×

On geometric interpretation of extended state observer: a preliminary study. (English) Zbl 1519.93085

In this paper, the authors investigate a geometric interpretation of extended state observer. More precisely, the authors have shown in this paper that the augmented system of the ESO (extended state observer) is unknown-state unknown-input completely reconstructable in finite time interval. An illustrative application is also provided.

MSC:

93B53 Observers
93B27 Geometric methods
93C41 Control/observation systems with incomplete information
93C05 Linear systems in control theory
Full Text: DOI

References:

[1] Åström, KJ; Kumar, PR, Control: A perspective, Automatica, 50, 1, 3-43 (2014) · Zbl 1298.93013 · doi:10.1016/j.automatica.2013.10.012
[2] Brockett, R.; Priya, D., New issues in the mathematics of control, Mathematics unlimited-2001 and beyond, 189-219 (2001), Berlin: Springer, Berlin · Zbl 1005.93002 · doi:10.1007/978-3-642-56478-9_9
[3] Tsien, HS; Qian, X., Engineering cybernetics (1954), New York, NY, USA: McGraw-Hill, New York, NY, USA
[4] Xie, L-L; Guo, L., How much uncertainty can be dealt with by feedback?, IEEE Transactions on Automatic Control, 45, 12, 2203-2217 (2000) · Zbl 0989.93052 · doi:10.1109/9.895559
[5] Stein, G., Respect the unstable, IEEE Control Systems Magazine, 23, 4, 12-25 (2003) · doi:10.1109/MCS.2003.1213600
[6] Gao, Z., On the centrality of disturbance rejection in automatic control, ISA Transactions, 53, 4, 850-857 (2014) · doi:10.1016/j.isatra.2013.09.012
[7] Zhou, K.; Doyle, JC, Essentials of robust control (1998), Englewood Cliffs, NJ, USA: Prentice Hall, Englewood Cliffs, NJ, USA
[8] Edwards, C.; Spurgeon, S., Sliding mode control: theory and applications (1998), London: CRC Press, London · doi:10.1201/9781498701822
[9] Krstic, M.; Kokotovic, PV; Kanellakopoulos, I., Nonlinear and adaptive control design (1995), New York, NY, USA: Wiley, New York, NY, USA
[10] Han, J., From pid to active disturbance rejection control, IEEE Transactions on Industrial Electronics, 56, 3, 900-906 (2009) · doi:10.1109/TIE.2008.2011621
[11] Chen, W-H; Yang, J.; Guo, L.; Li, S., Disturbance-observer-based control and related methods-an overview, IEEE Transactions on Industrial Electronics, 63, 2, 1083-1095 (2015) · doi:10.1109/TIE.2015.2478397
[12] Sariyildiz, E.; Oboe, R.; Ohnishi, K., Disturbance observer-based robust control and its applications: 35th anniversary overview, IEEE Transactions on Industrial Electronics, 67, 3, 2042-2053 (2019) · doi:10.1109/TIE.2019.2903752
[13] Basile, G.; Marro, G., On the observability of linear, time-invariant systems with unknown inputs, Journal of Optimization Theory and Applications, 3, 6, 410-415 (1969) · Zbl 0165.10203 · doi:10.1007/BF00929356
[14] Wonham, WM; Morse, AS, Decoupling and pole assignment in linear multivariable systems: a geometric approach, SIAM Journal on Control, 8, 1, 1-18 (1970) · Zbl 0206.16404 · doi:10.1137/0308001
[15] Morse, AS; Wonham, WM, Decoupling and pole assignment by dynamic compensation, SIAM Journal on Control, 8, 3, 317-337 (1970) · Zbl 0204.46401 · doi:10.1137/0308022
[16] Kalman, R.E. (1960). On the general theory of control systems. In: Proceedings First International Conference on Automatic Control, Moscow, USSR, pp. 481-492 . · Zbl 1261.68154
[17] Basile, G.; Marro, G., Controlled and conditioned invariants in linear system theory (1992), Englewood Cliffs, NJ, USA: Prentice Hall, Englewood Cliffs, NJ, USA · Zbl 0758.93002
[18] Isidori, A., Nonlinear control systems. 3rd edition. (1995), London: Springer, London · Zbl 0878.93001 · doi:10.1007/978-1-84628-615-5
[19] Chen, J., Gao, Z., Hu, Y., Shao, S. (2022). On the relationship between extended state observer and unknown input observer. arXiv preprint. arXiv:2208.12314.
[20] Hou, M.; Patton, RJ, Input observability and input reconstruction, Automatica, 34, 6, 789-794 (1998) · Zbl 0959.93006 · doi:10.1016/S0005-1098(98)00021-1
[21] Ansari, A.; Bernstein, DS, Deadbeat unknown-input state estimation and input reconstruction for linear discrete-time systems, Automatica, 103, 11-19 (2019) · Zbl 1415.93246 · doi:10.1016/j.automatica.2019.01.011
[22] Willems, J., Almost invariant subspaces: An approach to high gain feedback design-part ii: Almost conditionally invariant subspaces, IEEE Transactions on Automatic Control, 27, 5, 1071-1085 (1982) · Zbl 0491.93022 · doi:10.1109/TAC.1982.1103074
[23] Hovakimyan, N., Cao, C. (2010). \( \cal{L}_1\) adaptive control theory: Guaranteed robustness with fast adaptation. IEEE Control Systems Magazine, 31(5), 112-114. · Zbl 1214.93004
[24] Chen, W-H; Ballance, DJ; Gawthrop, PJ; O’Reilly, J., A nonlinear disturbance observer for robotic manipulators, IEEE Transactions on Industrial Electronics, 47, 4, 932-938 (2000) · doi:10.1109/41.857974
[25] Chen, J.; Hu, Y.; Gao, Z., On practical solutions of series elastic actuator control in the context of active disturbance rejection, Advanced Control for Applications, 3, 2, 69 (2021) · doi:10.1002/adc2.69
[26] Imai, H., & Akashi, H. (1981). Disturbance localization and pole shifting by dynamic compensation. IEEE Transactions on Automatic Control,26(1), 226-235. · Zbl 0464.93045
[27] Willems, JC; Commault, C., Disturbance decoupling by measurement feedback with stability or pole placement, SIAM Journal on Control and Optimization, 19, 4, 490-504 (1981) · Zbl 0467.93036 · doi:10.1137/0319029
[28] Padula, F., & Ntogramatzidis, L. (2019). On the well-posedness in the solution of the disturbance decoupling by dynamic output feedback with self bounded and self hidden subspaces. Automatica,106, 315-326. · Zbl 1429.93063
[29] Padula, F.; Ntogramatzidis, L., Fixed poles in the disturbance decoupling by dynamic output feedback for systems with direct feedthrough matrices, Automatica, 121 (2020) · Zbl 1448.93116 · doi:10.1016/j.automatica.2020.109159
[30] Willems, J. (1981). Almost invariant subspaces: An approach to high gain feedback design-Part I: Almost controlled invariant subspaces. IEEE Transactions on Automatic Control,26(1), 235-252. · Zbl 0463.93020
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.