A New Method for Controlling Fractional Linear Systems

Abstract

The study of fractional linear time-invariant (LTI) systems has been an area of active research over the past thirty years. Results indicate that such systems are becoming important in the representation of certain types of dynamical behavior in biology and engineering. Several methods have been developed for the representation, identification, and control of fractional LTI systems. The primary purpose of this paper is to introduce a new approach to their control. Its principal contribution is the transformation of a fractional LTI system into one without fractional terms (standard LTI system) using feedback and feedforward compensation. While the former may be quite difficult to control, tools widely available in linear systems theory may be used to control the latter. Transformation of a fractional system into a standard one requires compensators with fractional transfer functions. It is shown, using research results from the past two decades, that such functions can be realized using hardware and software subsystems. The authors demonstrate, using an example, that better control performance is possible with the new method when compared to current ones that are most common in the research literature. Robustness in the presence of noise and model uncertainties is also studied for the new method and currently available ones. Simulation results presented illustrate improvements achievable in control robustness with the new method.

Keywords

• fractional order derivative
• standard and fractional systems
• linear time-invariant
• feedback and feedforward compensation
• transfer function
• control performance and robustness