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Iterative Learning Control (ILC) is a well-known method for control of systems performing repetitive jobs with high precision. This paper presents Constrained Output ILC (COILC) for non-linear state space constrained systems. In the existing literature there is no general solution for applying ILC to such systems. This novel method is based on the Bounded Error Algorithm (BEA) and resolves the transient growth error problem, which is a major obstacle in applying ILC to non-linear systems. Another advantage of COILC is that this method can be applied to constrained output systems. Unlike other ILC methods the COILC method employs an algorithm that stops the iteration before the occurrence of a violation in any of the state space constraints. This way COILC resolves both the hard constraints in the non-linear state space and the transient growth problem. The convergence of the proposed numerical procedure is proved in this paper. The performance of the method is evaluated through a computer simulation and the obtained results are compared to the BEA method for controlling non-linear systems. The numerical experiments demonstrate that COILC is more computationally effective and provides better overall performance. The robustness and convergence of the method make it suitable for solving constrained state space problems of non-linear systems in robotics.
Czasopismo
Rocznik
Tom
Strony
157--176
Opis fizyczny
Bibliogr. 29 poz., tab., wykr., wzory
Twórcy
autor
- Faculty of Mathematics and Informatics, Sofia University, 1164 Sofia, 5 James Bourchier Blvd., Bulgaria
autor
- Faculty of Mathematics and Informatics, Sofia University, 1164 Sofia, 5 James Bourchier Blvd., Bulgaria.
autor
- Faculty of Mathematics and Informatics, Sofia University, 1164 Sofia, 5 James Bourchier Blvd., Bulgaria.
Bibliografia
- [1] M. Uchiyama: Formulation of high-speed motion pattern of a mechanical arm by trial, Trans. SICE (Soc. Instrum. Contr. Eng.), 14(6) (1978), 706–712.
- [2] G. Murray: Learning control of actuators in control systems, United States Patent US3555252 A, 1971.
- [3] S. Arimoto, S. Kawamura and F. Miyazaki: Iterative learning control for robot systems, Proceedings of IECON, Tokyo, Japan, 1984.
- [4] S. Arimoto, S. Kawamura and F. Miyazaki: Bettering operation of robots by learning, Journal of Robotic Systems, 1(2) (1984), 123–140.
- [5] G. Casalino and G. Bartolini: A learning procedure for the control of movements of robotic manipulators, IASTED Symposium on Robotics and Automation, Amsterdam, The Netherlands, (1984), 108–111.
- [6] J. Craig: Adaptive control of manipulators through repeated trials, Proc. of ACC, San Diego, CA, (1984).
- [7] K.L. Moore: Iterative learning control – an expository overview., Applied and Computational Control, Signals, and Circuits, Birkhauser Boston, (1999), 151–214.
- [8] J.-X. Xu and Y. Tan: Linear and Nonlinear Iterative Learning Control, Springer-Verlag Berlin Heidelberg, 2003.
- [9] M. Norrlof: Iterative Learning Control: Analysis, Design, and Experiments, Linkoping Studies in Science and Technology, PhD Dissertations, Linkoping, Sweden, 2000.
- [10] R. Longman: Iterative learning control and repetitive control for engineering practice, International Journal of Control, 73(10) (2000), 930–954.
- [11] D. Bristow and J. Singler: Analysis of Transient Growth in Iterative Learning Control Using Pseudospectra, Symposium on Learning Control, Shanghai, China, 2009.
- [12] D. Heizinger, B. Fenwick, B. Paden and F. Miyazaki: Robust Learning Control, Proc. of 28th Conference on Decision and Control, Tampa, FL, (1989), 436–440.
- [13] R. Longman and Y. Huang: The Phenomenon of Apparent Convergence Followed by Divergence in Learning and Repetitive Control, Intelligent Automation and Soft Computing, 8(2) (2002), 107–128.
- [14] K. Yovchev, K. Delchev and E. Krastev: Computer Simulation of Bounded Error Algorithm for Iterative Learning Control, Advances in Robot Design and Intelligent Control. RAAD 2016. Advances in Intelligent Systems and Computing, 540, A. Rodić and T. Borangiu, Eds., Springer, Cham, 2017.
- [15] D. A. Bristow and J.R. Singler: Robustness Analysis of Slow Learning in Iterative Learning Control Systems, 2011 American Control Conference on O’Farrell Street, San Francisco, CA, USA, (2011).
- [16] K.-H. Park and Z. Bien: A Study On Iterative Learning Control with Adjustment of Learning Interval for Monotone Convergence in the Sense of Sup-Norm, Asian Journal of Control, 4(1), (2002), 111–118.
- [17] K. Delchev: Iterative learning control for robotic manipulators: Abounded-error algorithm. International Journal of Adaptive Control and Signal Processing, 28(12), (2013).
- [18] K. Delchev: Iterative Learning Control for Nonlinear Systems: A Bounded-Error Algorithm, Asian Journal of Control, 15(3) (2013), 1–8.
- [19] S. Mishra, U. Topcu and M. Tomizuka: Optimization-based constrained iterative learning control, IEEE Trans. Control Syst. Technol., 19(6) (2011), 1613–1621.
- [20] B. Chu and D. Owens: Iterative learning control for constrained linear systems using projection method, International Workshop on Human Adaptive Mechatronics, Loughborough, GB, (2010).
- [21] Y. Tan and J. X. Xu: On iterative learning control for nonlinear time-varying systems with input saturation, Symposium on Learning Control at IEEE CDC 2009, Shanghai, (2009).
- [22] A. Schöllig and R. D’Andrea: Optimization-Based Iterative Learning Control for Trajectory Tracking, European Control Conference, Budapest, Hungary, (2009), 1505–1510.
- [23] K. Yovchev, K. Delchev and E. Krastev: State Space Constrained Iterative Learning Control for Robotic Manipulators, Asian Journal of Control, 20(1) (2018), 1–6.
- [24] G. Oriolo: An Iterative Learning Controller for Nonholonomic Mobile Robots, The International Journal of Robotics Research, 17(9) (1998), 954–970.
- [25] M. Guth, T. Seel and J. Raisch: Iterative Learning Control with variable pass length applied to trajectory tracking on a crane with output constraints, Proc. of 52nd IEEE Conf. on Decision and Control, Florence, Italy, (2013).
- [26] G. Sebastian, Y. Tan, D. Oetomo and I. Mareels: Feedback-based iterative learning design and synthesis with output constraints for robotic manipulators, IEEE Control Systems Letters, 2(3) (2018), 513–518.
- [27] M. R. Zamani, Z. Rahmani and B. Rezaie: A novel model predictive control strategy for constrained and unconstrained systems in presence of disturbance, IMA Journal of Mathematical Control and Information, (2019).
- [28] K. Yovchev: Finding the Optimal Parameters for Robotic Manipulator Applications of the Bounded Error Algorithm for Iterative Learning Control, Journal of Theoretical and Applied Mechanics, 47(4) (2017), 3–11.
- [29] D. Heizinger, B. Fenwick, B. Paden and F. Miyazaki: Stability of Learning Control with Disturbances and Uncertain Initial Condition, IEEE Trans. Autom. Control, 37(1) (1992), 110–114.
Uwagi
EN
1. The support by the Fund for Scientific Research at Sofia University “St. Kliment Ohridski” under grant 80-10-7/2019, is acknowledged.
PL
2. Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
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Bibliografia
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