Design of an observer for quantized output systems using orthogonal projection
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.
Key WordsObserver Quantized Outputs Orthogonal Projection Lyapunov Method
Unable to display preview. Download preview PDF.
- Curry, R. E., 1997, “Estimation Control with Quantized Measurements,” Cambridge. MA: M. I. T. Press.Google Scholar
- Joono Sur, 1997, “State Observers for Linear System with Quantized Outputs,” Ph. D. Thesis, University of California at Santa Barbara, CA.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- Khalil, H. K., 1992,Nonlinear Systems, NY Macmillan Publishing Company, Inc.Google Scholar
- Friendland, B., 1986,Control System Design, McGraw-Hill Book Company, Inc.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- Joono Sur and Brad E. Paden, 1997, ”Observers for Linear Systems with Quantized Outputs,”American Control Conference, Albuquerque, NM, pp. 3012–3016, June.Google Scholar
- 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.Google Scholar