High Gain Observer Based Backstepping Control Design for Nonlinear Single-Axis Driven Systems

(1) Rawnaq A. Mahmod Mail (University of Technology-Iraq, Iraq)
(2) Russul A. Kadhima Mail (University of Technology-Iraq, Iraq)
(3) * Mohanad Nawfal Mail (University of Technology-Iraq, Iraq)
(4) Huthaifa Al-Khazraji Mail (University of Technology-Iraq, Iraq)
*corresponding author

Abstract


In this paper, a backstepping (BS) control design approach is proposed for tracking angular position control problem of a single-input and single-output (SISO) nonlinear single-axis driven system. To implement proposed BS control, the states of the system should be available. To address this problem, a high gain observer (HGO) is introduced for estimating the states. The design parameters of the HGO based BS controller have been optimized using the circle search algorithm (CSA). Compare to other optimization algorithm, the CSA explores the search space in a circular trajectory which can enhance local exploitation. The CSA uses integral of absolute error (IAE) as the performance index for the tuning process. The effectiveness of the proposed controller is demonstrated through simulations. Firstly, for observer evaluation, simulation outcomes indicate that the HGO is capable to estimate the states of the system successfully. However, to evaluate the BS with other nonlinear controllers for tracking control problem, the synergetic (SG) control is proposed. The simulated data results based on IAE index revealed that the BS control has lower IAE value than the SG control where the value of the IAE of the system with the BS control is reduced by 19.4% in compares with the system with the SG control.

Keywords


Backstepping Control; Nonlinear Control; Tracking Control Problem; Single-Axis Driven Systems; High Gain Observer; Circle Search Algorithm; Synergetic Control

   

DOI

https://doi.org/10.31763/ijrcs.v5i3.1984
      

Article metrics

10.31763/ijrcs.v5i3.1984 Abstract views : 34 | PDF views : 30

   

Cite

   

Full Text

Download

References


[1] O. Saleem, M. Rizwan, A. A Zeb, A. H. Ali, and M. A. Saleem, "Online adaptive PID tracking control of an aero-pendulum using PSO-scaled fuzzy gain adjustment mechanism," Soft Computing, vol. 24, pp.10629-10643, 2020, https://doi.org/10.1007/s00500-019-04568-1.

[2] A. K. Hamoudi and L. T. Rasheed, "Design and Implementation of Adaptive Backstepping Control for Position Control of Propeller-Driven Pendulum System," Journal Européen des Systèmes Automatisés, vol. 56, no. 2, pp. 281-289, 2023, https://doi.org/10.18280/jesa.560213.

[3] T. Huba, T. Malatinec, and M. Huba, "Propeller-Pendulum for Nonlinear UAVs Control," International Journal of Online Engineering, vol. 9, no. 1, pp. 42-46, 2013, https://doi.org/10.3991/ijoe.v9i1.2409/.

[4] A. A. Al-Qassar, A. Q. Al-Dujaili, A. F. Hasan, A. J. Humaidi, I. K. Ibraheem and A. T. Azar, "Stabilization of single-axis propeller-powered system for aircraft applications based on optimal adaptive control design," Journal of Engineering Science and Technology (JESTEC), vol. 16, no. 3, pp. 1851-1869, 2021, https://jestec.taylors.edu.my/Vol%2016%20issue%203%20June%202021/16_3_1.pdf.

[5] J. N. Jiménez, M. M. Hernández, D. L. Alabazares, A. Rabhi, C. Pegard and E. T. García, "Identification Based Hammerstein-Wiener Neural Network for Propeller Pendulum PID control," 2024 IEEE International Conference on Engineering Veracruz (ICEV), pp. 1-6, 2024, https://doi.org/10.1109/ICEV63254.2024.10766040.

[6] R. Breganon et al., "Model identification and H? control of an aeropendulum," Journal of applied research and technology, vol. 21, no. 4, pp. 526-534, 2023, https://doi.org/10.22201/icat.24486736e.2023.21.4.1741.

[7] R. Rojas-Galván, J. R. García-Martínez, E. E. Cruz-Miguel, O. A. Barra-Vázquez, L. F. Olmedo-García, and J. Rodríguez-Reséndiz, "Hunting search algorithm-based adaptive fuzzy tracking controller for an aero-pendulum," Technologies, vol. 12, no. 5, p. 63, 2024, https://doi.org/10.3390/technologies12050063.

