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Volume 9 Issue 5
May  2022

IEEE/CAA Journal of Automatica Sinica

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K. H. He, C. Y. Dong, and  Q. Wang,  “Active disturbance rejection control for uncertain nonlinear systems with sporadic measurements,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 5, pp. 893–906, May 2022. doi: 10.1109/JAS.2022.105566
Citation: K. H. He, C. Y. Dong, and  Q. Wang,  “Active disturbance rejection control for uncertain nonlinear systems with sporadic measurements,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 5, pp. 893–906, May 2022. doi: 10.1109/JAS.2022.105566

Active Disturbance Rejection Control for Uncertain Nonlinear Systems With Sporadic Measurements

doi: 10.1109/JAS.2022.105566
Funds:  This work was supported by the National Natural Science Foundation of China (61833016, 61873295)
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  • This paper deals with the problem of active disturbance rejection control (ADRC) design for a class of uncertain nonlinear systems with sporadic measurements. A novel extended state observer (ESO) is designed in a cascade form consisting of a continuous time estimator, a continuous observation error predictor, and a reset compensator. The proposed ESO estimates not only the system state but also the total uncertainty, which may include the effects of the external perturbation, the parametric uncertainty, and the unknown nonlinear dynamics. Such a reset compensator, whose state is reset to zero whenever a new measurement arrives, is used to calibrate the predictor. Due to the cascade structure, the resulting error dynamics system is presented in a non-hybrid form, and accordingly, analyzed in a general sampled-data system framework. Based on the output of the ESO, a continuous ADRC law is then developed. The convergence of the resulting closed-loop system is proved under given conditions. Two numerical simulations demonstrate the effectiveness of the proposed control method.

     

