Genetic algorithm-enhanced linear quadratic control for balancing bicopter system with non-zero set point

Esa Apriaskar, Dhidik Prastiyanto, Aryo Baskoro Utomo, Akhyar Abdillah Manaf, Ilya Amelia, Dimas Alfarizky Ilham, Viyola Lokahita Bilqis, Chonlatee Photong


Bicopter is an unmanned aerial vehicle (UAV) with the advantage of saving energy consumption. However, the unique two rotors design presents a challenge in designing a controller that achieves good stability, fast settling time, and the ability to overcome oscillations simultaneously. This article proposes a new control method for bicopter that uses a genetic algorithm optimization approach in the linear quadratic (LQ-GA) control method. The GA is used to search for the best weighting matrix parameters, Q and R, in the Linear Quadratic (LQ) control scheme. The proposed control method was tested on a balancing bicopter test platform with an input in the form of difference in pulse width modulation (PWM) signals for both rotors and an output in the form of roll angle. The control system was evaluated based on the stability of the transient response and the generated control signal. The results of the tests showed that the proposed LQ-GA control method has better stability, faster settling time, and smaller overshoot than the existing PI and standard LQ control methods. Therefore, the proposed LQ-GA control method is the most suitable for use in a balancing bicopter system with a non-zero setpoint.


balancing bicopter; genetic algorithm; linear quadratic; roll angle; non-zero set point

Full Text:



R. Z. B. Bravo, A. Leiras, and F. L. Cyrino Oliveira, “The Use of UAVs in Humanitarian Relief: An Application of POMDP-Based Methodology for Finding Victims,” Prod Oper Manag, vol. 28, no. 2, pp. 421–440, Feb. 2019.

W. Sun, L. Dai, X. Zhang, P. Chang, and X. He, “RSOD: Real-time small object detection algorithm in UAV-based traffic monitoring,” Applied Intelligence, vol. 52, no. 8, pp. 8448–8463, Jun. 2022.

P. S. Ramesh and J. V. M. L. Jeyan, “Comparative analysis of the impact of operating parameters on military and civil applications of mini unmanned aerial vehicle (UAV),” in AIP Conference Proceedings, American Institute of Physics Inc., Dec. 2020.

S. M. Shavarani, M. Golabi, and G. Izbirak, “A capacitated biobjective location problem with uniformly distributed demands in the UAV‐supported delivery operation,” International Transactions in Operational Research, vol. 28, no. 6, pp. 3220–3243, Nov. 2021.

R. S. Adarsh and M. M. Dharmana, “Multi-terrain Multi-utility robot,” in Procedia Computer Science, Elsevier B.V., 2018, pp. 651–659.

O. B. Albayrak, Y. Ersan, A. S. Bağbaşı, A. T. Başaranoğlu, and K. B. Arıkan, “Design of a Robotic Bicopter,” 7th International Conference on Control, Mechatronics and Automation (ICCMA), pp. 98–103, 2019.

E. Apriaskar, D. Prastiyanto, A. A. Manaf, I. Amelia, and Fahmizal, “Multi-criteria Genetic Algorithm Optimization Approach for Balancing Bicopter Control,” IOP Conf Ser Earth Environ Sci, vol. 1203, no. 1, p. 012027, Jun. 2023.

S. Joksimovic, D. Ifenthaler, R. Marrone, M. De Laat, and G. Siemens, “Opportunities of artificial intelligence for supporting complex problem-solving: Findings from a scoping review,” Computers and Education: Artificial Intelligence, vol. 4, p. 100138, 2023.

S. Bari, S. S. Zehra Hamdani, H. U. Khan, M. ur Rehman, and H. Khan, “Artificial Neural Network Based Self-Tuned PID Controller for Flight Control of Quadcopter,” in 2019 International Conference on Engineering and Emerging Technologies (ICEET), IEEE, Feb. 2019, pp. 1–5.

A. A. Najm and I. K. Ibraheem, “Nonlinear PID controller design for a 6-DOF UAV quadrotor system,” Engineering Science and Technology, an International Journal, vol. 22, no. 4, pp. 1087–1097, Aug. 2019.

M. Tolba and B. Shirinzadeh, “Generic modeling and control of unbalanced multirotor UAVs,” Aerosp Sci Technol, vol. 121, Feb. 2022.

A. Eltayeb, M. Fuaad Rahmat, M. Ariffanan, and M. Basri, “Adaptive Feedback Linearization Controller for Stabilization of Quadrotor UAV,” International Journal Of Integrated Engineering, vol. 12, no. 4, pp. 1–17, 2020.

Q. Zhang, Z. Liu, J. Zhao, and S. Zhang, “Modeling and attitude control of Bi-copter,” in 2016 IEEE International Conference on Aircraft Utility Systems (AUS), IEEE, Oct. Pp.172-176, 2016.

A. Bhaskar, G. Verma, and S. Sharma, “MARVEL: A High Pitch Agile Bi-copter Wall-Climbing Robot,” in Advances in Robotics - 5th International Conference of The Robotics Society, New York, NY, USA: ACM, pp. 1–6, Jun. 2021.

Y. Qin, W. Xu, A. Lee, and F. Zhang, “Gemini: A Compact yet Efficient Bi-copter UAV for Indoor Applications,” IEEE Robot Autom Lett, pp. 1–1, 2020.