[8] A. K. Ahmed and H. Al-Khazraji, "Optimal Control Design for Propeller Pendulum Systems Using Gorilla Troops Optimization," Journal Européen des Systèmes Automatisés, vol. 56, no. 4, pp. 575-582, 2023, https://doi.org/10.18280/jesa.560407.

[9] M. H. Tanveer, C. Koduru, R. G. Roy, G. V. Lakhekar and C. Chun, "A Robust Control Technique for Pitch Control of an Aeropendulum," 2023 6th International Conference on Robotics, Control and Automation Engineering (RCAE), pp. 257-261, 2023, https://doi.org/10.1109/RCAE59706.2023.10398789.

[10] K. Charoensuk et al., "The Modelling and Control for Design Aero-Pendulum via Proportional–Integral–Derivative and Integral-Proportional Derivative," 2025 13th International Electrical Engineering Congress (iEECON), pp. 1-6, 2025, https://doi.org/10.1109/iEECON64081.2025.10987886.

[11] H. Al-Khazraji, K. Al-Badri, R. Al-Majeez, and A. J. Humaidi, "Synergetic control design based sparrow search optimization for tracking control of driven-pendulum system," Journal of Robotics and Control (JRC), vol. 5, no. 5, pp. 1549-1556, 2024, https://doi.org/10.18196/jrc.v5i5.22893.

[12] N. Rafiuddin, and Y. U. Khan, "Nonlinear controller design for mechatronic aeropendulum," International Journal of Dynamics and Control, vol. 11, no. 4, pp. 1662-1670, 2023, https://doi.org/10.1007/s40435-022-01080-7.

[13] N. S. Mahmood, A. J. Humaidi, R. S. Al-Azzawi and A. Al-Jodah, "Extended state observer design for uncertainty estimation in electronic throttle valve system," International Review of Applied Sciences and Engineering, vol. 15, no. 1, pp. 107-115, 2024, https://doi.org/10.1556/1848.2023.00662.

[14] H. K. Khalil and L. Praly, " High-gain observers in nonlinear feedback control," International Journal of Robust and Nonlinear Control, vol. 24, no. 6, pp. 993-1015, 2014, https://doi.org/10.1002/rnc.3051.

[15] R. A. Kadhim, M. Q. Kadhim, H. Al-Khazraji, and A. J. Humaidi, "Bee algorithm based control design for two-links robot arm systems," IIUM Engineering Journal, vol. 25, no. 2, pp. 367-380, 2024, https://doi.org/10.31436/iiumej.v25i2.3188.

[16] M. R. Sagita, A. Ma’arif, F. Furizal, C. Rekik, W. Caesarendra and R. Majdoubi, "Motion System of a Four-Wheeled Robot Using a PID Controller Based on MPU and Rotary Encoder Sensors," Control Systems and Optimization Letters, vol. 2, no. 2, pp. 257-265, 2024, https://doi.org/10.59247/csol.v2i2.150.

[17] S. A. AL-Samarraie and S. D. Salman, “Backstepping Nonlinear Control for Blood Glucose Based on Sliding Mode Meal Observer,” Al-Nahrain Journal for Engineering Sciences, vol. 21, no. 3, pp. 436–444, 2018, https://doi.org/10.29194/NJES.21030436.

[18] A. Ma’arif, M. A. M. Vera, M. S. Mahmoud, E. Umoh, A. J. Abougarair, and S. N. Rahmadhia, “Sliding Mode Control Design for Magnetic Levitation System,” Journal of Robotics and Control (JRC), vol. 3, no. 6, pp. 848-853, 2023, https://doi.org/10.18196/jrc.v3i6.12389.

[19] F. R. Yaseen and H. Al-Khazraji, "Optimized Vector Control Using Swarm Bipolar Algorithm for Five-Level PWM Inverter-Fed Three-Phase Induction Motor," International Journal of Robotics and Control Systems, vol. 5, no. 1, pp. 333-347, 2025, https://doi.org/10.31763/ijrcs.v5i1.1713.

[20] M. A. AL-Ali, O. F. Lutfy, and H. Al-Khazraji, "Investigation of Optimal Controllers on Dynamics Performance of Nonlinear Active Suspension Systems with Actuator Saturation," Journal of Robotics and Control (JRC), vol. 5, no. 4, pp. 1041-049, 2024, https://doi.org/10.18196/jrc.v5i4.22139.

[21] N. X. Chiem, "Cascade control for trajectory-tracking mobile robots based on synergetic control theory and Lyapunov functions," Control Systems and Optimization Letters, vol. 3, no. 1, pp. 14-19, 2025, https://doi.org/10.59247/csol.v3i1.169.

