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http://dx.doi.org/10.12989/sss.2020.25.1.037

Investigations on state estimation of smart structure systems  

Arunshankar, J. (Department of Instrumentation and Control Systems Engineering, PSG College of Technology)
Publication Information
Smart Structures and Systems / v.25, no.1, 2020 , pp. 37-45 More about this Journal
Abstract
This paper aims at enlightening the properties, computational and implementation issues related to Kalman filter based state estimation algorithms and sliding mode observers, by applying them for estimating the states of a smart structure system. The Kalman based estimators considered in this work are Kalman filter and information filter and, the sliding mode observers considered are Utkin observer and higher order sliding mode observer. A fourth order linear time invariant model of a piezo actuated beam is used in this work. This structure is embedded with four number of piezo patches, of which two act as sensors, one as disturbance actuator and the other as control actuator. The performance of the state estimation algorithms is evaluated through simulation, for the first two vibrating modes of the piezo actuated structure, when the structure is maintained at first mode and second mode resonance.
Keywords
smart structure; piezo actuated structure; state estimation; Kalman filter; information filter; Utkin observer; higher order sliding mode observer;
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Times Cited By KSCI : 8  (Citation Analysis)
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1 Sharma, R. and Aldeen, M. (2011), "Fault and disturbance reconstruction in non-linear systems using a network of interconnected sliding mode observers", IET Control. Theory. Appl., 5(6), 751-763. https://doi.org/10.1049/iet-cta.2009.0592   DOI
2 Shtessel, Y.B., Baev, S., Edwards, C. and Spurgeon, S.K. (2010), "HOSM observer for a class of non-minimum phase causal nonlinear MIMO systems", IEEE Trans. Autom. Control, 55(2), 543-548. https://doi.org/10.1109/TAC.2009.2037478   DOI
3 Utkin, V.I. (1992), Sliding Modes in Control and Optimization, Communications and Control Engineering Series, Springer-Verlag, Berlin, Germany.
4 Veluvolu, K.C. and Soh, Y.C. (2011), "Fault reconstruction and state estimation with sliding mode observers for Lipschitz nonlinear systems", IET Control. Theory. Appl., 5(11), 1255-1263. https://doi.org/10.1049/iet-cta.2010.0171   DOI
5 Wolin, E.J. and Ho, L.L. (1993), "Covariance matrices for track fitting with the Kalman filter", Nucl. Instrum. Methods Phys Res. Sect A., 329(3), 493-500. https://doi.org/10.1016/0168-9002(93)91285-U   DOI
6 Yao, J., Chin, L., Liu, W. and Lu, Y. (2002), "An approach to identification of variances for radar tracking systems", Signal. Process., 82, 875-879. https://doi.org/10.1016/S0165-1684(02)00162-7   DOI
7 Zhou, J. and Luecke, R.H. (1995), "Estimation of the covariances of the process noise and measurement noise for a linear discrete dynamic system", Comput. Chem. Eng., 19(2), 187-195. https://doi.org/10.1016/0098-1354(94)E0046-P   DOI
8 Arunshankar, J. and Umapathy, M. (2012), "Control of a piezo actuated structure using robust loop shaping controller with GPC based precompensator involving data fusion", Int. J. Imaging Robot., 8(2), 85-100.
9 Capisani, L.M., Ferrara, A., Loza, A.F. and Fridman, L.M. (2012), "Manipulator fault diagnosis via higher order sliding-mode observers", IEEE Trans. Ind. Electron., 59(10), 3979-3986. https://doi.org/10.1109/TIE.2012.2189534   DOI
10 Arunshankar, J., Umapathy, M. and Bandyopadhyay, B. (2013), "Experimental evaluation of discrete sliding mode controller for piezo actuated structure with multisensor data fusion", Smart. Struct. Syst., Int. J., 11(6), 569-587. https://doi.org/10.12989/sss.2013.11.6.569   DOI
11 Chao, P.C.P. and Shen, C.Y. (2009), "Sensorless tilt compensation for a three-axis optical pickup using a sliding-mode controller equipped with a sliding-mode observer", IEEE Trans. Contr. Syst. Technol., 17(2), 267-282. https://doi.org/10.1109/TCST.2008.924560   DOI
12 Edwards, C. and Spurgeon, S.K. (1998), Sliding Mode Control: Theory and Applications, Taylor and Francis Ltd., UK.
13 Kalman, R.E. (1960), "A new approach to linear filtering and prediction problem", Trans. ASME, Series D, J. Basic Eng., 82(1), 35-45. https://doi.org/10.1109/9780470544334.ch9   DOI
14 Khan, M.K., Spurgeon, S.K. and Levant, A. (2003), "Simple output-feedback 2-sliding controller for systems of relative degree two", Proceedings of the European Control Conference, Cambridge, UK.