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  • [1]
    Z. H. Zhao, J. Yang, S. H. Li, and W. H. Chen, “Composite nonlinear bilateral control for teleoperation systems with external disturbances,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1220–1229, Sept. 2019. doi: 10.1109/JAS.2018.7511273
    [2]
    X. J. Wang, Q. H. Wu, H. J. Wang, and X. H. Yin, “Adaptive neural tracking control for a class of non-lower triangular non-linear systems with dead zone and unmodelled dynamics,” IET Control Theory Appl., vol. 13, no. 5, pp. 672–682, Mar. 2019. doi: 10.1049/iet-cta.2018.5353
    [3]
    Y. Z. Hua, X. W. Dong, Q. D. Li, and Z. Ren, “Distributed time-varying formation robust tracking for general linear multiagent systems with parameter uncertainties and external disturbances,” IEEE Trans. Cybern., vol. 47, no. 8, pp. 1959–1969, Aug. 2017. doi: 10.1109/TCYB.2017.2701889
    [4]
    J. Q. Han, “From PID to active disturbance rejection control,” IEEE Trans. Ind. Electron., vol. 56, no. 3, pp. 900–906, Mar. 2009. doi: 10.1109/TIE.2008.2011621
    [5]
    K. H. He, C. Y. Dong, A. Yan, Q. Y. Zheng, B. Liang, and Q. Wang, “Composite deep learning control for autonomous bicycles by using deep deterministic policy gradient,” in Proc. 46th Annu. Conf. IEEE Industrial Electronics Society, Singapore, 2020, pp. 2766−2773.
    [6]
    L. Wang and J. B. Su, “Trajectory tracking of vertical take-off and landing unmanned aerial vehicles based on disturbance rejection control,” IEEE/CAA J. Autom. Sinica, vol. 2, no. 1, pp. 65–73, Jan. 2015. doi: 10.1109/JAS.2015.7032907
    [7]
    Z. J. Zhao and Z. J. Liu, “Finite-time convergence disturbance rejection control for a flexible timoshenko manipulator,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 1, pp. 157–168, Jan. 2021. doi: 10.1109/JAS.2020.1003378
    [8]
    Z. Q. Gao, “Scaling and bandwidth-parameterization based controller tuning,” in Proc. American Control Conf., Denver, USA, 2003, pp. 4989–4996.
    [9]
    S. Shao and Z. Gao, “On the conditions of exponential stability in active disturbance rejection control based on singular perturbation analysis,” Int. J. Control, vol. 90, no. 10, pp. 2085–2097, May 2017. doi: 10.1080/00207179.2016.1236217
    [10]
    B. Z. Guo and Z. L. Zhao, “On the convergence of an extended state observer for nonlinear systems with uncertainty,” Syst. Control Lett., vol. 60, no. 6, pp. 420–430, Jun. 2011. doi: 10.1016/j.sysconle.2011.03.008
    [11]
    Z. L. Zhao and B. Z. Guo, “A novel extended state observer for output tracking of mimo systems with mismatched uncertainty,” IEEE Trans. Autom. Control, vol. 63, no. 1, pp. 211–218, Jan. 2017.
    [12]
    T. T. Jiang, C. D. Huang, and L. Guo, “Control of uncertain nonlinear systems based on observers and estimators,” Automatica, vol. 59, pp. 35–47, Sep. 2015. doi: 10.1016/j.automatica.2015.06.012
    [13]
    M. P. Ran, Q. Wang, C. Y. Dong, and L. H. Xie, “Active disturbance rejection control for uncertain time-delay nonlinear systems,” Automatica, vol. 112, p. 108692, Feb. 2020.
    [14]
    R. C. Roman, R. E. Precup, and E. M. Petriu, “Hybrid data-driven fuzzy active disturbance rejection control for tower crane systems,” Eur. J. Control, vol. 58, pp. 373–387, Mar. 2021. doi: 10.1016/j.ejcon.2020.08.001
    [15]
    Y. Y. Wang, X. X. Yang, and H. C. Yan, “Reliable fuzzy tracking control of near-space hypersonic vehicle using aperiodic measurement information,” IEEE Trans. Ind. Electron., vol. 66, no. 12, pp. 9439–9447, Dec. 2019. doi: 10.1109/TIE.2019.2892696
    [16]
    S. Suzuki, A. Isidori, and T. J. Tarn, “H control of continuous systems with sampled measurement,” in Proc. 33rd IEEE Conf. Decision and Control, Lake Buena Vista, USA, 1994, pp. 2553−2558.
    [17]
    P. Naghshtabrizi and J. P. Hespanha, “Designing an observer-based controller for a network control system,” in Proc. 44th IEEE Conf. Decision and Control, Seville, Spain, 2005, pp. 848−853.
    [18]
