Parity equations-based unknown input estimator for multiple-input multiple-output linear systems

• Autorzy: Sumisławska M. , Larkowski T. , Burnham K. J.
• Języki publikacji: EN

Abstrakty

EN

This paper presents a novel approach to the problem of unknown input estimation of multiple-input multiple-output systems. In the setup considered the measured output signals are affected by white zero-mean Gaussian measurement noise. The observer developed here is based on the parity equations concept and the Lagrange multiplier method is used to obtain an analytical solution for the filter parameters, hence minimising the unwanted effect of the noise. The paper extends the concept of the parity equation based unknown input observer approach, which has been previously developed by the authors for the case of single-input single-output systems. A simulation study is carried out, which illustrates a potential application of the proposed approach to a steel rolling mill for the purpose of improving the control performance.

Słowa kluczowe

EN

filtering; observers; parity equations; unknown input observer

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Systems Science
• Rocznik: 2010
• Tom: Vol. 36, no 3
• Strony: 49--59
• Opis fizyczny: Bibliogr. 21 poz., rys., tab., wykr.

Twórcy

autor

Sumisławska M.

autor

Larkowski T.

autor

Burnham K. J.

• Control Theory and Applications Centre (CTAC), Coventry University, Priory Street, Coventry, CV1 5FB, UK,

Bibliografia

• [1] Bertsekas D.P., Constrained Optimisation and Lagrange Multiplier Methods, Academic Press, Inc., London, 1982.
• [2] Darouach M., Zasadzinski M., Unbiased minimum ariance estimation for systems with unknown exogenous inputs, Automatica, Vol. 33, No. 4, 1997, 717-719.
• [3] Ding S.X., Model-based Fault Diagnosis Techniques: Design Schemes, Algorithms and Tools, Springer-Verlag, Berlin, 2008.
• [4] Edelmayer A., Fault Detection in Dynamic Systems: From State Estimation to Direct Input Recontruction Methods, D.Sc. Thesis, Hungarian Academy of Sciences, Budapest, 2005.
• [5] Floquet T., Barbot J., State and unknown input estimation for linear discrete-time systems, Automatica, Vol. 42, No. 11, 2006, 1883-1889.
• [6] Gertler J., Analytical redundancy methods in fault detection and isolations, Proceedings of the IF AC Symposium SAFEPROCESS, Baden-Baden, 1991, 9-21.
• [7] Gertler J., Kunver M., A new structural framework for parity equation-based failure detection and isolation, Automatica, 1990, Vol. 26, No. 2, 381-388.
• [8] Gertler J., Monajemy R., Generating directional residuals with dynamic parity equations, Automatica, Vol. 31, No. 4, 1995, pp. 627-635.
• [9] Gillijns S., de Moor B., Unbiased minimum variance input and state estimation for linear discrete-time systems, Automatica, Vol. 43, 2007, 111-116.
• [10] Unbiased minimum variance input and state estimation for linear discrete-time systems with direct feedtrough, Automatica, Vol. 43, 2007, 934-937.
• [11] Hsieh C., Robust two-stage Kalman filters for systems with unknown inputs, IEEE Transactions on Automatic Control, Vol. 45, No. 12, 2000, 2374-2378.
• [12] Jelali M., Kroll A., Hydraulic servo-systems: modelling, identification and control, Springer-Verlag, London, 2003.
• [13] Kirtikar S., Palanthandalam-Madapusi H., Zattoni E., Bernstein D.S., l-delay input reconstruction for discrete-time linear systems, Procedings of the Conference on Decision and Control, Shanghai, China, 2009, 1848-1853.
• [14] Li W., Shah S., Structured residual vector-based approach to sensor fault detection and isolation, Journal of Process Control, Vol. 12, 2002, 429-443.
• [15] Luenberger D.G., Observing the state of linear systems, IEEE Trans. Mil. Electr., Vol. MIL-8, 1964, 70-80.
• [16] Marro G., Zattoni E., Unknown-state, unknown-input reconstruction in discrete-time nonminimum-phase systems: Geometric approach, Automatica, Vol. 46, 2010, 815-822.
• [17] Papadopoulos E.G., Chasparis G. C., Analysis and model-based control of servomechanisms with friction, Proceedings of the International Conference on Intelligent Robots and Systems (IROS 2002), Lausanne, Switzerland, 2002.
• [18] Putra D., Control of Limit Cycling in Frictional Mechanical Systems, Ph.D. Thesis, Technische Universiteit Eindhoven, Eindhoven, 2004.
• [19] Sumislawska M., Burnham K.J., Hearns G., Larkowski T.M., Reeve P.J., Parity equation-based friction compensation applied to a rolling mill, Proceedings of the UKACC International Conference on CONTROL 2010, Coventry, UK, 2010.
• [20] Sumislawska M., Burnham K.J., Larkowski T.M., Design of unknown input estimator of a linear system based on parity equations, Procedings of the XVII International Conference on Systems Science, Wrocław, Poland, 2010.
• [21] Yildiz S.K., Forbes J.F., Huang B., Zhang J., Wang F., Vaculik V., Dudzic M., Dynamic modelling and simulation of a hot strip finishing mill, Applied Mathematical Modelling, Vol. 33, 2009, 3208-3225.