This book explores the design and analysis of fractional-order and active disturbance rejection control, examining both the theoretical foundations and their practical applications. It covers fractional-order Proportional-Integral-Derivative (PID) control, fractional-order Active Disturbance Rejection (ADR) control, and the combined fractional-order PID-ADR control. The book begins with an analysis of the three-parameter fractional-order PID controller, demonstrating its application to the Permanent Magnet Synchronous Motor (PMSM) speed servo system, due to its comprehensive inclusion of proportional, integral, and differential elements. It then delves into Active Disturbance Rejection Control and Periodic Disturbance Compensation, comparing the performance of each controller based on various parameters. This comparison enables readers to critically evaluate the advantages and limitations of each approach before implementation. Offering a thorough guide to fractional-order and active disturbance rejection control, the book also includes numerical methods for assessing and developing these systems. The book will be of particular interest to professionals working with numerical methods, fractional-order systems and control, PID controller, active disturbance rejection, control design and production, and is especially relevant to those in mechanical, industrial, and electrical engineering.