Kybernetika 58 no. 4, 547-563, 2022

Sliding mode differentiator via improved adaptive notch filter

Juan Wang, Hehong Zhang, Yuanlong Yu, Zhihong Dan, Gaoxi Xiao, Qiuming Gu and Chao ZhaiDOI: 10.14736/kyb-2022-4-0547


To tackle the difficulty in tuning the parameters of sliding mode differentiator (SMD), an improved adaptive notch filter based real-time parameter tuning scheme (denoted as ANF-SMD) is presented. Specifically, the integral feedback of the system output errors is introduced in constructing the cost function for the adaptive notch filter so as to estimate the real-time amplitude and frequency of given inputs. Then, upon the deterministic formula between the parameters of the SMD and the input signals, the parameters of the SMD can be adjusted adaptively as inputs vary. Simulation results show that the proposed ANF-SMD scheme performs well in signal filtering and differentiation estimation. The effectiveness of the proposed ANF-SMD is further experimentally verified on the pressure signal processing for the altitude ground test facility.


sliding mode differentiator, parameter tuning scheme, adaptive notch filter, altitude ground test facility


93A30, 93Cxx


  1. K. A. Alattas, J. Mostafaee, A. K. Alanazi, S. Mobayen, M. T. Vu, A. Zhilenkov and H. M. Abo-Dief: Nonsingular terminal sliding mode control based on adaptive barrier function for nth-order perturbed nonlinear systems. Mathematics 10 (2022), 1, 43.   DOI:10.1155/2022/1342051
  2. H. Alwi and C. Edwards: An adaptive sliding mode differentiator for actuator oscillatory failure case reconstruction. Automatica 49 (2013), 2, 642-651.   DOI:10.1016/j.automatica.2012.11.042
  3. K. H. Ang, G. Chong and Y. Li: PID control system analysis, design, and technology. IEEE Trans. Control Syst. Technol. 13 (2005), 4, 559-576.   DOI:10.1109/TCST.2005.847331
  4. P. F. Ashwood: An altitude test facility for large turbofan engines. J. Aircr. 10 (1973), 8, 468-474.   DOI:10.2514/3.60249
  5. J.-P. Barbot, A. Levant, M. Livne and D. Lunz: Discrete differentiators based on sliding modes. Automatica 112 (2020).   DOI:10.1016/j.automatica.2019.108633
  6. B. Castillo-Toledo, S. D. Gennaro and A. López-Cuevas: Tracking through singularities using sliding mode differentiators. Kybernetika 51 (2015), 1, 20-35.   DOI:10.14736/kyb-2015-1-0020
  7. F. Deza, E. Busvelle, J. P. Gauthier and D. Rakotopara: High gain estimation for nonlinear systems. Syst. Control Lett. 18 (1992), 4, 295-299.   DOI:10.1016/0167-6911(92)90059-2
  8. M. Ghanes, J.-P. Barbot, L. Fridman, A. Levant and R. Boisliveau: A new varying-gain-exponent-based differentiator/observer: An efficient balance between linear and sliding-mode algorithms. IEEE Trans. Automat. Control 65 (2020), 12, 5407-5414.   DOI:10.1109/TAC.2020.2973609
  9. M. Ghanes, J. A. Moreno and J.-P. Barbot: Arbitrary order differentiator with varying homogeneity degree. Automatica 138 (2022), p.110111.   CrossRef
  10. H. Gui: Observer-based fault-tolerant spacecraft attitude tracking using sequential lyapunov analyses. IEEE Trans. Automat. Control (2021).   CrossRef
  11. J. Han: From PID to active disturbance rejection control. IEEE Trans. Ind. Electron. 56 (2009), 3, 900-906.
  12. J. P. Hu: On robust consensus of multi-agent systems with communication delays. Kybernetika 45 (2009), 5, 768-784.   DOI:10.1109/TMAG.2008.2011420
  13. J. P. Hu, G. R. Chen and H. X. Li: Distributed event-triggered tracking control of leader-follower multi-agent systems with communication delays. Kybernetika 47 (2011), 4, 630-643.   CrossRef
  14. S. Ibrir: Linear time-derivative trackers. Automatica 40 (2004), 3, 397-405.   DOI:10.1016/j.automatica.2003.09.020
  15. Kilic, Dogushan, Brem, T. Benjamin, Klein, Felix and et al.: Characterization of gas-phase organics using proton transfer reaction time-of-flight mass spectrometry: aircraft turbine engines. Environ. Sci. Technol. 51 (2017), 7, 3621-3629.   DOI:10.1021/acs.est.6b04077
  16. A. Levant: Robust exact differentiation via sliding mode technique. Automatica 34 (1998), 3, 379-384.   DOI:10.1016/S0005-1098(97)00209-4
  17. A. Levant and X. Yu: Sliding-mode-based differentiation and filtering. IEEE Trans. Automat. Contr. 63 (2018), 9, 3061-3067.   DOI:10.1109/TAC.2018.2797218
