Abstract
This paper presents a state observer for linear systems with quantized outputs. The observer employs an orthogonal projection operation at quantizer output discontinuities to enhance its convergence rate for quantized output systems. Although there may be a significant quantization error on average, it is possible to design observers with an exponentially stable tracking error. We explain how to construct the orthogonal projection operation in a Hilbert space and prove the stability of the proposed observer by using the Lyapunov second method. In order to assess the value of the orthogonal projection operation in the proposed observer, the simple motor system with an optical encoder has been analyzed numerically.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Curry, R. E., 1997, “Estimation Control with Quantized Measurements,” Cambridge. MA: M. I. T. Press.
Joono Sur, 1997, “State Observers for Linear System with Quantized Outputs,” Ph. D. Thesis, University of California at Santa Barbara, CA.
Delchamps, D. F., 1988, “New Techniques for Analyzing the Effects of Output Quantization in Feedback System,”Proceedings of the 1988 Conference on Information Sciences and Systems, Princeton, NJ, pp. 228–232.
Delchamps, D. F., 1989a, “Controlling the Flow of Information in Feedback Systems with Measurement Quantization,”Proceedings of the 28th Conference on Decision and Control, Tampa, Florida, December.
Delchamps, D. F., 1989b, “Extracting State Information from a Quantized Output Record,”Systems and Control Letter 13, pp. 365–372, North-Holland.
Khalil, H. K., 1992,Nonlinear Systems, NY Macmillan Publishing Company, Inc.
Friendland, B., 1986,Control System Design, McGraw-Hill Book Company, Inc.
Miller, R. K., Michel, A. N. and Farrel, J. A., 1989, “Quantize Effects on Steady State Error Specifications of Digital Feedback Control Systems,”IEEE trans. Automat. Control, Vol. 34 No. 6.
Schweppe, F. C., 1968, “Recursive State Estimation: Unknown but Bounded Errors and System Inputs,”IEEE Trans. Automt. Control, Vol. AC-13, pp. 22–28.
Haller, G. and Steppan, G., 1996, “Micro-Chaos in Digital Control,”Journal of Nonlinear Science, Vol. 6, No. 5, pp. 415–448.
Joono Sur and Brad E. Paden, 1996, “State Observer for SISO Linear Systems with Quantized Outputs,” CCEC-96-0520 University of California at Santa Barbara, CA.
Joono Sur and Brad E. Paden, 1997, ”Observers for Linear Systems with Quantized Outputs,”American Control Conference, Albuquerque, NM, pp. 3012–3016, June.
Rotea, M. A. and Williamson, D., 1994, “Optimal Realization of finite Wordlength Digital Controllers via Affine Matrix Inequalities,”Proceedings of American Control Conference, pp. 445–449.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sur, J., Park, Yi. Design of an observer for quantized output systems using orthogonal projection. KSME International Journal 13, 517–523 (1999). https://doi.org/10.1007/BF03186442
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF03186442