ control for the trajectory tracking of a quadcopter. Paper presented at: Proceedings of the7th International Conference on Systems and Control (ICSC); 2018:348‐353; Valencia, Spain. https://doi.org/10.1109/ICoSC.2018.8587839 · doi:10.1109/ICoSC.2018.8587839 |
| [26] | RotondoD, NejjariF, PuigV. Model reference quasi‐LPV control of a quadrotor UAV. Paper presented at: Proceedings of IEEE Conference on Control Applications; 2014:736‐741; Antibes, France. https://doi.org/10.1109/CCA.2014.6981428 · doi:10.1109/CCA.2014.6981428 |
| [27] | Guzmán‐RabasaJA, López‐EstradaFR, González‐ContrerasBM, Valencia‐PalomoG, ChadliM, Pérez‐PatricioM. Actuator fault detection and isolation on a quadrotor unmanned aerial vehicle modeled as a linear parameter‐varying system. Measur Control. 2019;52(9‐10):1228‐1239. https://doi.org/10.1177/0020294018824764. · doi:10.1177/0020294018824764 |
| [28] | López‐EstradaFR, PonsartJC, TheilliolD, ZhangY, Astorga‐ZaragozaMC. LPV model‐based tracking control and robust sensor fault diagnosis for a quadrotor UAV. J Intell Robot Syst. 2016;84(1‐4):163‐177. https://doi.org/10.1007/s10846‐015‐0295‐y. · doi:10.1007/s10846‐015‐0295‐y |
| [29] | LuB, WuF, KimSW. Switching LPV control of an F‐16 aircraft via controller state reset. IEEE Trans Control Syst Technol. 2006;14(2):267‐277. https://doi.org/10.1109/TCST.2005.863656. · doi:10.1109/TCST.2005.863656 |
| [30] | YangD, LiuY, ZhaoJ. Guaranteed cost control for switched LPV systems via parameter and state‐dependent switching with dwell time and its application. Opt Control Appl Methods. 2017;38(4):601‐617. https://doi.org/10.1002/oca.2274. · Zbl 1371.93104 · doi:10.1002/oca.2274 |
| [31] | CisnerosPSG, HoffmannC, BartelsM, WernerH. Linear parameter‐varying controller design for a nonlinear quad‐rotor helicopter model for high speed trajectory tracking. Paper presented at: Proceedings of American Control Conference; 2016:486‐491; Boston, MA. https://doi.org/10.1109/ACC.2016.7524961 · doi:10.1109/ACC.2016.7524961 |
| [32] | ZhengEH, XiongJJ, LuoJL. Second order sliding mode control for a quadrotor UAV. ISA Trans. 2014;53(4):1350‐1356. https://doi.org/10.1016/j.isatra.2014.03.010. · doi:10.1016/j.isatra.2014.03.010 |
| [33] | SvachaJ, PaulosJ, LoiannoG, et al. IMU‐based inertia estimation for a quadrotor using Newton‐Euler dynamics. IEEE Robot Automat Lett. 2020;5(3):3861‐3867. https://doi.org/10.1109/LRA.2020.2976308. · doi:10.1109/LRA.2020.2976308 |
| [34] | BaranyiP. TP model transformation as a way to LMI‐based controller design. IEEE Trans Ind Electron. 2004;51(2):387‐400. https://doi.org/10.1109/TIE.2003.822037. · doi:10.1109/TIE.2003.822037 |
| [35] | WuX, XiaoB, QuY. Modeling and sliding mode‐based attitude tracking control of a quadrotor UAV with time‐varying mass. ISA Trans. 2019. https://doi.org/10.1016/j.isatra.2019.08.017. · doi:10.1016/j.isatra.2019.08.017 |
| [36] | PhamTH, IchalalD, MammarS. LPV and nonlinear‐based control of an autonomous quadcopter under variations of mass and moment of inertia. Paper presented at: Proceedings of IFAC Symposium on Systems Structure and Control; 2019:176‐183; Sinaia, Romania. https://doi.org/10.1016/j.ifacol.2019.12.371 · doi:10.1016/j.ifacol.2019.12.371 |
