Simulation studies of fractional-order control systems

Abstract

Today, many systems are characterized by a non-integer order model based on fractional calculus. Fractional calculus has been intensively used to generalize many different types of control methods and strategies to solve certain problems faced by classical control, such as overshoot and resonance. In this project, we will discuss the fundamental concepts of fractional calculus and fractional-order control systems. A mathematical literature review on fractional calculus will be addressed first. Several elementary special functions that are essential in fractional calculus will be introduced. Next, the definitions of fractional calculus that are used for control systems will be described, followed by the explanation of Laplace transform and its applications on fractional calculus. In the second part, the fundamental concepts of fractional-order control system will be addressed. The analysis and evaluations of fractional-order transfer functions will be explained in detail. In addition, the type of plant model that are used in fractional-order control systems will be stated explicitly. Finally, we will move on to analyze the fractional-order PID controllers. The integer-order PID controllers will be addressed before the fractional-order PID controllers. Next, we will design and model the various types of fractional-order control systems, so that evaluation of the system’s output performances due to a unit-step input can be made. Based on these results, we will derive a conclusion on the effectiveness of fractional-order PID controllers in control systems. Throughout this project, we will be using the MATLAB/Simulink software to solve fractional calculus problems, as well as to perform an in-depth analysis of integer and fractional-order control systems.