Fractional-Order Control: Theory and Applications in Motion Control

Fractional-order differential equations can be likened to the concept of fraction-order control (FOC). Studies of FOC have been conducted in the 19th century by Liouville, Homgren and Riemann as well as Eular, Lagrange and others. In the fractional-order calculus, the most frequently encountered definitions is called the Grunwald-Letnikov definition. However, one of the most problematic and doubtful points of FOC's application is in respect with frequency domains. Nevertheless, such systems have an infinite dimension and the memorization of past inputs must be realized to realize fractional-order controllers perfectly. FOC's open up a new dimension for control theory and can have different characteristics when expanded into a fractional-order field. FOC systems have the special advantage of providing more flexibility and insight in control design and thus exhibit a clear edge for designing robust control system.