| Summary: | 碩士 === 國立成功大學 === 化學工程研究所 === 82 === In this thesis, two different approaches have been proposed to
deal withthe problem of model reduction of 2-D (two-
dimensional) systems1. The first is frequency-domain approach
which uses the 2-D bilinear Routh γ-δ expansion to represent
the system. The properties of system can beeasily obtained from
the expansion coefficients of γand δ. Besides, the quasi-
Newton method is applied to find the parameters ofγand δ,
such that integral of squared error between the impulse
response of the system and reduced model is minimized. The
second approach is based on the time-domain representation of
the system. In this approach, the balanced realization is
carried out to reveal the contribution of each state to the
system impulse response energy. The reduction is performed by
truncating these states which have least contribution to the
system impulse response energy. For carrying out the balanced
realization for a general 2-D system, an efficient algorithm is
provided to calculate the controllability and observability
gramians. However, for 2-D systems having a separable
denominator polynomials, the gramians can be easily computed by
the parametric Routh algorithm. In addition to dealing with
model reduction problem, an efficient 2-D Fast Fourier Transf-
orm(FFT) is proposed for the numerical inversion of the Laplace
transforms and the calculation of the coefficients of a 2-D
Taylor expansion series. With this algorithm, the impulse
response of a 2-D system can be accurately obtained.
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