Estimation with unknown inputs and uncertainties for sampled-data systems based on quasi sliding mode. (English) Zbl 1478.93097
Summary: In this work, we consider the problem of simultaneously estimating the system states and unknown inputs in a linear sampled-data system, whose dynamics is influenced by external disturbances and uncertainties. Hardware limitations prevent an estimation scheme for a sampled-data system from achieving finite-time convergence, which is a typical property of existing sliding mode observers for dynamical continuous-time systems, because the sampling period is finite. Due to the sampling process, an approximate implementation of such an observer, designed for a continuous-time system, may not retain the desired performance in the sampled-data context. In this paper, we present an observer which takes advantage of the quasi-sliding motion concept to simultaneously estimate the state variables and the unknown input signals in a sampled-data context. A theoretical study is conducted to formally justify the convergence properties of the observer whilst simulation results are provided to show the efficiency of the proposed scheme.
MSC:
| 93B12 | Variable structure systems |
| 93C57 | Sampled-data control/observation systems |
| 93B53 | Observers |
References:
| [1] | Alwi, H.; Edwards, C., Fault tolerant control using sliding modes with on-line control allocation, Automatica, 44, 7, 1859-1866 (2008) · Zbl 1149.93313 · doi:10.1016/j.automatica.2007.10.034 |
| [2] | Bejarano, F. J.; Fridman, L., High order sliding mode observer for linear systems with unbounded unknown inputs, International Journal of Control, 83, 9, 1920-1929 (2010) · Zbl 1213.93019 · doi:10.1080/00207179.2010.501386 |
| [3] | Chakrabarty, A.; Ayoub, R.; Żak, S. H.; Sundaram, S., Delayed unknown input observers for discrete-time linear systems with guaranteed performance, Systems & Control Letters, 103, 9-15 (2017) · Zbl 1370.93063 · doi:10.1016/j.sysconle.2017.02.005 |
| [4] | Chandra, K. P. B.; Alwi, H.; Edwards, C., Fault detection in uncertain LPV systems with imperfect scheduling parameter using sliding mode observers, European Journal of Control, 34, 1-15 (2017) · Zbl 1358.93045 |
| [5] | Charandabi, B. A.; Marquez, H. J., A novel approach to unknown input filter design for discrete-time linear systems, Automatica, 50, 11, 2835-2839 (2014) · Zbl 1300.93166 |
| [6] | Darouach, M.; Zasadzinski, M.; Xu, S. J., Full-order observers for linear systems with unknown inputs, IEEE Transactions on Automatic Control, 39, 3, 606-609 (1994) · Zbl 0813.93015 |
| [7] | Edwards, C.; Spurgeon, S. K.; Patton, R. J., Sliding mode observers for fault detection and isolation, Automatica, 36, 4, 541-553 (2000) · Zbl 0968.93502 |
| [8] | Floquet, T.; Barbot, J. P., State and unknown input estimation for linear discrete-time systems, Automatica, 42, 11, 1883-1889 (2006) · Zbl 1222.93215 |
| [9] | Floquet, T.; Edwards, C.; Spurgeon, S. K., On sliding mode observers for systems with unknown inputs, International Journal of Adaptive Control and Signal Processing, 21, 8-9, 638-656 (2007) · Zbl 1128.93008 · doi:10.1002/acs.958 |
| [10] | Fridman, L.; Levant, A.; Davila, J., Observation of linear systems with unknown inputs via high-order sliding-modes, International Journal of Systems Science, 38, 10, 773-791 (2007) · Zbl 1128.93312 |
| [11] | Gucik-Derigny, D.; Raïssi, T.; Zolghadri, A., A note on interval observer design for unknown input estimation, International Journal of Control, 89, 1, 25-37 (2016) · Zbl 1332.93066 |
| [12] | Han, X.; Fridman, E.; Spurgeon, S., Sampled-data sliding mode observer for robust fault reconstruction: A time-delay approach [Secial issue on 2010-2012 advances in variable structure systems and sliding mode algorithms], Journal of the Franklin Institute, 351, 4, 2125-2142 (2014) · Zbl 1372.93063 |
| [13] | Kokotovic, P.; Khalil, H.; O’Reilly, J., Singular perturbation methods in control: Analysis and design (1986), Academic Press · Zbl 0646.93001 |
| [14] | Levant, A., Discretization issues of high-order sliding modes, IFAC Proceedings Volumes, 44, 1, 1904-1909 (2011) |
| [15] | Livne, M.; Levant, A., Proper discretization of homogeneous differentiators, Automatica, 50, 8, 2007-2014 (2014) · Zbl 1297.93046 |
| [16] | Marro, G., Bernstein, D. S., & Zattoni, E. (2010, December). Geometric methods for unknown-state, unknown-input reconstruction in discrete-time nonminimum-phase systems with feedthrough terms. 49th IEEE conference on decision and control (CDC), Atlanta, GA, USA (pp. 6022-6027). |
| [17] | Marro, G.; Zattoni, E.; Bernstein, D. S., Geometric insight and structure algorithms for unknown-state, unknown-input reconstruction in linear multivariable systems, IFAC Proceedings Volumes, 44, 1, 11320-11325 (2011) |
| [18] | Milosavljevic, C., General conditions for the existence of quasi-sliding mode on the switching hyper-plane in discrete variable structure systems, Automation and Remote Control, 46, 3, 307-314 (1985) · Zbl 0583.93043 |
| [19] | Nguyen, T.; Edwards, C.; Azimi, V.; Su, W. C., Improving control effort in output feedback sliding mode control of sampled-data systems, IET Control Theory & Applications, 13, 13, 2128-2137 (2019) · Zbl 07907008 |
| [20] | Nguyen, T.; Su, W. C.; Gajic, Z.; Edwards, C., Higher accuracy output feedback sliding mode control of sampled-data systems, IEEE Transactions on Automatic Control, 61, 10, 3177-3182 (2016) · Zbl 1359.93095 |
| [21] | Nguyen, T., Su, W. C., & Gajic, Z. (2010, June 30-July 02). On \(####\) state regulation with output feedback sliding mode control for sampled-data systems. Proceedings of the american control conference (pp. 1823-1828). Baltimore, USA. |
| [22] | Sundaram, S.; Hadjicostis, C. N., Delayed Observers for linear systems with unknown inputs, IEEE Transactions on Automatic Control, 52, 2, 334-339 (2007) · Zbl 1366.93644 |
| [23] | Tan, C. P.; Edwards, C., Sliding mode observers for robust detection and reconstruction of actuator and sensor faults, International Journal of Robust and Nonlinear Control, 13, 5, 443-463 (2003) · Zbl 1036.93025 · doi:10.1002/rnc.723 |
| [24] | Tan, C. P.; Edwards, C., Robust fault reconstruction in uncertain linear systems using multiple sliding mode observers in cascade, IEEE Transactions on Automatic Control, 55, 4, 855-867 (2010) · Zbl 1368.93131 |
| [25] | Yan, X. G.; Edwards, C., Nonlinear robust fault reconstruction and estimation using a sliding mode observer, Automatica, 43, 9, 1605-1614 (2007) · Zbl 1128.93389 |
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