Observer design for systems with unknown inputs

• Autorzy: Stefen Hui , Stanisław H. Żak
• Języki publikacji: EN

Abstrakty

EN

Design procedures are proposed for two different classes of observers for systems with unknown inputs. In the first approach, the state of the observed system is decomposed into known and unknown components. The unknown component is a projection, not necessarily orthogonal, of the whole state along the subspace in which the available state component resides. Then, a dynamical system to estimate the unknown component is constructed. Combining the output of the dynamical system, which estimates the unknown state component, with the available state information results in an observer that estimates the whole state. It is shown that some previously proposed observer architectures can be obtained using the projection operator approach presented in this paper. The second approach combines sliding modes and the second method of Lyapunov resulting in a nonlinear observer. The nonlinear component of the sliding mode observer forces the observation error into the sliding mode along a manifold in the observation error space. Design algorithms are given for both types of observers.

Słowa kluczowe

EN

uncertain systems; unknown input observer (UIO); state observation; second method of Lyapunov; projection operators

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2005
• Tom: 15
• Numer: 4
• Strony: 431-446

Daty

wydano

2005

otrzymano

2005-06-01

poprawiono

2005-09-01

Twórcy

autor

Stefen Hui

• Department of Mathematical Sciences, San Diego State University,, San Diego, CA 92182, USA

autor

Stanisław H. Żak

• School of Electrical and Computer Engineering Purdue University, West Lafayette, IN 479072035, USA

