tailieunhanh - Sabatier Agrawal Machado Advances in Fractional Calculus Episode 10

Tham khảo tài liệu 'sabatier agrawal machado advances in fractional calculus episode 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | COMPLEX ORDER-DISTRIBUTIONS USING CONJUGATED ORDER DIFFERINTEGRALS Jay L. Adams1 Tom T. Hartley2 and Carl F. Lorenzo3 1 Department of Electrical and Computer Engineering The University of Akron Akron OH 44325-3904 E-mail JLA36@ 2 Department of Electrical and Computer Engineering The University of Akron Akron OH 44325-3904 E-mail TomHartley@ 3 NASA Glenn Research Center Cleveland oH 44135 E-mail Abstract This paper develops the concept of the complex order-distribution. This is a continuum of fractional differintegrals of complex order. Two types of complex order-distributions are considered uniformly distributed and Gaussian distributed. It is shown that these basis distributions can be summed to approximate other complex order-distributions. Conjugated differintegrals introduced in this paper are an essential analytical tool applied in this development. Con-jugated-order differintegrals are fractional derivatives whose orders are complex conjugates. These conjugate-order differintegrals allow the use of complex-order differintegrals while still resulting in real time-responses and real transfer-functions. An example is presented to demonstrate the complex order-distribution concept. This work enables the generalization of fractional system identification to allow the search for complex order-derivatives that may better describe realtime behaviors. Keywords Fractional-order systems fractional calculus conjugated-order differintegrals complex order-distributions. complex-order differintegrals. 1 Introduction This paper uses the concept of conjugate-order differintegrals for the development of complex order-distributions. Order distributions have been introduced by Hartley and Lorenzo 1 2 as the continuum extension of collections of fractional-order operators. In that discussion the distribution of order was required implicitly to be real but it was able to include any real number. This concept of an order-distribution is