  18. G. Liu, J. Li, S. Zheng, Q. Chen and H. Liu: Suppression of Synchronous current using double input improved adaptive notch filter algorithm. IEEE Trans. Ind. Electron. 67 (2020), 10, 8599-8607.   DOI:10.1109/TIE.2019.2947852
  19. M. Meller: Frequency guided generalized adaptive notch filtering-tracking analysis and optimization. IEEE Trans. Signal Process. 63 (2015), 22, 6003-6012.   DOI:10.1109/TSP.2015.2461522
  20. M. Nasiri, S. Mobayen and A. Arzani: PID-type terminal sliding mode control for permanent magnet synchronous generator based enhanced wind energy conversion systems. CSEE J. Power Energy Syst.   DOI:10.17775/CSEEJPES.2020.06590
  21. T. R. Oliveira, V. H. P. Rodrigues and L. Fridman: Generalized model reference adaptive control by means of global HOSM differentiators. IEEE Trans. Automat. Control 64 (2019), 5, 2053-2060.   DOI:10.1109/TAC.2018.2862466
  22. Y. Orlov, Y. Aoustin and C. Chevallereau: Finite time stabilization of a perturbed double integrator-part I: Continuous sliding mode-based output feedback synthesis. IEEE Trans. Automat. Control 56 (2011), 3, 614-618.   DOI:10.1109/TAC.2010.2090708
  23. G. Rinaldi, P. P. Menon, C. Edwards, A. Ferrara and Y. Shtessel: Adaptive dual-layer super-twisting sliding mode observers to reconstruct and mitigate disturbances and communication attacks in power networks. Automatica 129 (2021), p.109656.   DOI:10.1016/j.automatica.2021.109656
  24. Y. X. Su, C. H. Zheng, P. C. Mueller and B. Y. Duan: A simple improved velocity estimation for low-speed regions based on position measurements only. IEEE Trans. Control Syst. Technol. 14 (2006), 5, 937-942.   DOI:10.1109/TCST.2006.876917
  25. X. Wang, Z. Chen and G. Yang: Finite-time-convergent differentiator based on singular perturbation technique. IEEE Trans. Automat. Control 52 (2007), 9, 1731-1737.   DOI:10.1109/TAC.2007.904290
  26. F. Wang and L. He: FPGA-based predictive speed control for PMSM system using integral sliding-mode disturbance observer. IEEE Trans. Ind. Electron. 68 (2021), 2, 972-981.   DOI:10.1109/TIE.2020.2969107
  27. J. Wang, Y. Xie, Y, Yu, G. Xiao, L. Zhang, Z. Dan and et al.: A practical parameter tuning algorithm for super-twisting algorithm based differentiator and its application in altitude ground test facility. ISA Trans., under review.   CrossRef
  28. J. Wang, H. Zhang, G. Xiao, Z. Dan, S. Zhang and Y. Xie: A comparison study of tracking differentiator and robust exact differentiator. In: 2020 China Automation Conference 2020, pp. 1359-1364.   CrossRef
  29. F. Wu, L. Gao, X. Wu, X. Feng, L. Leng and Y. Li: Aerodynamic modeling and transient performance improvement of a free jet altitude test facility. In: International Conference on Artificial Intelligence and Security, Springer, Singapore 2020, pp. 618-630.   CrossRef
  30. W. Wu, H. Sun, Y. Cai, S. Jiang and J. Xiong: Tracking multiple maneuvering targets hidden in the DBZ based on the MM-GLMB filter. IEEE Trans. Signal Process. 68 (2020), 2912-2924.   DOI:10.1109/TSP.2020.2988635
  31. H. Yang, L. Cheng, J. Zhang and Y. Xia: Leader-follower trajectory control for quadrotors via tracking differentiators and disturbance observers. IEEE Trans Syst Man Cybern.: Syst. 51 (2021), 1, 601-609.   DOI:10.1109/TSMC.2018.2872872
  32. Y. Yan, S. Yu and X. Yu: Euler's discretization effect on a sliding-mode control system with supertwisting algorithm. IEEE Trans. Automat. Control 66 (2021), 6, 2817-2824.   DOI:10.1109/TAC.2020.3010493
  33. H. Zhang, G. Xiao, X. Yun and Y. Xie: On convergence performance of discrete-time optimal control based tracking differentiator. IEEE Trans. Ind. Electron. 68 (2021), 4, 3359-3369.   DOI:10.1109/TIE.2020.2979530
  34. H. Zhang, Y. Xie, G. Xiao, C. Zhai and Z. Long: A simple discrete-time tracking differentiator and its application to speed and position detection system for a maglev train. IEEE Trans. Control Syst. Technol. 27 (2019), 4, 1728-1734.   DOI:10.1109/TCST.2018.2832139
  35. L. Zhao, H. Cheng, J. Zhang and Y. Xia: Angle attitude control for a 2-DOF parallel mechanism of PMAs using tracking differentiators. IEEE Trans. Ind. Electron. 66 (2019), 11, 8659-8669.   DOI:10.1109/TIE.2018.2884215