Computationally Efficient Functional Observer for LTI System Based on a Multirate Output Sampling Algorithm

Abstract:

This paper proposes a technique for computing a vector linear functional of the system states of a linear time invariant (LTI) system. The concept of multirate output observations has been used to design the observer. The paper also proves that the complete state observability of a system is not a necessary condition for the existence of a functional observer. The proposed technique reduces the computational time and complexity of the hardware and software of the observer system considerably due to static structure of observer as well as involvement of reduced dimension matrices in computation of the functional. The proposed technique has been validated using numerical examples.

• Periodical: Advanced Materials Research (Volumes 403-408)
• Pages: 3875-3883
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.403-408.3875
• Online since: November 2011
• Authors: S. Janardhanan, Saurabh Inamdar
• Keywords: Functional Observer, Multirate Output Sampling

References

[1] M. Aldeen and H. Trinh. Reduced-order linear functional observer for linear systems. IEE Proceedings on Control Theory and Applications, 146(5): 399–405, September (1999).

DOI: 10.1049/ip-cta:19990585

[2] M.J. Er and Brian D.O. Anderson. Design of reduced-order multirate output linear functional observer based compensators. Automatica, 31(2): 237–242, Feb. (1995).

DOI: 10.1016/0005-1098(94)00063-o

[3] P. Murdoch. Observer design for a linear functional of the state vector. IEEE Transactions on Automatic Control, 18(3): 308–310, June (1973).

DOI: 10.1109/tac.1973.1100304

[4] Ramji Das Gupta, Frederick W. Fairman, and Takao Hinamoto. A direct procedure for the design of single functional observer. IEEE Transactions on Circuits and Systems, CAS-28(4): 294–300, April (1981).

DOI: 10.1109/tcs.1981.1084991

[5] Chia-Chi Tsui. An algorithm for the design of single functional observers. IEEE Transactions on Circuits and Systems, CAS-32(1): 100– 102, January (1985).

DOI: 10.1109/tcs.1985.1085591

[6] David G. Luenberger. An introduction to observers. IEEE Transactions on Automatic Control, 16(6): 596–602, Dec. (1971).

DOI: 10.1109/tac.1971.1099826

[7] Chia-Chi Tsui. What is the minimum function observer order ? Journal of The Franklin Institute, 335(4): 623–628, MAY (1998).

DOI: 10.1016/s0016-0032(96)00141-x

[8] Chia-Chi Tsui. On the order reduction of linear function observers. IEEE Transactions on Automatic Control, AC-31: 447–449, MAY (1986).

DOI: 10.1109/tac.1986.1104298

[9] Chia-Chi Tsui. A new algorithm for design of multifunctional observers. IEEE Transactions on Automatic Control, AC-30: 89–93, (1985).

DOI: 10.1109/tac.1985.1103795

[10] S. Janardhanan and Saurabh Inamdar. Multirate output feedback sliding mode control design using reduced order functional observer. In The 11th International Workshop on Variable Structure Systems, pages 395–398, June (2010).

DOI: 10.1109/vss.2010.5544544