Dynamic sliding mode control based on a full-order observer: Underactuated electro-mechanical system regulation

Ordaz, Patricio ; Romero-Trejo, Hugo ; Cuvas, Carlos ; Sandre, Omar

International Journal of Applied Mathematics and Computer Science, Tome 34 (2024) no. 1, pp. 29-43.

Résumé

This paper concerns the synthesis of a nonlinear robust output controller based on a full-order observer for a class of uncertain disturbed systems. The proposed method guarantees that, in finite time, the system trajectories go inside a minimal neighborhood ultimately bounded. To this end, the attractive ellipsoid method is enhanced by applying the dynamic sliding mode control performance properties. Furthermore, in order to guarantee the stability of the trajectory around the trivial solution in the uniform-ultimately bounded sense, the feasibility of a specific matrix inequality problem is provided. With this feasible set of matrix inequalities, the separation principle of the controller/observer scheme considered also holds. To achieve a system performance improvement, a numerical algorithm based on the small size ultimate bound is presented. Finally, to illustrate the theoretical performance of the designed controller/observer, a numerical example dealing with the stabilization of a disturbed electromechanical system with uncertain and unmodeled dynamics is presented.

Détail

Keywords: output feedback, output observer, sliding mode control, attractive ellipsoid method, uncertain system, nonlinear system
Mots-clés : sprzężenie zwrotne, obserwator wejściowy, sterowanie ślizgowe, układ niepewny, układ nieliniowy

Bibliographie

[1] Andrade-Da Silva, J.M., Edwards, C. and Spurgeon, S.K. (2009). Linear matrix inequality based dynamic output feedback sliding mode control for uncertain plants, American Control Conference, ACC’09, St. Louis, USA, pp. 763-768.

[2] Atassi, A.N. and Khalil, H.K. (1999). A separation principle for the stabilization of a class of nonlinear systems, IEEE Transactions on Automatic Control 44(9): 1672-1687.

[3] Cao, K., Qian, C. and Gu, J. (2023). Global sampled-data stabilization via static output feedback for a class of nonlinear uncertain systems, International Journal of Robust and Nonlinear Control 33(4): 2913-2929.

[4] Choi, H.H. and Ro, K. (2005). LMI-based sliding-mode observer design method, IEE Proceedings: Control Theory and Applications 152(1): 113-115.

[5] Gahinet, P. and Pierre, A. (1994). A linear matrix inequality approach to H∞ control, International Journal of Robust and Nonlinear Control 4(4): 421-448.

[6] Haddad, W.M. and Chellaboina, V. (2011). Nonlinear Dynamical Systems and Control: A Lyapunov-based Approach, Princeton University Press, Princeton.

[7] Jafari, M. and Mobayen, S. (2019). Second-order sliding set design for a class of uncertain nonlinear systems with disturbances: An LMI approach, Mathematics and Computers in Simulation 156: 110-125, DOI: 10.1016/j.matcom.2018.06.015.

[8] Khalil, K.M. and Elshenawy, A. (2021). Robust model integral predictive control design for reference tracking dc servomechanism, 2021 10th International Conference on Intelligent Computing and Information Systems (ICICIS), Cairo, Egypt, pp. 243-253.

[9] Kukurowski, N., Mrugalski, M., Pazera, M. and Witczak, M. (2022). Fault-tolerant tracking control for a non-linear twin-rotor system under ellipsoidal bounding, International Journal of Applied Mathematics and Computer Science 32(2): 171-183, DOI: 10.34768/amcs-2022-0013.

[10] Liu, H. and Khalil, H.K. (2019). Output feedback stabilization using super-twisting control and high-gain observer, International Journal of Robust and Nonlinear Control 29(3): 601-617.

[11] Luna, L., Asiain, E. and Garrido, R. (2020). Servo velocity control using a p+ ADOB controller, IFAC-PapersOnLine 53(2): 1300-1305.

[12] Ordaz, P., Ordaz, M., Cuvas, C. and Santos, O. (2019). Reduction of matched and unmatched uncertainties for a class of nonlinear perturbed systems via robust control, International Journal of Robust and Nonlinear Control 29(8): 2510-2524.

[13] Peng, C., Zhang, A. and Li, J. (2021). Neuro-adaptive cooperative control for high-order nonlinear multi-agent systems with uncertainties, International Journal of Applied Mathematics and Computer Science 31(4): 635-645, DOI: 10.34768/amcs-2021-0044.

[14] Poznyak, A., Polyakov, A. and Azhmyakov, V. (2014). Attractive Ellipsoids in Robust Control, Springer, Boston.

[15] Rudenko, O. and Hedberg, C. (2013). Strong and weak nonlinear dynamics: Models, classification, examples, Acoustical Physics 59(6): 644-650.

[16] Ruderman, M. (2015). Presliding hysteresis damping of LuGre and Maxwell-slip friction models, Mechatronics 30: 225-230, DOI: 10.1016/j.mechatronics.2015.07.007.

[17] Sánchez, B., Cuvas, C., Ordaz, P., Santos-Sánchez, O. and Poznyak, A. (2019). Full-order observer for a class of nonlinear systems with unmatched uncertainties: Joint attractive ellipsoid and sliding mode concepts, IEEE Transactions on Industrial Electronics 67(7): 5677-5686.

[18] Shtessel, Y., Edwards, C., Fridman, L. and Levant, A. (2014). Sliding Mode Control and Observation, Springer, New York.

[19] Silva, J.M.A.-D., Edwards, C. and Spurgeon, S.K. (2009). Sliding-mode output-feedback control based on LMIs for plants with mismatched uncertainties, IEEE Transactions on Industrial Electronics 56(9): 3675-3683.

[20] Tsinias, J. and Theodosis, D. (2016). Luenberger-type observers for a class of nonlinear triangular control systems, IEEE Transactions on Automatic Control 61(12): 3797-3812.

[21] Utkin, V., Poznyak, A., Orlov, Y.V. and Polyakov, A. (2020). Road Map for Sliding Mode Control Design, Springer, Cham.

[22] Zhang, H., Zhao, X., Zhang, L., Niu, B., Zong, G. and Xu, N. (2022). Observer-based adaptive fuzzy hierarchical sliding mode control of uncertain under-actuated switched nonlinear systems with input quantization, International Journal of Robust and Nonlinear Control 32(14): 8163-8185.