# Under Control: Empowering Disturbance Observer Controllers with the Fourier Transform

 Scientists leverage a powerful mathematical tool to extend the applicability of a popular type of controller Scientists from the National Korea Maritime and Ocean University and Yonsei University, Korea, combine the fuzzy disturbance observer-based control theory with the Fourier transform to design a controller that can handle nonperiodic, nonlinear disturbances. This feature makes their approach suitable for dynamic real-world systems such as drones, which have to deal with nonperiodic disturbances like the wind and changes in air resistance. As modern society progresses, and automated systems become more sophisticated and complex, the importance of designing advanced and reliable controllers skyrockets. Controllers monitor system variables and ensure that processes and machines operate stably within defined limits. Over the last two decades, controllers based on the disturbance observer-based control (DOBC) theory have become increasingly popular. These controllers measure external disturbances affecting the system and compensate them as necessary in order to keep the system stable. However, existing implementations of this theory can only manage periodic disturbances, which greatly limits their applicability―in the real world, disturbances can take many forms and are usually nonperiodic. In a recent study published in IEEE Access, a pair of Korean scientists tackled this problem through an innovative approach: combining the DOBC theory with a powerful mathematical tool called the Fourier transform. Dr Han Sol Kim from the National Korea Maritime and Ocean University explains their reasoning: “The Fourier transform can be used to represent a nonperiodic disturbance as a sum of infinite periodic disturbances. Then, by selecting the most dominant periodic disturbances only, we can design distinct DOBCs that compensate for each one.” To achieve this, the scientists began with the Takagi-Sugeno fuzzy model, an approach that represents complex nonlinear systems―which describe many real-world dynamic systems―as linear subsystems. By combining a slightly modified version of this fuzzy modelling method with the DOBC theory and applying the Fourier transform, they managed to design a controller with a better response compared with other state-of-the-art methods, as shown through simulations. This controller design could be particularly useful for modern technological systems such as unmanned aerial vehicles (UAVs), commonly known as drones. The performance of UAVs largely depends on how well they can automatically handle external disturbances such as the wind and changes in air resistance. In this regard, Dr Kim remarks: “Without properly compensating for disturbances, UAVs can cause accidents, harming people and destroying property. I believe that our method will be an efficient solution for UAV systems because it can guarantee robust performance against disturbances.” Their approach is purely theoretical so far, but they plan on implementing it in a real hardware platform in the near future. If all goes well, we might just have a new effective method for keeping our machines under control. Reference Authors: Sounghwan Hwang1 and Han Sol Kim2 Title of original paper: Extended Disturbance Observer-Based Integral Sliding Mode Control for Nonlinear System via T？S Fuzzy Model Journal: IEEE Access DOI: 10.1109/ACCESS.2020.3004241 Affiliations: 1Department of Electrical and Electronic Engineering, Yonsei University 2Department of Control and Automation Engineering, National Korea Maritime and Ocean University *Corresponding author’s email: [email protected] About the authors Han Sol Kim received his B.S. degree in Electronic and Computer Engineering from Hanyang University, South Korea, in 2011 and his M.S. and Ph.D. degrees in Electrical and Electronic Engineering from Yonsei University, Korea, in 2012 and 2018, respectively. He worked with Samsung Korea from 2018 to 2019 as a Senior Engineer. Since 2019, he has been with the Department of Control and Automation Engineering at the National Korea Maritime and Ocean University, where he is currently an Assistant Professor. His current research interests include intelligent robots, intelligent control, and unmanned aerial vehicles.   Sounghwan Hwang received his B.S. degree from the Division of Robotics, Kwangwoon University, South Korea, in 2017, and his M.S. degree in Electrical and Electronic Engineering from Yonsei University, South Korea, in 2019. His current research interests include control theory, dynamic systems, nonlinear system control, model predictive control, and data-driven approaches for dynamic system analysis.