    T. Ahmed-Ali, R. Postoyan, and F. Lamnabhi-Lagarrigue, “Continuous-discrete adaptive observers for state affine systems,” Automatica, vol. 45, no. 12, pp. 2986–2990, Dec. 2009. doi: 10.1016/j.automatica.2009.09.005
    [19]
    M. Nadri, H. Hammouri, and R. M. Grajales, “Observer design for uniformly observable systems with sampled measurements,” IEEE Trans. Autom. Control, vol. 58, no. 3, pp. 757–762, Mar. 2012.
    [20]
    T. N. Dinh, V. Andrieu, M. Nadri, and U. Serres, “Continuous-discrete time observer design for Lipschitz systems with sampled measurements,” IEEE Trans. Autom. Control, vol. 60, no. 3, pp. 787–792, Mar. 2014.
    [21]
    V. Andrieu, M. Nadri, U. Serres, and J. C. Vivalda, “Self-triggered continuous–discrete observer with updated sampling period,” Automatica, vol. 62, pp. 106–113, Dec. 2015. doi: 10.1016/j.automatica.2015.09.018
    [22]
    G. L. Zhao and J. Mi, “Continuous-discrete adaptive observers for a class of nonlinear systems with sampled output,” in Proc. 36th Chinese Control Conf., Dalian, China, 2017, pp. 787−792.
    [23]
    L. Etienne, L. Hetel, D. Efimov, and M. Petreczky, “Observer synthesis under time-varying sampling for Lipschitz nonlinear systems,” Automatica, vol. 85, pp. 433–440, Nov. 2017. doi: 10.1016/j.automatica.2017.07.050
    [24]
    I. Karafyllis and C. Kravaris, “From continuous-time design to sampled-data design of observers,” IEEE Trans. Autom. Control, vol. 54, no. 9, pp. 2169–2174, Sep. 2009. doi: 10.1109/TAC.2009.2024390
    [25]
    I. Bouraoui, M. Farza, T. Ménard, R. B. Abdennour, M. M’Saad, and H. Mosrati, “Observer design for a class of uncertain nonlinear systems with sampled outputs—application to the estimation of kinetic rates in bioreactors,” Automatica, vol. 55, pp. 78–87, May 2015. doi: 10.1016/j.automatica.2015.02.036
    [26]
    T. Ahmed-Ali, E. Fridman, F. Giri, L. Burlion, and F. Lamnabhi-Lagarrigue, “Using exponential time-varying gains for sampled-data stabilization and estimation,” Automatica, vol. 67, pp. 244–251, May 2016. doi: 10.1016/j.automatica.2016.01.048
    [27]
    D. Y. Zhang and Y. J. Shen, “Continuous sampled-data observer design for nonlinear systems with time delay larger or smaller than the sampling period,” IEEE Trans. Autom. Control, vol. 62, no. 11, pp. 5822–5829, Nov. 2017. doi: 10.1109/TAC.2016.2638043
    [28]
    L. Etienne, L. Hetel, and D. Efimov, “Observer analysis and synthesis for perturbed Lipschitz systems under noisy time-varying measurements,” Automatica, vol. 106, pp. 406–410, Aug. 2019. doi: 10.1016/j.automatica.2019.04.003
    [29]
    C. Tréangle, M. Farza, and M. M’Saad, “Filtered high gain observer for a class of uncertain nonlinear systems with sampled outputs,” Automatica, vol. 101, pp. 197–206, Mar. 2019. doi: 10.1016/j.automatica.2018.12.002
    [30]
    O. Bernard, G. Sallet, and A. Sciandra, “Nonlinear observers for a class of biological systems: Application to validation of a phytoplanktonic growth model,” IEEE Trans. Autom. Control, vol. 43, no. 8, pp. 1056–1065, Aug. 1998. doi: 10.1109/9.704977
    [31]
    H. B. Zhang, X. M. Liu, H. H. Ji, Z. S. Hou, and L. L. Fan, “Multi-agent-based data-driven distributed adaptive cooperative control in urban traffic signal timing,” Energies, vol. 12, no. 7, p. 1402, Apr. 2019.
    [32]
    X. L. Tao, J. Q. Yi, Z. Q. Pu, and T. Y. Xiong, “Robust adaptive tracking control for hypersonic vehicle based on interval type-2 fuzzy logic system and small-gain approach,” IEEE Trans. Cybern., vol. 51, no. 5, pp. 2504–2517, May 2019.
    [33]
    K. H. He, C. Y. Dong, and Q. Wang, “Active disturbance rejection adaptive control for uncertain nonlinear systems with unknown time-varying dead-zone input,” Asian J. Control, 2021, DOI: 10.1002/asjc.2514.
    [34]
    J. Lee, R. Mukherjee, and H. K. Khalil, “Output feedback stabilization of inverted pendulum on a cart in the presence of uncertainties,” Automatica, vol. 54, pp. 146–157, Apr. 2015. doi: 10.1016/j.automatica.2015.01.013
    [35]
    Q. Zheng, L. Q. Gao, and Z. Q. Gao, “On validation of extended state observer through analysis and experimentation,” J. Dyn. Syst. Meas. Control, vol. 134, no. 2, p. 024505, Mar. 2012.
