Robust Adaptive Control for Fractional-Order Systems with Disturbance and Saturation

Chapter 3Fractional-Order PID Controller and Fractional-Order Disturbance Observer

3.1 Problem Statement

Over the past decades, some important results on fractional-order controllers have been proposed for various systems [1] [192–194]. Podlubny [1] introduced the concept of a fractional-order controller, including a fractional-order integrator and a fractional-order differentiator. A well-known fractional-order controller was presented by Oustaloup et al. [192]. Li et al. [193] proposed a novel fractional-order controller, based on Lyapunov stability theory; fractional-order chaotic and hyperchaotic systems were controlled by the proposed fractional-order controller. A novel chaotic system without equilibrium was proposed, and a fractional-order controller was designed to control the chaotic system without equilibrium, by Shao and Chen [194]. Fractional-order controllers are effective in controlled systems, as has been proved in the mentioned works. Furthermore, FODOs have been widely studied for the control of fractional-order systems [169] [195–198]. Shao et al. [169] studied FODO-based adaptive sliding-mode synchronization control for a class of fractional-order chaotic systems with unknown bounded disturbances. A robust adaptive neural control was proposed for a fractional-order rotational mechanical system in the presence of system uncertainties and external disturbances ...