E. Apriaskar, F. Fahmizal, N. A. Salim, and D. Prastiyanto, “Performance Evaluation of Balancing Bicopter using P, PI, and PID Controller,” Jurnal Teknik Elektro, vol. 11, no. 2, pp. 44–49, Dec. 2019.

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, Nov. 2021.

M. F. Shehzad, A. Bilal, and H. Ahmad, “Position & Attitude Control of an Aerial Robot (Quadrotor) With Intelligent PID and State feedback LQR Controller: A Comparative Approach,” in 2019 16th International Bhurban Conference on Applied Sciences and Technology (IBCAST), IEEE, Jan. 2019, pp. 340–346.

K. Choutri, M. Lagha, L. Dala, and M. Lipatov, “Quadrotors UAVs Swarming Control Under Leader-Followers Formation,” in 2018 22nd International Conference on System Theory, Control and Computing (ICSTCC), IEEE, Oct. 2018, pp. 794–799.

S. Bagheri, T. Jafarov, L. Freidovich, and N. Sepehri, “Beneficially combining LQR and PID to control longitudinal dynamics of a SmartFly UAV,” in 2016 IEEE 7th Annual Information Technology, Electronics and Mobile Communication Conference (IEMCON), IEEE, Oct. 2016, pp. 1–6.

M. Taherinezhad, A. Ramirez-Serrano, and A. Abedini, “Robust Trajectory-Tracking for a Bi-Copter Drone Using INDI: A Gain Tuning Multi-Objective Approach,” Robotics, vol. 11, no. 5, Oct. 2022.

J. A. Prakosa, H. Wang, E. Kurniawan, S. Agmal, and M. J. Kholili, “Experimental studies of linear quadratic regulator (LQR) cost matrices weighting to control an accurate take-off position of bicopter unmanned aerial vehicles (UAVs),” Journal of Mechatronics, Electrical Power, and Vehicular Technology, vol. 13, no. 2, pp. 101–112, 2022.

Y. Hu, Z. Sun, L. Cao, Y. Zhang, and P. Pan, “Optimization configuration of gas path sensors using a hybrid method based on tabu search artificial bee colony and improved genetic algorithm in turbofan engine,” Aerosp Sci Technol, vol. 112, p. 106642, May 2021.

L. Liang, J. Yuan, S. Zhang, and P. Zhao, “Design a software realtime operation platform for wave piercing catamarans motion control using linear quadratic regulator based genetic algorithm,” PLoS One, vol. 13, no. 4, p. e0196107, Apr. 2018.

E. Joelianto, D. Christian, and A. Samsi, “Swarm control of an unmanned quadrotor model with LQR weighting matrix optimization using genetic algorithm,” Journal of Mechatronics, Electrical Power, and Vehicular Technology, vol. 11, no. 1, pp. 1–10, Jul. 2020.

X. Hu, H. Zou, and L. Wang, “Design of the Linear Quadratic Structure Based Predictive Functional Control for Industrial Processes Against Partial Actuator Failures Using GA Optimization,” Int J Control Autom Syst, vol. 17, no. 3, pp. 597–605, Mar. 2019.

A. I. Abdulla and I. K. Mohammed, “Aircraft pitch control design using LQG controller based on genetic algorithm,” Telkomnika (Telecommunication Computing Electronics and Control), vol. 21, no. 2, pp. 409–417, Apr. 2023.

Fahmizal, M. Arrofiq, E. Apriaskar, and A. Mayub, “Rigorous Modelling Steps on Roll Movement of Balancing Bicopter using Multi-level Periodic Perturbation Signals,” in 2019 6th International Conference on Instrumentation, Control, and Automation (ICA), IEEE, Jul. 2019, pp. 52–57.

Q. Xu, Z. Wang, and Z. Zhen, “Information fusion estimation-based path following control of quadrotor UAVs subjected to Gaussian random disturbance,” ISA Trans, vol. 99, pp. 84–94, Apr. 2020.

S. Mirjalili, “Genetic Algorithm,” In Evolutionary Algorithms and Neural Networks. Studies in Computational Intelligence, vol 780. Springer, Cham.2019, pp. 43–55.

A. K. Joseph, A. Bousbaine, and A. Fareha, “A Wireless communication system for a quadrotor helicopter,” in 2018 53rd International Universities Power Engineering Conference (UPEC), IEEE, Sep. 2018, pp. 1–5.

D. D’Amato, J. Loncarski, V. G. Monopoli, F. Cupertino, L. P. Di Noia, and A. Del Pizzo, “Impact of PWM Voltage Waveforms in High-Speed Drives: A Survey on High-Frequency Motor Models and Partial Discharge Phenomenon,” Energies (Basel), vol. 15, no. 4, p. 1406, Feb. 2022.

H. Zhang, P. Wan, J. Geng, Z. Liu, and Z. Chen, “A Fast Transient Response Digital LDO with a TDC-Based Signal Converter,” Electronics (Basel), vol. 9, no. 1, p. 132, Jan. 2020.

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM


  • There are currently no refbacks.

Copyright (c) 2023 Journal of Mechatronics, Electrical Power, and Vehicular Technology

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