Abstract
Flight controllers for micro-air UAVs are generally designed using proportional-integral-derivative (PID) methods, where the tuning of gains is difficult and time-consuming, and performance is not guaranteed. In this paper, we develop a rigorous method based on the sliding mode analysis and nonlinear backstepping to design a PID controller with guaranteed performance. This technique provides the structure and gains for the PID controller, such that a robust and fast response of the UAV (unmanned aerial vehicle) for trajectory tracking is achieved. First, the second-order sliding variable errors are used in a rigorous nonlinear backstepping design to obtain guaranteed performance for the nonlinear UAV dynamics. Then, using a small angle approximation and rigorous geometric manipulations, this nonlinear design is converted into a PID controller whose structure is naturally determined through the backstepping procedure. PID gains that guarantee robust UAV performance are finally computed from the sliding mode gains and from stabilizing gains for tracking error dynamics. We prove that the desired Euler angles of the inner attitude controller loop are related to the dynamics of the outer backstepping tracker loop by inverse kinematics, which provides a seamless connection with existing built-in UAV attitude controllers. We implement the proposed method on actual UAV, and experimental flight tests prove the validity of these algorithms. It is seen that our PID design procedure yields tighter UAV performance than an existing popular PID control technique.
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The author Mr. Kartal thanks Turkish Aerospace for the scholarship granted.
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Yusuf KARTAL studied Electrical & Electronics Engineering at Bilkent University (Turkey) obtaining the B.Sc. degree in 2015. He is a Master in Science student at Aerospace Engineering Department in University of Texas at Arlington. His main interests include algorithms for multi-robot systems, nonlinear control, optimal path planning, unmanned aerial vehicles, machine learning and distributed control.
Patrik KOLARIC has received his B.Sc. and M.Sc. degrees at Faculty of Electrical Engineering and Computing, Zagreb, Croatiain 2014 and 2016, respectively. He is pursuing the Ph.D. under Dr. Frank L. Lewis’s supervision at University of Texas at Arlington. He is research assistant in Autonomous System Lab at UTA Research Institute where he works on topics related to robotics. His areas of interests include reinforcement learning, machine learning, robotics and control.
Victor G. LOPEZ has received the B.Sc. degree from the Universidad Autonoma de Campeche, Mexico, in 2010 and the M.Sc. degree from the Research and Advanced Studies Center (CINVESTAV), Mexico, in 2013. He is currently a Ph.D. student at the University of Texas at Arlington, TX, U.S.A. His research interests include cyber-physical systems, game theory, distributed control, reinforcement learning and robust control.
Atilla DOGAN is an associate professor in the Department of Mechanical and Aerospace Engineering at University of Texas at Arlington (UTA) and co-director of the AVL Lab (Autonomous Vehicle Lab). He has received his Ph.D. from Aerospace Engineering Department of the University of Michigan at Ann Arbor in 2000. Before joining UTA, he worked for Ford Motor Company as a product development engineer in the Department of Transmission Electronics for more than two years. He was a summer faculty research fellow at the Air Force Research Lab in Wright-Patterson Air Force Base in Summers 2007 to 2010. His current research work includes path planning and dynamic target tracking in adversarial environments, modeling, simulation and control of multiple aerial vehicles, applied to formation flight and aerial refueling.
Frank LEWIS Member, National Academy of Inventors. Fellow IEEE, Fellow IFAC, Fellow AAAS, Fellow U.K. Institute of Measurement & Control, PE Texas, U.K. Chartered Engineer. UTA Distinguished Scholar Professor, UTA Distinguished Teaching Professor, and Moncrief-O’Donnell Chair at the University of Texas at Arlington Research Institute. China Liaoning Friendship Award. He obtained the B.Sc. in Physics/EE and the MSEE at Rice University, the M.Sc. in Aeronautical Engineering from Univ. W. Florida, and the Ph.D. at Ga. Tech. He works in feedback control, intelligent systems, cooperative control systems, and nonlinear systems. He is author of 7 U.S. patents, numerous journal special issues, 374 journal papers, and 20 books, including Optimal Control, Aircraft Control, Optimal Estimation, and Robot Manipulator Control which are used as university textbooks worldwide. He received the Fulbright Research Award, NSF Research Initiation Grant, ASEE Terman Award, Int. Neural Network Soc. Gabor Award, U.K. Inst Measurement & Control Honeywell Field Engineering Medal, IEEE Computational Intelligence Society Neural Networks Pioneer Award, AIAA Intelligent Systems Award. Received Outstanding Service Award from Dallas IEEE Section, selected as Engineer of the year by Ft. Worth IEEE Section. Was listed in Ft. Worth Business Press Top 200 Leaders in Manufacturing. Texas Regents Outstanding Teaching Award 2013. He is Distinguished Visiting Professor at Nanjing University of Science & Technology and Project 111 Professor at Northeastern University in Shenyang, China. Founding Member of the Board of Governors of the Mediterranean Control Association.
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Kartal, Y., Kolaric, P., Lopez, V. et al. Backstepping approach for design of PID controller with guaranteed performance for micro-air UAV. Control Theory Technol. 18, 19–33 (2020). https://doi.org/10.1007/s11768-020-9145-y
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DOI: https://doi.org/10.1007/s11768-020-9145-y