Fractional Order Calculus and Its Applications in Mechatronic System Controls Organizers

Abstract

The purpose of this tutorial workshop is to introduce the fractional calculus and its applications in controller designs. Fractional order calculus, or integration and differentiation of an arbitrary order or fractional order, is a new tools that extends the descriptive power of the conventional calculus. The tools of fractional calculus support mathematical models that in many cases more accurately describe the dynamic response of actual systems in electrical, mechanical, and automatic control applications etc. The theoretical and practical interest of these fractional order operators is nowadays well established, and its applicability to science and engineering can be considered as emerging new topics. The need to digitally compute the fractional order derivative and integral arises frequently in many fields especially in automatic control and digital signal processing. Fractional order proportional-integral-derivative (PID) controllers are based on the fractional order calculus where the derivative or integral can be of a non-integer order. Due to the extra tuning knobs, it is expected that better control performance can be achieved if the fractional order PID controller is used. Fractional calculus has much to offer science and engineering by providing not only new mathematical tools, but more importantly, its application suggests new insights into the system dynamics as well as controls.