An Input-Output Criterion for Linear Model Deduction

Author:

Walker Douglas G.1,Stein Jeffrey L.1,Ulsoy A. Galip1

Affiliation:

1. Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109

Abstract

Model order deduction algorithms have been developed in an effort to automate the production of accurate, minimal complexity models of dynamic systems in order to aid in the design of these systems. Previous algorithms, MODA and Extended MODA, deduce models independent of system inputs and outputs. FD-MODA uses frequency response methods to deduce models of a single input-output pair. In this paper, an input-output criterion based on controllability and observability is combined with the frequency based criterion used by MODA. The new model deduction algorithm, IO-MODA, compares the ratio of the adjacent diagonal values of the system gramian to a user specified threshold. The gramian is computed from a balanced realization of the system. IO-MODA generates an accurate multiple-input multiple-output model of minimum order with physically meaningful states. This model is called a proper MIMO model. An example problem is used to demonstrate this new model deduction algorithm. [S0022-0434(00)02103-1]

Publisher

ASME International

Subject

Computer Science Applications,Mechanical Engineering,Instrumentation,Information Systems,Control and Systems Engineering

Reference12 articles.

1. Wilson, B. H., and Stein, J. L., 1995, “An Algorithm for Obtaining Proper Models of Distributed and Discrete Systems,” ASME J. Dyn. Syst., Meas., Control, 117, No. 4, pp. 534–540.

2. Ferris, J., Stein, J. L., and Bernitsas, M., 1998, “Development Of Proper Models of Hybrid Systems,” ASME J. Dyn. Syst., Meas., Control, 120, No. 3, pp. 328–333.

3. Wilson, B. H., Taylor, J. H., and Eryilmaz, B., 1995. “A Frequency Domain Model-Order-Deduction Algorithm for Linear Systems,” ASME Winter Annual Meeting, Proceedings of the Symposium on Automated Modeling for Design, San Francisco, CA., Nov. 12–17, ASME, New York, NY.

4. Kailath, T., 1980, Linear Systems, Prentice Hall, Englewood Cliffs, NJ.

5. Moore, B. C., 1978, “Singular Value Analysis of Linear Systems,” Proceedings IEEE CDC, pp. 66–73.

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