    [36]
    Z. Q. Pu, R. Y. Yuan, J. Q. Yi, and X. M. Tan, “A class of adaptive extended state observers for nonlinear disturbed systems,” IEEE Trans. Ind. Electron., vol. 62, no. 9, pp. 5858–5869, Sep. 2015. doi: 10.1109/TIE.2015.2448060
    [37]
    A. Benallegue, A. Mokhtari, and L. Fridman, “High-order sliding-mode observer for a quadrotor UAV,” Int. J. Robust Nonlinear Control, vol. 18, no. 4–5, pp. 427–440, Mar. 2008. doi: 10.1002/rnc.1225
    [38]
    M. Fliess, R. Marquez, E. Delaleau, and H. Sira-Ramírez, “Correcteurs proportionnels-intégraux généralisés,” ESAIM:Control,Optimisation and Calculus of Variations, vol. 7, pp. 23–41, Jan. 2002. doi: 10.1051/cocv:2002002
    [39]
    L. B. Freidovich and H. K. Khalil, “Performance recovery of feedback-linearization-based designs,” IEEE Trans. Autom. Control, vol. 53, no. 10, pp. 2324–2334, Nov. 2008. doi: 10.1109/TAC.2008.2006821
    [40]
    D. W. Shi, J. Xue, L. X. Zhao, J. Z. Wang, and Y. Huang, “Event-triggered active disturbance rejection control of DC torque motors,” IEEE/ASME Trans. Mechatron., vol. 22, no. 5, pp. 2277–2287, Oct. 2017. doi: 10.1109/TMECH.2017.2748887
    [41]
    J. K. Sun, J. Yang, S. H. Li, and W. X. Zheng, “Sampled-data-based event-triggered active disturbance rejection control for disturbed systems in networked environment,” IEEE Trans. Cybern., vol. 49, no. 2, pp. 556–566, Feb. 2019. doi: 10.1109/TCYB.2017.2780625
    [42]
    M. P. Ran, Q. Wang, and C. Y. Dong, “Stabilization of a class of nonlinear systems with actuator saturation via active disturbance rejection control,” Automatica, vol. 63, pp. 302–310, Jan. 2016. doi: 10.1016/j.automatica.2015.10.010
    [43]
    H. Omran, L. Hetel, M. Petreczky, J. P. Richard, and F. Lamnabhi-Lagarrigue, “Stability analysis of some classes of input-affine nonlinear systems with aperiodic sampled-data control,” Automatica, vol. 70, pp. 266–274, Aug. 2016. doi: 10.1016/j.automatica.2016.02.013
    [44]
    A. Teel and L. Praly, “Tools for semiglobal stabilization by partial state and output feedback,” SIAM J. Control Optim., vol. 33, no. 5, pp. 1443–1488, Sep. 1995. doi: 10.1137/S0363012992241430
    [45]
    H. K. Khalil, “Cascade high-gain observers in output feedback control,” Automatica, vol. 80, pp. 110–118, Jun. 2017. doi: 10.1016/j.automatica.2017.02.031
    [46]
    K. H. He, C. Y. Dong, and Q. Wang, “Cascade integral predictors and feedback control for nonlinear systems with unknown time-varying input-delays,” Int. J. Control Autom. Syst., vol. 18, no. 5, pp. 1128–1138, May 2020. doi: 10.1007/s12555-019-0405-x
    [47]
    J. H. Ahrens and H. K. Khalil, “High-gain observers in the presence of measurement noise: A switched-gain approach,” Automatica, vol. 45, no. 4, pp. 936–943, Apr. 2009. doi: 10.1016/j.automatica.2008.11.012
    [48]
    G. Phanomchoeng and R. Rajamani, “Observer design for Lipschitz nonlinear systems using Riccati equations,” in Proc. American Control Conf., Baltimore, USA, 2010, pp. 6060−6065.

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    Highlights

    • Expand the application scope of ADRC. This paper is the first attempt of ADRC application in sporadic-in-measurement systems. The structure of the proposed ADRC is developed, in which a predictor-based continuous time observer executes state and uncertainty estimation based on intermittent measurements
    • New methodology for state estimation with sampled measurements. Different from all existing estimation techniques for systems with sampled measurements, the proposed ESO does not require the knowledge of the nonlinear dynamics and eliminates some restriction on the system nonlinearity
    • Rigorous convergence proofs for both the ESO and the closed-loop systems
    • Implementation consideration. We provide algorithms and explanations on how to design various parameters in the ADRC architecture. A simulation on the control of flexible robot manipulator is carried out to verify the effectiveness

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