[22] H. Al-Khazraji, W. Guo and A. J. Humaidi, "Improved cuckoo search optimization for production inventory control systems," Serbian Journal of Electrical Engineering, vol. 21, no. 2, pp. 187-200, 2024, https://doi.org/10.2298/SJEE2402187A.

[23] R. M. Naji, H. Dulaimi and H. Al-Khazraji, “An Optimized PID Controller Using Enhanced Bat Algorithm in Drilling Processes,” Journal Européen des Systèmes Automatisés, vol. 57, no. 3, pp. 767-772, 2024, https://doi.org/10.18280/jesa.570314.

[24] N. Setiawan, W. Caesarendra, and R. Majdoubi, “Implementation of Kalman Filter on Pid Control System for DC Motor Under Noisy Condition,” Buletin Ilmiah Sarjana Teknik Elektro, vol. 6, no. 3, pp. 271-280, 2024, https://doi.org/10.12928/biste.v6i3.11236.

[25] A. Ma’arif, A. I. Cahyadi, S. Herdjunanto and O. Wahyunggoro, "Tracking Control of High Order Input Reference Using Integrals State Feedback and Coefficient Diagram Method Tuning," IEEE Access, vol. 8, pp. 182731-182741, 2020, https://doi.org/10.1109/ACCESS.2020.3029115.

[26] R. Al-Majeez, K. Al-Badri, H. Al-Khazraji and S. M. Ra'afat, “Design of A Backstepping Control and Synergetic Control for An Interconnected Twin-Tanks System: A Comparative Study," International Journal of Robotics and Control Systems, vol. 4, no. 4, pp. 2041-2054, 2024, https://doi.org/10.31763/ijrcs.v4i4.1682.

[27] H. Al-Khazraji, R. M. Naji and M. K. Khashan, "Optimization of Sliding Mode and Back-Stepping Controllers for AMB Systems Using Gorilla Troops Algorithm," Journal Européen des Systèmes Automatisés, vol. 57, no. 2, pp. 417-424, 2024, https://doi.org/10.18280/jesa.570211.

[28] H. Al-Khazraji, K. Al-Badri, R. Almajeez, and A. J. Humaidi, "Synergetic control-based sea lion optimization approach for position tracking control of ball and beam system," International Journal of Robotics and Control Systems, vol. 4, no. 4, pp. 1547-1560, 2024, https://doi.org/10.31763/ijrcs.v4i4.1551.

[29] F. R. Al-Ani, O. F. Lutfy and H. Al-Khazraji, "Optimal Synergetic and Feedback Linearization Controllers Design for Magnetic Levitation Systems: A Comparative Study," Journal of Robotics and Control (JRC), vol. 6, no. 1, pp. 22-30, 2025, https://doi.org/10.18196/jrc.v6i1.24452.

[30] H. Al-Khazraji, S. Khlil, and Z. Alabacy, "Industrial picking and packing problem: Logistic management for products expedition," Journal of Mechanical Engineering Research and Developments, vol. 43, no. 2, pp. 74-80, 2020, https://ijmert.com/index.php/ijmert/article/view/74.

[31] S. Khlil, H. Al-Khazraji, and Z. Alabacy, "Solving assembly production line balancing problem using greedy heuristic method," IOP Conference Series: Materials Science and Engineering, vol. 745, no. 1, pp. 1-7, 2020, https://doi.org/10.1088/1757-899X/745/1/012068.

[32] A. Dafid et al., “Optimizing K-Nearest Neighbors with Particle Swarm Optimization for Improved Classification Accuracy,” Jurnal Ilmiah Teknik Elektro Komputer dan Informatika (JITEKI), vol. 11, no. 2, pp. 238-250, 2025, https://doi.org/10.26555/jiteki.v11i2.30775.

[33] H. Al-Khazraji, S. Khlil and Z. Alabacy, "Solving mixed-model assembly lines using a hybrid of ant colony optimization and greedy algorithm," Engineering and Technology Journal, vol. 40, no. 1, pp.172-180, 2022, https://doi.org/10.30684/etj.v40i1.2153.

[34] S. Tahcfulloh, D. Maulianawati, and D. Wiharyanto, “Optimizing 2.4GHz Wireless Networks in Shrimp Ponds with Particle Swarm Optimization,” Jurnal Ilmiah Teknik Elektro Komputer dan Informatika, vol. 10, no. 4, pp. 817-832, 2024, https://doi.org/10.26555/jiteki.v10i4.30236.