15 Kim, K., Choi, J., Koo, G. and Sohn, H. (2016), "Dynamic displacement estimation by fusing biased high-sampling rate acceleration and low-sampling rate displacement measurements using two-stage Kalman estimator", Smart. Struct. Syst., Int. J., 17(4), 647-667. https://doi.org/10.12989/sss.2016.17.4.647   DOI
16 Kurode, S., Spurgeon, S.K., Bandyopadhyay, B. and Gandhi, P.S. (2013), "Sliding mode control for slosh-free motion using a nonlinear sliding surface", IEEE/ASME Trans. Mechatron., 8(2), 714-724. https://doi.org/10.1109/TMECH.2011.2182056
17 Lei, Y., Chen, F. and Zhou, H. (2015), "A two-stage and two-step algorithm for the identification of structural damage and unknown excitations: numerical and experimental studies", Smart. Struct. Syst., Int. J., 15(1), 57-80. https://doi.org/10.12989/sss.2015.15.1.057   DOI
18 Lee, D.J., Park, Y. and Park, Y.S. (2012a), "Robust $H{\infty}$ sliding mode descriptor observer for fault and output disturbance estimation of uncertain systems", IEEE Trans. Autom. Control., 57(11), 2928-2934. https://doi.org/10.1109/TAC.2012.2195930   DOI
19 Lee, S., Jeon, M. and Shin, V. (2012b), "Distributed estimation fusion with application to a multisensory vehicle suspension system with time delays", IEEE Trans. Ind. Electron., 59(11), 4475-4482. https://doi.org/10.1109/TIE.2011.2182010   DOI
20 Lei, Y., Liu, C., Jiang, Y.Q. and Mao, Y.K. (2013), "Substructure based structural damage detection with limited input and output measurements", Smart. Struct. Syst., Int. J., 12(6), 619-640. https://doi.org/10.12989/sss.2013.12.6.619   DOI
21 Lei, Y., Luo, S. and Su, Y. (2016), "Data fusion based improved Kalman filter with unknown inputs and without collocated acceleration measurements", Smart. Struct. Syst., Int. J., 18(3), 375-387. https://doi.org/10.12989/sss.2016.18.3.375   DOI
22 Liu, L., Zhu, J., Su, Y. and Lei, Y. (2016), "Improved Kalman filter with unknown inputs based on data fusion of partial acceleration and displacement measurements", Smart. Struct. Syst., Int. J., 17(6), 903-915. https://doi.org/10.12989/sss.2016.17.6.903   DOI
23 Ma, T.W., Bell, M., Lu, W. and Xu, N.S. (2014), "Recovering structural displacements and velocities from acceleration measurements", Smart. Struct. Syst., Int. J., 14(2), 191-207. https://doi.org/10.12989/sss.2014.14.2.191   DOI
24 Mehra, R.K. (1970), "On the identification of variances and adaptive Kalman filtering", IEEE Trans. Autom. Control, 15(2), 175-184. https://doi.org/10.1109/TAC.1970.1099422   DOI
25 Rao, K.S., Raja Rajeswari, K. and Lingamurty, K.S. (2009), "Unscented Kalman filter with application to bearings-only target tracking", IETE J. Res., 55(2), 63-67.   DOI
26 Mutambara, A.G.O. (1999), "Information based estimation for both linear and nonlinear systems", Proceedings of the American Control Conference, San Diego, CA, USA.
27 Palanisamy, R.P., Cho, S., Kim, H. and Sim, S.H. (2015), "Experimental validation of Kalman filter-based strain estimation in structures subjected to non-zero mean input", Smart. Struct. Syst., Int. J., 15(2), 489-503. https://doi.org/10.12989/sss.2015.15.2.489   DOI
28 Pisano, A. and Usai, E. (2011), "Sliding mode control: a survey with applications in math", Math. Comput. Simulat., 81, 954-979. https://doi.org/10.1016/j.matcom.2010.10.003   DOI
29 Rolink, M., Boukhobza, T. and Sauter, D. (2006), "High order sliding mode observer for fault actuator estimation and its application to the three tanks benchmark", Workshop on Advanced Control and Diagnosis, Nancy, France.