Reduced-order modelling of linear discrete-time systems via continued-fraction expansion of a z transfer function about z = 1 and z = a alternately |
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Authors: | CHYI HWANG CHEE-FAI YUNG |
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Affiliation: | 1. Department of Chemical Engineering , National Cheng K ung University , Tainan, Taiwan, 700, Republic of China;2. Department of Electrical Engineering , National Cheng Kung University , Tainan, Taiwan, 700, Republic of China. |
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Abstract: | A new time-domain procedure is suggested for obtaining reduced-order models of linear time-invariant discrete-time systems. The procedure is based on presenting a new form of continued-fraction expansion (CFE) about z = 1 and z = a alternately, and deriving a realization form for the CFE. An algorithm is presented for obtaining the new CFE of the z transfer function of a linear discrete-time system from its state-space model directly, without having to determine the corresponding rational z transfer function. Also presented is a systematic approach to deriving two similarity transformation matrices: one is used to transform a state-space model from a general form to the CFE canonical form, and the other is used to transform a state-space model from the phase-variable canonical form to the CFE canonical form. Finally, an approximate aggregation matrix is constructed to relate the state vector of the original system to that of a reduced model obtained by the present method. The proposed procedure is illustrated with examples. |
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