[35] Z. A.Waheed, A. J. Humaidi, "Design of Optimal Sliding Mode Control of Elbow Wearable Exoskeleton System Based on Whale Optimization Algorithm," Journal Europeen Des Systemes Automatises, vol. 55, no. 4, pp. 459-466, 2022,
https://doi.org/10.18280/jesa.550404.

[36] F. R. Al-Ani, O. F. Lutfy, and H. Al-Khazraji, "Optimal Backstepping and Feedback Linearization Controllers Design for Tracking Control of Magnetic Levitation System: A Comparative Study," Journal of Robotics and Control (JRC), vol. 5, no. 6, pp. 1888-1896, 2024, https://doi.org/10.18196/jrc.v6i1.24452.

[37] M. Q. Kadhim, F. R. Yaseen, H. Al-Khazraji and A. J. Humaidi, "Application of Terminal Synergetic Control Based Water Strider Optimizer for Magnetic Bearing Systems," Journal of Robotics and Control (JRC), vol. 5, no. 6, pp. 1973-1979, 2024, https://doi.org/10.18196/jrc.v5i6.23867.

[38] H. Al-Khazraji and L. T. Rasheed, "Performance evaluation of pole placement and linear quadratic regulator strategies designed for mass-spring-damper system based on simulated annealing and ant colony optimization," Journal of Engineering, vol. 27, no. 11, pp. 15-31, 2021, https://doi.org/10.31026/j.eng.2021.11.02.

[39] L.T. Rasheed, "An optimal modified Elman-PID neural controller design for DC/DC Boost converter model," Journal of Engineering Science and Technology (JESTEC), vol. 18, no. 2, pp. 880-901, 2023, https://jestec.taylors.edu.my/Vol%2018%20Issue%202%20April%202023/18_2_4.pdf.

[40] A. K. Ahmed, H. Al-Khazraji, and S. M. Raafat, "Optimized PI-PD control for varying time delay systems based on modified Smith predictor," International Journal of Robotics and Control Systems, vol. 17, no. 1, pp. 331-342, 2024, https://doi.org/10.22266/ijies2024.0229.30.

[41] M. H. Qais, H. M. Hasanien, R. A. Turky, S. Alghuwainem, M. Tostado-Véliz, and F. Jurado, "Circle search algorithm: A geometry-based metaheuristic optimization algorithm," Mathematics, vol. 10, no. 10, p. 1626, 2022, https://doi.org/10.3390/math10101626.

[42] G. A. Ghazi et al., "Circle Search Algorithm-Based Super Twisting Sliding Mode Control for MPPT of Different Commercial PV Modules," IEEE Access, vol. 12, pp. 33109-33128, 2024, https://doi.org/10.1109/ACCESS.2024.3372412.

[43] F. R. Yaseen and H. Al-Khazraji, "Optimized Vector Control Using Swarm Bipolar Algorithm for Five-Level PWM Inverter-Fed Three-Phase Induction Motor," International Journal of Robotics and Control Systems, vol. 5, no. 1, pp. 333-347, 2025, https://doi.org/10.31763/ijrcs.v5i1.1713.

[44] H. Al-Khazraji, C. Cole, and W. Guo, "Analysing the impact of different classical controller strategies on the dynamics performance of production-inventory systems using state space approach," Journal of Modelling in Management, vol. 13, no. 1, pp. 211-235, 2018, https://doi.org/10.1108/JM2-08-2016-0071.


Refbacks

  • There are currently no refbacks.


Copyright (c) 2025 Rawnaq A. Mahmod, Rawnaq A. Mahmod, Russul A. Kadhima, Mohanad Nawfal, Huthaifa Al-Khazraji

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

 


About the JournalJournal PoliciesAuthor Information

International Journal of Robotics and Control Systems
e-ISSN: 2775-2658
Website: https://pubs2.ascee.org/index.php/IJRCS
Email: ijrcs@ascee.org
Organized by: Association for Scientific Computing Electronics and Engineering (ASCEE)Peneliti Teknologi Teknik IndonesiaDepartment of Electrical Engineering, Universitas Ahmad Dahlan and Kuliah Teknik Elektro
Published by: Association for Scientific Computing Electronics and Engineering (ASCEE)
Office: Jalan Janti, Karangjambe 130B, Banguntapan, Bantul, Daerah Istimewa Yogyakarta, Indonesia