Abstract
For a class of uncertain nonlinear systems with sector-bounded nonlinearity, a proportional-integral state observer is designed in a dissipativity framework. The dissipativity ensures the bounded estimation errors against the bounded disturbance and an integral term in the observer structure can provide additional degrees of freedom in the observer design that can be used to improve the estimation performance. In this study, a dissipative condition for the proposed observer is found in terms of a linear matrix inequality (LMI). In order to specify the dissipativity, the L2 gain between the disturbance and the weighted sum of estimation errors is adopted as the supply rate in the dissipativity framework. In addition, the notion of the proposed design method is extended to the exponential dissipativity. The effectiveness of the proposed observer is demonstrated through a numerical example.
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References
A. J. Krener and A. Isidori, Linearization by output injection and nonlinear observers, Syst. Contr. Lett., 3 (1983) 47–52.
D. Bestle and M. Zeitz, Canonical form observer design for nonlinear time-variable systems, Int. J. of Control, 38 (1983) 419–431.
B. L. Walcott, M. J. Corless and S. H. Zak, Comparative study of non-linear state-observation technique, Int. J. of Control, 45 (1987) 2109–2132.
E. A. Misawa and J. K. Hedrick, Nonlinear observers — a state-of-the-art survey, Trans. of the ASME, J. of Dynam. Syst. Meas. Contr., 111 (1989) 344–352.
F. E. Thau, Observing the state of non-linear dynamic systems, Int. J. of Control, 17 (1973) 471–479.
S. Raghavan and J. K. Hedrick, Observer design for a class of nonlinear systems, Int. J. of Control, 59 (1994) 515–528.
A. Howell, Nonlinear observer design and fault diagnostics for automated longitudinal vehicle control, Ph.D. dissertation, Univ. of California, Berkeley (2002).
H. Shim, J. H. Seo and A. R. Teel, Nonlinear observer design via passivation of error dynamics, Automatica, 39 (2003) 885–892.
A. Alessandri, Observer design for nonlinear systems by using input-to-state stability, Proc. of the 43rd IEEE Conf. on Decision and Control (2004) 3892–3897.
D. Söffker, T.-J. Yu and P. C. Müller, State estimation of dynamical systems with nonlinearities by using proportionalintegral observer, Int. J. Systems Sci., 26 (9) (1995) 1571–1582.
B. Shafai, S. Beale, H. H. Niemann and J. L. Stoustrup, LTR design of discrete-time proportional-integral observers, IEEE Trans. Autom. Control, 41 (7) (1996) 1056–1062.
K. K. Busawon and P. Kabore, Disturbance attenuation using proportional integral observers, Int. J. of Control, 74(6) (2001) 618–627.
B. Shafai and H. M. Oloomi, Output derivative estimation and disturbance attenuation using PI observer with application to a class of nonlinear systems, Proc. of the 35th Southeastern Symposium (2003) 196–200.
G. Zames, On the input-output stability of time-varying nonlinear feedback systems-part I: conditions derived using concepts of loop gain, conicity, and positivity, IEEE Trans. Autom. Control, 11(2) (1966) 228–238.
S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear matrix inequalities in system and control theory, Philadelphia: SIAM (1994).
D. Hill and P. Moylan, The stability of nonlinear dissipative systems, IEEE Trans. Autom. Control, 21(5) (1976) 708–711.
V. Chellaboina and W. M. Haddad, Exponentially dissipative nonlinear dynamical systems: a nonlinear extension of strict positive realness, Mathematical Problems in Engineering (1) (2003) 25–45.
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This paper was recommended for publication in revised form by Editor Yeon June Kang
Jongchul Jung received his B.S. and M.S. degree in Precision Mechanical Engineering and his Ph.D. degree in Automotive Engineering from Hanyang University, Seoul, Korea in 1996, 1998, and 2006, respectively. He was with the University of Michigan-Dearborn in Dearborn, MI, USA as a post-doctoral researcher for 2 years after graduation. Now he is with LS Industrial Systems Co., Ltd., Anyang, Korea as an engineer, where he is working in develo** control systems for fuel cell systems. He has a research background in vehicle dynamics and control, fuel cell systems, robust observer design, estimation and control theory, and convex optimization.
Donghwi Lee received his B.S degree in Precision Mechanical Engineering and his M.S degree in Automotive Engineering from Hanyang University, Seoul, Korea in 2007, 2009 respectively. He is currently pursuing a doctoral course in Automotive Engineering at Hanyang University. His research interests include vehicle dynamics and chassis control systems.
Kunsoo Huh received his Ph.D. from the University of Michigan, Ann Arbor in 1992. He is currently a Professor at the Department of Automotive Engineering, and the Director of Hybrid Vehicle Education Center, at the Hanyang University, Korea. His research interests include machine monitoring and control, with emphasis on their applications to vehicular systems. His current research focuses include integrated chassis control systems, EMB/EHB fault tolerant control, pre-crash control systems. He has served as an Editor for the IJAT (International Journal of Automotive Technology) from 2008-present.
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Jung, J., Lee, D. & Huh, K. Dissipative proportional integral observer for a class of uncertain nonlinear systems. J Mech Sci Technol 25, 1551–1555 (2011). https://doi.org/10.1007/s12206-011-0330-2
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DOI: https://doi.org/10.1007/s12206-011-0330-2