Abstract
A procedure for approximating fractional-order systems by means of integer-order state-space models is presented. It is based on the rational approximation of fractional-order operators suggested by Oustaloup. First, a matrix differential equation is obtained from the original fractional-order representation. Then, this equation is realized in a state-space form that has a sparse block-companion structure. The dimension of the resulting integer-order model can be reduced using an efficient algorithm for rational L2 approximation. Two numerical examples are worked out to show the performance of the suggested technique.
Highlights
Many natura] and artificial systems can profitably be modelled or controlled by means of fractionalorder systems [l], [2], [12]. lndeed, there is already a vast and qua]jfied literature on this subject [7], [3], [15], [14] so that further motivation for their study is superfluous
From this model it is easy to derive a block-companion integer-order state-space representation that is suited to simulation (Section N). The dimension of this model increases with its accuracy, wruch can make the design of a controller difficult. To reduce this dimension without diminishing appreciably the response accuracy, resort can be made to the efficient algorithm for L2 model reduction suggested in [] (Section V)
Two numerical examples taken from the literature confirm the validity of such an approach (Section VI)
Summary
Many natura] and artificial systems can profitably be modelled or controlled by means of fractionalorder systems [l], [2], [12]. lndeed, there is already a vast and qua]jfied literature on this subject [7], [3], [15], [14] so that further motivation for their study is superfluous. Starting from the original state-space form of the original fractional-order system (Section II) and applying the integer--0rder approximation of a fractional operator suggested in [20], a matrix fraction description of the integer-order approximating model is obtained (Section III). From this model it is easy to derive a block-companion integer-order state-space representation that is suited to simulation (Section N). The dimension of this model increases with its accuracy, wruch can make the design of a controller difficult To reduce this dimension without diminishing appreciably the response accuracy, resort can be made to the efficient algorithm for L2 model reduction suggested in [] (Section V). Two numerical examples taken from the literature confirm the validity of such an approach (Section VI)
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