zbMATH — the first resource for mathematics

On the convergence of an extended state observer for nonlinear systems with uncertainty. (English) Zbl 1225.93056
Summary: The extended state observer first proposed by J. Q. Han in [“A class of extended state observers for uncertain systems”, Control Decis. 10, No. 1, 85–88 (1995)] is the key link toward the active disturbance rejection control that is taking off as a technology after numerous successful applications in engineering. Unfortunately, there is no rigorous proof of convergence to date. In this paper, we attempt to tackle this long unsolved extraordinary problem. The main idea is to transform the error equation of objective system with its extended state observer into an asymptotic stable system with a small disturbance, for which the effect of total disturbance error is eliminated by the high-gain.

93C10 Nonlinear systems in control theory
93B07 Observability
93D20 Asymptotic stability in control theory
93C41 Control/observation systems with incomplete information
Full Text: DOI
[1] Corless, M.J.; Tu, J., State/input estimation for a class of uncertain systems, Automatica, 34, 757-764, (1998) · Zbl 0932.93008
[2] Darouach, M.; Zasadzinski, M.; Xu, J.S., Full-order observers for linear systems with uncertain inputs, IEEE trans. automat. control, 39, 606-609, (1994) · Zbl 0813.93015
[3] Gourshankar, V.; Kudva, P.; Ramar, K., Reduced order observer for multivariable systems with inaccessible disturbance inputs, Internat. J. control, 25, 311-319, (1977) · Zbl 0342.93012
[4] Koshkouei, A.; Zinober, A., Sliding mode controller observer design for SISO linear systems, Internat. J. systems sci., 29, 1363-1373, (1998) · Zbl 1065.93515
[5] Kudva, P.; Viswanadham, N.; Ramakrishna, A., Observers for linear systems with unknown inputs, IEEE trans. automat. control, 25, 113-115, (1980) · Zbl 0443.93012
[6] Slotine, J.; Hedrick, J.; Misawa, E., On sliding observers for nonlinear systems, Trans. ASME, J. dyn. syst. meas. control, 109, 245-252, (1987) · Zbl 0661.93011
[7] Walcott, B.L.; Corless, M.J.; Zak, S.H., Comparative study of non-linear state-observation technique, Internat. J. control, 45, 2109-2132, (1987) · Zbl 0627.93012
[8] Walcott, B.L.; Zak, S.H., State observation of nonlinear uncertain dynamical systems, IEEE trans. automat. control, 32, 166-170, (1987) · Zbl 0618.93019
[9] Besancon, G., Nonlinear observers and applications, (2007), Springer Verlag New York
[10] Huang, Y.; Han, J.Q., A new synthesis method for uncertain systems-the self-stable region approach, Internat. J. systems sci., 30, 33-38, (1999) · Zbl 1065.93544
[11] Han, J.Q., A class of extended state observers for uncertain systems, Control decis., 10, 1, 85-88, (1995), (in Chinese)
[12] Han, J.Q., From PID to active disturbance rejection control, IEEE trans. ind. electron., 56, 900-906, (2009)
[13] Freidovich, L.B.; Khalil, H.K., Performance recovery of feedback-linearization-based designs, IEEE trans. automat. control, 53, 2324-2334, (2008) · Zbl 1367.93498
[14] H.K. Khalil, High-gain observers in nonlinear feedback control, in: Int. Conf. Control, Automation and Systems, Korea, October 14-17, 2008. · Zbl 1380.93002
[15] Hou, Y.; Gao, Z.; Jiang, F.; Boulter, B.T., Active disturbance rejection control for web tension regulation, IEEE conf. decis. control, 4974-4979, (2001)
[16] R. Miklosovic, Z. Gao, A dynamic decoupling method for controlling high performance turbofan engines, in: Proc. of the 16th IFAC World Congress, Czech Republic, July 4-8, 2005.
[17] Zheng, Q.; Gong, L.; Lee, D.H.; Gao, Z., Active disturbance rejection control for MEMS gyroscopes, Amer. contr. conf., 4425-4430, (2008)
[18] Q. Zheng, L.L. Dong, Z. Gao, Control and rotation rate estimation of vibrational MEMS gyroscopes, in: IEEE Multi-Conference on Systems and Control, 2007, pp. 118-123.
[19] Q. Zheng, Z. Gao, On applications of active disturbance rejection control, in: Chinese Control Conference, 2010, pp. 6095-6100.
[20] Zheng, Q.; Chen, Z.; Gao, Z., A dynamic decoupling control approach and its applications to chemical processes, Amer. contr. conf., 5176-5181, (2007)
[21] W. Zhou, Z. Gao, An active disturbance rejection approach to tension and velocity regulations in Web processing lines, in: IEEE Multi-conference on Systems and Control, 2007, pp. 842-848.
[22] Gao, Z., Scaling and bandwith-parameterization based controller tuning, Amer. contr. conf., 4989-4996, (2003)
[23] Khalil, H., High-gain observer in nonlinear feedback control, ()
[24] Khalil, H.K., Nonlinear systems, (2002), Prentice Hall New Jersey · Zbl 0626.34052
[25] Zheng, Q.; Gao, L.; Gao, Z., On stability analysis of active disturbance rejection control for nonlinear time-varying plants with unknow dynamics, IEEE conf. decis. control, 3501-3506, (2007)
[26] Yang, X.X.; Huang, Y., Capability of extended state observer for estimating uncertainties, Amer. contr. conf., 3700-3705, (2009)
[27] Perruquetti, W.; Floquet, T.; Moulay, E., Finite-time observers: application to secure communication, IEEE trans. automat. control, 53, 356-360, (2008) · Zbl 1367.94361
[28] Rosier, L., Homogeneous Lyapunov function for homogeneous continuous vector field, Systems control lett., 19, 467-473, (1992) · Zbl 0762.34032
[29] Bhat, S.P.; Bernstein, D.S., Geometric homogeneity with applications to finite-time stability, Math. control signals systems, 17, 101-127, (2005) · Zbl 1110.34033
[30] B.Z. Guo, Z.L. Zhao, On convergence of tracking differentiator, Internat. J. Control (in press). · Zbl 1246.93085
[31] Dabroom, A.H.; Khalll, H.K., Discrete-time implementation of high-gain observers for numerical differentiation, Internat. J. control, 72, 1523-1537, (1999) · Zbl 0941.93541
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.