| [37] | AboudoniaA, El‐BadawyA, RashadR. Disturbance observer‐based feedback linearization control of an unmanned quadrotor helicopter. Proc Inst Mech Eng I J Syst Control Eng. 2016;230(9):877‐891. https://doi.org/10.1177/0959651816656951. · doi:10.1177/0959651816656951 |
| [38] | LeeD, KimHJ, SastryS. Feedback linearization vs. adaptive sliding mode control for a quadrotor helicopter. Int J Control Autom Syst. 2009;7(3):419‐428. https://doi.org/10.1007/s12555‐009‐0311‐8. · doi:10.1007/s12555‐009‐0311‐8 |
| [39] | YuanS, SchutterBD, BaldiS. Adaptive asymptotic tracking control of uncertain time‐driven switched linear systems. IEEE Trans Automat Contr. 2016;62(11):5802‐5807. https://doi.org/10.1109/TAC.2016.2639479. · Zbl 1390.93467 · doi:10.1109/TAC.2016.2639479 |
| [40] | ZhangL, ShiP. Model reduction for switched LPV systems with average dwell time. IEEE Trans Automat Contr. 2008;53(10):2443‐2448. https://doi.org/10.1109/TAC.2008.2007860. · Zbl 1367.93115 · doi:10.1109/TAC.2008.2007860 |
| [41] | ZhangL, ZhuangS, ShiP. Non‐weighted quasi‐time‐dependent H_∞ filtering for switched linear systems with persistent dwell‐time. Automatica. 2015;54:201‐209. https://doi.org/10.1016/j.automatica.2015.02.010. · Zbl 1318.93094 · doi:10.1016/j.automatica.2015.02.010 |
| [42] | HespanhaJP. Uniform stability of switched linear systems: extensions of LaSalle’s invariance principle. IEEE Trans Automat Contr. 2004;49(4):470‐482. https://doi.org/10.1109/TAC.2004.825641. · Zbl 1365.93348 · doi:10.1109/TAC.2004.825641 |
| [43] | WangX, ShirinzadehB, AngMH. Nonlinear double‐integral observer and application to quadrotor aircraft. IEEE Trans Ind Electron. 2015;62(2):1189‐1200. https://doi.org/10.1109/TIE.2014.2341571. · doi:10.1109/TIE.2014.2341571 |
| [44] | ZhangY, ChenZ, ZhangX, SunQ, SunM. A novel control scheme for quadrotor UAV based upon active disturbance rejection control. Aerosp Sci Technol. 2018;79:601‐609. https://doi.org/10.1016/j.ast.2018.06.017. · doi:10.1016/j.ast.2018.06.017 |
| [45] | HanC, WuL, LamHK, et al. Nonfragile control with guaranteed cost of T‐S fuzzy singular systems based on parallel distributed compensation. IEEE Trans Fuzzy Syst. 2013;22(5):1183‐1196. https://doi.org/10.1109/TFUZZ.2013.2286415. · doi:10.1109/TFUZZ.2013.2286415 |
| [46] | López‐EstradaFR, Santos‐EstudilloO, Valencia‐PalomoG, Gómez‐PeñateS, Hernández‐GutiérrezC. Robust qLPV tracking fault‐tolerant control of a 3 DOF mechanical crane. Math Comput Appl. 2020;25(3):48. https://doi.org/10.3390/mca25030048. · doi:10.3390/mca25030048 |
| [47] | SunW, NingZ. Quantised output‐feedback design for networked control systems using semi‐Markov model approach. Int J Syst Sci. 2020;51(9):1637‐1652. https://doi.org/10.1080/00207721.2020.1772400. · Zbl 1483.93497 · doi:10.1080/00207721.2020.1772400 |
| [48] | CaiB, WengR, ZhangRX, YeL, ZhangL. Stabilization of a class of fuzzy stochastic jump systems with partial information on jump and sojourn parameters. Sci China Technol Sci. 2020;1‐11. https://doi.org/10.1007/s11431‐019‐1514‐8. · doi:10.1007/s11431‐019‐1514‐8 |
| [49] | ZhangL, CaiB, TanT, ShiY. Stabilization of non‐homogeneous hidden semi‐Markov jump systems with limited sojourn‐time information. Automatica. 2020;117:108963. https://doi.org/10.1016/j.automatica.2020.108963. · Zbl 1441.93333 · doi:10.1016/j.automatica.2020.108963 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
