zbMATH — the first resource for mathematics

A nonlinear extended state observer based on fractional power functions. (English) Zbl 1372.93048
Summary: In this paper, we investigate a nonlinear Extended State Observer (ESO) constructed from piecewise smooth functions consisted of linear and fractional power functions. This structure of ESO was first proposed in the 1990’s and has been widely used in active disturbance rejection control for engineering problems. Its convergence, however, has remained an open problem up to this day. The main objective of this paper is to provide a convergence theory with explicit error estimation. The performances of this type ESO are studied by numerical simulation and compared with linear ESO. The numerical results show that the ESO proposed in this paper enjoys the advantages of smaller peaking value and better measurement noise tolerance.

93B07 Observability
93C10 Nonlinear systems in control theory
93B35 Sensitivity (robustness)
Full Text: DOI
[1] Andrieu, V.; Praly, L.; Astolfi, A., Homogeneous approximation, recursive observer design, and output feedback, SIAM Journal on Control and Optimization, 47, 1814-1850, (2008) · Zbl 1165.93020
[2] Astolfi, D.; Marconi, L., A high-gain nonlinear observer with limited gain power, IEEE Transactions on Automatic Control, 60, 3059-3064, (2015) · Zbl 1360.93112
[3] Bhat, S. P.; Bernstein, D. S., Geometric homogeneity with applications to finite-time stability, Mathematics of Control, Signals, and Systems, 17, 101-127, (2005) · Zbl 1110.34033
[4] Freidovich, L. B.; Khalil, H. K., Performance recovery of feedback-linearization-based designs, IEEE Transactions on Automatic Control, 53, 2324-2334, (2008) · Zbl 1367.93498
[5] Gao, Z. (2003). Scaling and bandwith-parameterization based controller tuning. In American control conference, (pp.4989-4996).
[6] Guo, B. Z.; Zhao, Z. L., On the convergence of an extended state observer for nonlinear systems with uncertainty, Systems & Control Letters, 60, 420-430, (2011) · Zbl 1225.93056
[7] Han, J. Q., From PID to active disturbance rejection control, IEEE Transactions on Industrial Electronics, 56, 900-906, (2009)
[8] Jiang, T. T.; Huang, C. D.; Guo, L., Control of uncertain nonlinear systems based on observers and estimators, Automatica, 59, 35-47, (2015) · Zbl 1326.93073
[9] Khalil, H. K., Nonlinear systems, (2002), Prentice Hall New Jersey · Zbl 0626.34052
[10] Levant, A., Higher-order sliding modes, differentiation and output-feedback control, International Journal of Control, 76, 924-941, (2003) · Zbl 1049.93014
[11] Li, S. H.; Yang, J.; Chen, W. H.; Chen, X., Generalized extended state observer based control for systems with mismatched uncertainties, IEEE Transactions on Industrial Electronics, 59, 4792-4802, (2012)
[12] Perruquetti, W.; Floquet, T.; Moulay, E., Finite-time observers: application to secure communication, IEEE Transactions on Automatic Control, 53, 356-360, (2008) · Zbl 1367.94361
[13] Praly, L.; Jiang, Z. P., Linear output feedback with dynamic high gain for nonlinear systems, Systems & Control Letters, 53, 107-116, (2004) · Zbl 1157.93494
[14] Rosier, L., Homogeneous Lyapunov function for homogeneous continuous vector field, Systems & Control Letters, 19, 467-473, (1992) · Zbl 0762.34032
[15] Sun, B.; Gao, Z., A DSP-based active disturbance rejection control design for a 1-kw H-bridge DC-DC power converter, IEEE Transactions on Industrial Electronics, 52, 1271-1277, (2005)
[16] Xia, Y. Q.; Fu, M. Y., Compound control methodology for flight vehicles, (2013), Springer-Verlag Berlin · Zbl 1304.93012
[17] Xue, W. C.; Bai, W. Y.; Yang, S.; Song, K.; Huang, Y.; Xie, H., ADRC with adaptive extended state observer and its application to air-fuel ratio control in gasoline engines, IEEE Transactions on Industrial Electronics, 62, 5847-5857, (2015)
[18] Yan, B.; Tian, Z.; Shi, S.; Wang, Z., Fault diagnosis for a class of nonlinear systems, ISA Transactions, 47, 386-394, (2008)
[19] Yang, B.; Lin, W., Homogeneous observers, iterative design, and global stabilization of high-order nonlinear systems by smooth output feedback, IEEE Transactions on Automatic Control, 49, 1069-1080, (2004) · Zbl 1365.93209
[20] Yao, J. Y.; Jiao, Z. X.; Ma, D. W., Extended-state-observer-based output feedback nonlinear robust control of hydraulic systems with backstepping, IEEE Transactions on Industrial Electronics, 61, 6285-6293, (2014)
[21] Zhao, Z. L.; Guo, B. Z., Extended state observer for uncertain lower triangular nonlinear systems, Systems & Control Letters, 85, 100-108, (2015) · Zbl 1322.93025
[22] Zheng, Q., & Gao, Z. (2012). An energy saving, factory-validated disturbance decoupling control design for extrusion processes. In Word congress on intelligent control and automation (pp. 2891-2896).
[23] Zheng, Q., Gao, L., & Gao, Z.Q. (2007). On stability analysis of active disturbance rejection control for nonlinear time-varying plants with unknow dynamics. In IEEE conference on decision and control, (pp. 3501-3506).
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.