• IMEN SAIDI Ecole Nationale d'ingénieurs de Tunis Author
  • NAHLA TOUATI Université de Tunis, Ecole Nationale Supérieure d’Ingénieurs de Tunis, Tunisia Author




Nonlinear underactuated system, Iterative learning control algorithm, Stability, Tracking, Maximum absolute of errors


This paper proposed the iterative learning control for nonlinear underactuated systems. To improve the convergence speed of iterative learning control for such systems and reduce the fluctuation of the system error, an exponential variable gain D-type closed-loop iterative learning control algorithm was chosen. MATLAB simulation analysis was then performed on an underactuated, nonlinear, and unstable system, namely the inertia wheel inverted pendulum. The simulation results show that the algorithm is effective. Good tracking performance was achieved. The system converges to stable limit cycles after a few iterations, ensuring smooth errors and satisfactory convergence speed.


H. S. Ahn, Y. Chen, K. L. Moore, Iterative learning control: brief survey and categorization, IEEE Transactions on Systems, Man and Cybernetics, Part C (Applications and Reviews), 37, 6, pp. 1099–1121 (2007).

S. Arimoto, S. Kawamura, F. Miyazaki, Bettering operation of robotics by leaning, Journal of Robotic systems, 1, 2, pp. 123–140 (1984).

D. Meng, K. L. Moore, Robust iterative learning control for non-repetitive uncertain systems, IEEE Transactions on Automatic Control, 62, 2, pp. 907–913 (2017).

Y. Li, A. An, J. Wang, H. Zhang, Iterative learning control of exponential variable gain based on initial state learning for upper limb rehabilitation robot, Chinese Automation Congress, 11, 22, pp. 4947–4952 (2019).

F. Bouakrif, Iterative Learning Control for Strictly Unknown Nonlinear Systems Subject to External Disturbances, International Journal of Control, Automation, and Systems, 9, 4, pp. 642-648 (2011).

N. Ali, W. Alam, M. Pervaiz, J. Iqbal, Nonlinear adaptive backstepping control of permanent magnet synchronous motor, Rev. Roum. Sci. Techn.– Électrotechn. et Énerg., 66, 1, pp. 9–14, (2021).

R. Arun, R. Muniraj, M. S.W. Iruthayarajan, Performance analysis of proportional integral derivative controller with delayed external reset and proportional integral derivative controller for time delay process, Rev. Roum. Sci. Techn.– Électrotechn. et Énerg., 66, 4, pp. 267–273, (2021).

R. Muniraj, M. Willjuice Iruthayarajan, R. Arun, T. Sivakumar, Parameter optimization of multi objective robust proportional integral derivative controller with filter using multi objective evolutionary algorithms, Rev. Roum. Sci. Techn. – Électrotechn. et Énerg., 64, 3, p. 259-265, (2019)

Y. Q. Chen, K. L. Moore, J. Yu, T. Zhang, Iterative Learning Control and Repetitive Control in Hard Disk Drive Industry—a Tutorial, International Journal of Adaptive Control and Signal Processing, 22, 4, pp. 325–343 (2008).

F. Bouakrif, Reference model iterative learning control for linear systems, 18th Mediterranean Conference on Control and Automation, Marrakech, 2010.

I. Saidi, N. Touati, Nonlinear Predictive Control for Trajectory Tracking of Underactuated Mechanical Systems, Przegląd Elektrotechniczny, 97, 6, pp. 30-33 (2021).

I. Bejaoui, I. Saidi, D. Soudani, New Internal Model Controller design for discrete over-actuated multivariable system,” 4th International Conference on Control Engineering & Information Technology, Tunisia, 2016.

Y. Hu, B. Zuo, J. Li, Fast Algorithm of Open-Closed Loop PD-type Iterative Learning Control for DC motor, IEEE 2006 6th World Congress on Intelligent Control and Automation, China, 2006.

R. Longman, Iterative Learning Control and Repetitive Control for Engineering Practice, Automation and Systems, 73, 10, pp. 930–954 (2012).

D. Ke, Q. Ai, W. Meng, C. Zhang, Q. Liu, Fuzzy PD-type Iterative Learning Control of a Single Pneumatic Muscle Actuator, Intelligent Robotics and Applications, 7, 16, pp. 812–822 (2017).

Y. Sun, Z. A. Li, Open-loop D-type Iterative Learning Control for a Class of Nonlinear systems with Arbitrary Initial Value, Journal of System Simulation, 20, 24, pp. 6767-6770 (2008).

Q. Jia, R. Ma , C. Zhang, R. Varatharajoo, Spacecraft Attitude Fault-tolerant Stabilization Against Loss of Actuator Effectiveness: A Novel Iterative Learning Sliding Mode Approach, Advances in Space Research, 72, 2, pp. 529-540 (2023).

S. Lu, S. Jingzhuo, Adaptive PI control of ultrasonic motor using iterative learning methods, ISA Transactions, In press, 2023.

Y. Qiongxia, H. Zhongsheng, X. Jian-Xin, D-Type ILC Based Dynamic Modeling and Norm Optimal ILC for High-Speed Trains, IEEE Transactions on Control Systems Technology, 26, 2, pp. 652 – 663 (2017).

M. X. Sun, B. J. Huang, X. Z. Zhang, PD-type iterative learning control for a class of nonlinear systems, Acta Automatica Sinica, 4, 5, pp. 711-714 (1998).

A. Norouzi, C. R. Koch, Integration of PD-type Iterative Learning Control with Adaptive Sliding Mode Control, 21st IFAC World Congress, 53, 2, pp. 6213–6218 (2020).

Y. Li, A. An, J. Wang, H. Zhang, Iterative Learning Control of Exponential Variable Gain Based on Initial State Learning for Upper Limb Rehabilitation Robot, Chinese Automation Congress , 2019.

R.O. Saber, Global Stabilization of a Flat Underactuated System: the Inertia Wheel Pendulum, Proceedings of the 40th IEEE Conference on Decision and Control, pp. 306–308 (2001).

S. Andary, A. Chemori, S. Krut, Control of the Underactuated Inertia Wheel Inverted Pendulum for Stable Limit Cycle Generation, Advanced Robotics, 3, 15, 1999–2014 (2009).

N. H. Manai, I. Saidi, D. Soudani, Predictive control of an underactuated System, Proceedings of the 2nd International Conference on Advanced Systems and electric Technologie, Hammamet, Tunisia, pp. 90 -95 2019.

I. Saidi, N. Touati, Sliding Mode Control to Stabilization of Nonlinear Underactuated Mechanical Systems, Przegląd Elektrotechniczny, 97, 7, pp. 106-109 (2021).

O. Khan, M. Pervaiz, E. Ahmad, J. Iqbal, On the derivation of novel model and sophisticated control of flexible joint manipulator, Rev. Roum. Sci. Techn. – Electrotechn. et Energ., 62, 1, pp. 103–108 (2017).

A. Hfaiedh, A. Chemori, A. Abdelkrim, Stabilization of the Inertia Wheel Inverted Pendulum by Advanced IDA-PBC Based Controllers: Comparative Study and Real-Time Experiments, 17th International Multi-Conference on Systems, Signals & Devices, Tunisia, 2020






Automatique et ordinateurs | Automation and Computer Sciences

How to Cite