Abstract
In this paper, we propose a new method for auto-tuning an aircraft maneuvering controller using black-box optimization. Assuming that we do not have a deep understanding of the complex nature and behavior of the controlled aircraft model, we propose a data-efficient Proportional Integral Derivatives (PID) tuning method with explorations on the aircraft responses from the sampled control inputs. More specifically, we utilize Bayesian optimization (BO) with Gaussian process (GP) to create a black-box model of the aircraft response corresponding to the sampled control parameters. We tested the feasibility and performance of the proposed data-driven tuning method with a six degrees of freedom (6DoF) nonlinear aircraft model. We also experimented with various GP kernel structures and hyperparameters to find the most suitable kernel function. Compared to the conventional tuning method, our proposed method shows shorter flight time and smaller deviations from the waypoints. The proposed data-driven tuning method can be an alternative to traditional model-based or model-free tuning methods, especially when the objective functions are expensive to evaluate and only a small number of experiments are available.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. L. Stevens, F. L. Lewis, and E. N. Johnson, Aircraft Control and Simulation: Dynamics, Controls Design, and Autonomous Systems, John Wiley & Sons, 2015.
K. J. Åström and T. Hägglund, PID Controllers: Theory, Design, and Tuning, vol. 2. Research Triangle Park, NC, Instrument Society of America, 1995.
K. H. Ang, G. Chong, and Y. Li, “PID control system analysis, design, and technology,” IEEE Transactions on Control Systems Technology, vol. 13, no. 4, pp. 559–576, 2005.
N. J. Killingsworth and M. Krstić, “PID tuning using extremum seeking: online, model-free performance optimization,” IEEE Control Systems, vol. 26, no. 1, pp. 70–79, 2006.
P. J. Fleming and R. C. Purshouse, “Evolutionary algorithms in control systems engineering: A survey,” Control Engineering Practice, vol. 10, no. 11, pp. 1223–1241, 2002.
Z. S. Hou and Z. Wang, “From model-based control to data-driven control: Survey, classification and perspective,” Information Sciences, vol. 235, pp. 3–35, 2013.
D. Kim, H. S. Oh, and I. C. Moon, “Black-box modeling for aircraft maneuver control with Bayesian optimization,” International Journal of Control, Automation, and Systems, vol. 17, no. 6, pp. 1558–1568, 2019.
H. Hjalmarsson, “Iterative feedback tuning-an overview,” International Journal of Adaptive Control and Signal Processing, vol. 16, no. 5, pp. 373–395, 2002.
M. M. Polycarpou, “Stable adaptive neural control scheme for nonlinear systems,” IEEE Transactions on Automatic Control, vol. 41, no. 3, pp. 447–451, 1996.
S. Schaal and C. Atkeson, “Learning control in robotics,” IEEE Robotics Automation Magazine, vol. 17, no. 2, pp. 20–29, 2010.
J. Kober, J. A. Bagnell, and J. Peters, “Reinforcement learning in robotics: A survey,” The International Journal of Robotics Researce, vol. 32, no. 11, pp. 1238–1274, 2013.
A. Marco, P. Hennig, J. Bohg, S. Schaal, and S. Trimpe, “Automatic LQR tuning based on Gaussian process global optimization,” Proc. of IEEE International Conference on Robotics and Automation (ICRA), IEEE, pp. 270–277, May 2016.
F. Berkenkamp, A. P. Schoellig, and A. Krause, “Safe controller optimization for quadrotors with Gaussian processes,” Proc. of IEEE International Conference on Robotics and Automation (ICRA), IEEE, pp. 491–496, May 2016.
R. Calandra, A. Seyfarth, J. Peters, and M. P. Deisenroth, “An experimental comparison of Bayesian optimization for bipedal locomotion,” Proc. of IEEE International Conference on Robotics and Automation (ICRA), pp. 1951–1958, 2014.
M. Neumann-Brosig, A. Marco, D. Schwarzmann, and S. Trimpe, “Data-efficient auto-tuning with Bayesian optimization: An industrial control study,” IEEE Transactions on Control Systems Technology, vol. 28, no. 3, pp. 730–740, 2020.