Bibliografia

• Bhattacharyya S. P. (1978): Observer design for linear systems with unknown inputs. - IEEE Trans. Automat. Contr., Vol. AC-23, No. 3, pp. 483-484.
• Chang S.-K., You W.-T., and Hsu P.-L. (1997): Design of general structured observers for linear systems with unknown inputs. - J. Franklin Instit., Vol. 334B, No. 2, pp. 213-232.
• Chen J., Patton R. J., and Zhang H.-Y. (1996): Design of unknown input observers and robust fault detection filters. - Int. J. Contr., Vol. 63, No. 1, pp. 85-105.
• Chen J. and Patton R. J. (1999): Robust Model-Based Fault Diagnosis for Dynamic Systems. - Boston: Kluwer.
• Choi H. H. and Ro K.-S. (2005): LMI-based sliding-mode observer design method.- IEE Proc. Contr. Theory Appl., Vol. 152, No. 1, pp. 113-115.
• Corless M. and Tu J. (1998): State and input estimation for a class of uncertain systems. - Automatica, Vol. 34, No. 6, pp. 757-764.
• Darouach M., Zasadzinski M., and Xu S. J. (1994): Full-order observers for linear systems with unknown inputs. - IEEE Trans. Automat. Contr., Vol. 39, No. 3, pp. 606-609.
• Dawson D. M., Hu J., and Burg T. C. (1998): Nonlinear Control of Electric Machinery.- New York: Marcel Dekker.
• Edwards C. and Spurgeon S. K. (1998): Sliding Mode Control: Theory and Applications. - London: Taylor and Francis.
• Edwards C., Spurgeon S. K., and Patton R. J. (2000): Sliding mode observers for fault detection and isolation. - Automatica, Vol. 36, No. 4, pp. 541-553.
• Ellis G. (2002): Observers in Control Systems; A Practical Guide. - San Diego: Academic Press.
• Gantmacher F. R. (1990): The Theory of Matrices, Vol. 1, 2nd Ed.. - New York: Chelsea Publishing Company.
• Ha Q. P., Trinh H., Nguyen H. T., and Tuan H. D. (2003): Dynamic output feedback sliding-mode control using pole placement and linear functional observers. - IEEE Trans. Industr. Electron., Vol. 50, No. 5, pp. 1030-1037.
• Hou M. and Muller P. C. (1992): Design of observers for linear systems with unknown inputs. - IEEE Trans. Automat. Contr., Vol. 37, No. 6, pp. 871-875.
• Hou M., Pugh A. C. and Muller P. C. (1999): Disturbance decoupled functional observers. - IEEE Trans. Automat. Contr., Vol. 44, No. 2, pp. 382-386.
• Hostetter G. and Meditch J. S. (1973): Observing systems with unmeasurable inputs.- IEEE Trans. Automat. Contr., Vol. AC-18, No. 3, pp. 307-308.
• Hui S. and Żak S. H. (1990): Control and observation of uncertain systems: A variable structure systems approach, In: Control and Dynamic Systems; Advances in Theory and Applications, Vol. 34: Advances in Control Mechanics, Part 1 of 2 (C. T. Leondes, Ed.). - San Diego: Academic Press, pp. 175-204.
• Hui S. and Żak S. H. (1993): Low-order state estimators and compensators for dynamical systems with unknown inputs. - Syst. Contr. Lett., Vol. 21, No. 6, pp. 493-502.
• Hui S. and Żak S. H. (2005): Low-order unknown input observers. -Proc. Amer. Contr. Conf., Portland, OR, pp. 4192-4197.
• Jiang B., Staroswiecki M., and Cocquempot V. (2004): Fault estimation in nonlinear uncertain systems using robust sliding-mode observers. - IEE Proc. Contr. Theory Appl., Vol. 151, No. 1, pp. 29-37.
• Kaczorek T. (1998): Vectors and Matrices in Control and Electrical Engineering, 2nd Ed.. - Warsaw: WNT, (in Polish).
• Koshkouei A. J. and Zinober A. S. I. (2004); Sliding mode state observation for non-linear systems. - Int. J. Contr., Vol. 77, No. 2, pp. 118-127.
• Kudva P., Viswanadham N., and Ramakrishna A. (1980): Observers for linear systems with unknown inputs. - IEEE Trans. Automat. Contr., Vol. AC-25, No. 1, pp. 113-115.
• Kurek J. E. (1983): The state vector reconstruction for linear systems with unknown inputs. - IEEE Trans. Automat. Contr., Vol. AC-28,No. 12, pp. 1120-1122.
• Krzemiński S. and Kaczorek T. (2004): Perfect reduced-order unknown-input observer for standard systems. - Bull. Polish Acad. Sci., Techn. Sci., Vol. 52, No. 2, pp. 103-107.
• Luenberger D. G. (1966): Observers for multivariable systems. - IEEE Trans. Automat. Contr., Vol. AC-11, No. 2, pp. 190-197.
• Luenberger D. G. (1971): An introduction to observers. - IEEE Trans. Automat. Contr., Vol. AC-16, No. 6, pp. 596-602.
• Luenberger D. G. (1979): Introduction to Dynamic Systems: Theory, Models, and Applications. - New York: Wiley.
• Millerioux G. and Daafouz J. (2004): Unknown input observers for switched linear discrete time systems. - Proc. Amer. Contr. Conf., Boston, MA, pp. 5802-5805.
• O'Reilly J. (1983): Observers for Linear Systems. - London: Academic Press.
• Robenack K. R and Lynch A. F. (2004): An efficient method for observer designwith approximately linear error dynamics. - Int. J. Contr., Vol. 77, No. 7, pp. 607-612.
• Saif M. and Xiong Y. (2003): Sliding mode observers and their application in fault diagnosis, In: Fault Diagnosis and Fault Tolerance for Mechatronic Systems (F. Caccavale and L. Villani, Eds.). - Berlin: Springer, pp. 1-57.
• Solsona J. A. and Valla M. I. (2003): Disturbance and nonlinear Luenberger observers for estimating mechanical variables in permanent magnet synchronous motors under mechanical parameters uncertainties. - IEEE Trans. Industr. Electron., Vol. 50, No. 4, pp. 717-725.
• Smith L. (1984): Linear Algebra, 2nd Ed.. - New York: Springer.
• Sundareswaran K. K., McLane P. J. and Bayoumi M. M. (1977): Observers for linear systems with arbitrary plant disturbances. - IEEE Trans. Automat. Contr., Vol. AC-22, No. 5, pp. 870-871.
• Utkin V., Guldner J., and Shi J. (1999): Sliding Mode Control in Electromechanical Systems. - London: Taylor and Francis.
• Walcott B. L. and Żak S. H. (1987): State observation of nonlinear uncertain dynamical systems. - IEEE Trans. Automat. Contr., Vol. AC-32, No. 2, pp. 166-170.
• Walcott B. L., Corless M. J., and Żak S. H. (1987): Comparative study of non-linear state-observation techniques. - Int. J. Contr., Vol. 45, No. 6, pp. 2109-2132.
• Walcott B. L. and Żak S. H. (1988): Combined observer-controller synthesis for uncertain dynamical systems with applications. - IEEE Trans. Sys., Man Cybern., Vol. 18, No. 1, pp. 88-104.
• Wang S.-H., Davison E. J. and Dorato P. (1975): Observing the states of systems with unmeasurable disturbances. - IEEE Trans. Automat. Contr., Vol. AC-20,No. 5, pp. 716-717.
• Xiang J., Su H., and Chu J. (2005): On the design of Walcott-Zak sliding mode observer. - Proc. Amer. Contr. Conf. Portland, OR, pp. 2451-2456.
• Yang F. and Wilde R. W. (1988): Observers for linear systems with unknown inputs. - IEEE Trans. Automat. Contr., Vol. 33, No. 7, pp. 677-681.
• Żak S. H. and Walcott B. L. (1990): State observation of nonlinear control systems via the method of Lyapunov, In: Deterministic Control of Uncertain Systems (A. S. I. Zinober, Ed.). - London: Peter Peregrinus Ltd,Ch. 16, pp. 333-350.
• Żak S. H. and Hui S. (1993): Output feedback variable structure controllers and state estimators for uncertain nonlinear dynamic systems. - IEE Proc. Contr. Theory Appl., Vol. 140, No. 1, pp. 41-50.
• Żak S. H., Walcott B. L., and Hui S. (1993): Variable structure control and observation of nonlinear uncertain systems, In: Variable Structure Control for Robotics and Aerospace Applications (K.-K. D. Young, Ed.). - Amsterdam: Elsevier, Ch. 4, pp. 59-88.
• Żak S. H. (2003): Systems and Control. - New York: Oxford University Press.