C. E. Rasmussen and C. K. Williams, Gaussian Processes for Machine Learning, vol. 1, MIT Press, Cambridge, 2006.
M. B. Christopher, Pattern Recognition and Machine Learning, Springer-Verlag, New York, 2016.
E. Snelson and Z. Ghahramani, “Local and global sparse Gaussian process approximations,” Artificial Intelligence and Statistics, pp. 524–531, 2007.
E. Brochu, V. M. Cora, and N. De Freitas, “A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning,” arXiv preprint, arXiv:1012.2599, 2010.
D. R. Jones, “A taxonomy of global optimization methods based on response surfaces,” Journal of Global Optimization, vol. 21, no. 4, pp. 345–383, 2001.
J. Azimi, A. Fern, and X. Z. Fern, “Batch Bayesian optimization via simulation matching,” Advances in Neural Information Processing Systems, pp. 109–117, 2010.
H. J. Kushner, “A new method of locating the maximum point of an arbitrary multipeak curve in the presence of noise,” Journal of Basic Engineering, vol. 86, no. 1, pp. 97–106, 1964.
I. Rhee, S. Park, and C. K. Ryoo, “A tight path following algorithm of an UAS based on PID control,” Proceedings of SICE Annual Conference, IEEE, pp. 1270–1273, 2010.
K. B. Judd and T. W. Mclain, “Spline based path planning for unmanned air vehicles,” Proc. of AIAA Guidance, Navigation, and Control Conference and Exhibit, p. 4238, 2001.
D. Jung and P. Tsiotras, “On-line path generation for small unmanned aerial vehicles using B-spline path templates,” Proc. of AIAA Guidance, Navigation, and Control Conference and Exhibit, IEEE, p. 7135, 2008.
S. Park, J. Deyst, and J. P. How, “A new nonlinear guidance logic for trajectory tracking,” Proc. of AIAA Guidance, Navigation, and Control Conference and Exhibit, p. 4900, 2004.
S. Park, J. Deyst, and J. P. How, “Performance and Lyapunov stability of a nonlinear path following guidance method,” Journal of Guidance, Control, and Dynamics, vol. 30, no. 6, pp. 1718–1728, 2007.
A. Elsayed, A. Hafez, A. N. Ouda, H. E. H. Ahmed, and H. M. Abd-Elkader, “Design of longitudinal motion controller of a small unmanned aerial vehicle,” International Journal of Intelligent Systems and Applications, vol. 7, no. 10, p. 37, 2015.
S. R. B. dos Santos and N. M. F. de Oliveira, “Longitudinal autopilot controllers test platform hardware in the loop,” Proc. of Systems Conference (SysCon), IEEE, pp. 379–386, April 2011.
S. H. Choi, J. H. Lee, S. H. Lee, H. D. Yoo, J. Koo, and T. G. Kim, “6 DoF aircraft simulation model capable of handling maneuver events (WIP),” Proc. of the Summer Computer Simulation Conference (SCSC), Society for Computer Simulation International, p. 54, July 2016.
Author information
Authors and Affiliations
Corresponding author
Additional information
Dohyung Kim is a principal researcher in the Modeling and Simulation Team at ADD. He received his M.S. degree in electrical engineering and a Ph.D. degree in industrial and systems engineering from KAIST, in 2005 and 2019, respectively. His research interests include modeling & simulation, machine learning, and their application to the defense system.
Hyun-Shik Oh is a principal researcher and leader of the Modeling and Simulation Team at ADD. He received his M.S. degree in aeronautical engineering from Korea Aviation University in 1996, and a Ph.D. degree in aerospace engineering from KAIST in 2017. His research interests include guidance and control of aerospace systems and engagement simulation of weapon systems.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Kim, D., Oh, HS. Black-box Optimization of PID Controllers for Aircraft Maneuvering Control. Int. J. Control Autom. Syst. 20, 703–714 (2022). https://doi.org/10.1007/s12555-020-0915-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-020-0915-6