PARAMETER OPTIMIZATION OF LQR CONTROLLER APPLIED TO THREE DEGREES OF FREEDOM SYSTEM WITH HYBRID APPROACH

Yıl 2024, Cilt: 12 Sayı: 2, 494 – 510, 01.06.2024

Yasin Büyüker , İlhan İlhan

https://doi.org/10.36306/konjes.1291710

Öz

There have been numerous studies on the control of quadcopters. These studies mainly aim to control the flight behavior of quadcopters. To achieve this, researchers have been developing new tools and testing new methods. One of the developed tools is the 3-DOF Hover system, which enables researchers to analyze the flight behaviors of quadcopters, such as roll, pitch, and yaw, even in a physically limited area or only in a computer environment. The control method applied in the control of the 3-DOF Hover system has been determined by the manufacturer as Linear-Quadratic Regulator (LQR). LQR has control parameters that are complex to calculate. This complex calculation process creates an optimization problem. Beyond controlling the 3-DOF Hover system using LQR, this study focuses on calculating the complex control parameters of LQR using optimization algorithms when controlling a dynamic system with LQR.
This study includes well-known algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Simulated Annealing (SA), as well as an innovative approach known Gray Wolf Optimization (GWO). These algorithms were selected due to their proven effectiveness in various studies. Based on the results obtained from these algorithms, a hybrid algorithm incorporating SA and GWO is proposed. The aim of this hybrid algorithm is to combine the advantages of different methods and achieve a more effective and efficient optimization process. The mentioned hybrid algorithm, obtained by combining SA and GWO, is named hSA-GWO. This hSA-GWO is compared with traditional algorithms, and the comparison results show that the proposed hybrid algorithm can be used as an alternative and competitive method for controlling the flight behaviors of quadcopters.

Anahtar Kelimeler

Hybrid Algorithm, LQR Control, Optimization Algorithms, Quadcopter

Kaynakça

• S. Mohanty and A. Misra, “3 DOF Autonomous Control Analysis of an Quadcopter Using Artificial Neural Network,” Studies in Computational Intelligence, vol. 885, pp. 39–57, 2020, doi: 10.1007/978-3-030-38445-6_4/COVER.
• “3 DOF Hover- Quanser.” https://www.quanser.com/products/3-dof-hover/ (accessed Apr. 17, 2023).
• M. K. Bayrakceken and A. Arisoy, “An Educational Setup for Nonlinear Control Systems: Enhancing the Motivation and Learning in a Targeted Curriculum by Experimental Practices [Focus on Education],” IEEE Control Syst, vol. 33, no. 2, pp. 64–81, Mar. 2013, doi: 10.1109/MCS.2012.2234971.
• Ö. Bayraktar and A. Güldaş, “Quadrotor İtme ve Tork Katsayılarının Optimizasyonu ve Matlab/Simulink ile Simülasyonu,” Politeknik Dergisi, vol. 23, no. 4, pp. 1197–1204, Dec. 2020, doi: 10.2339/POLITEKNIK.636950.
• B. Alagoz, A. Ates, and C. Yeroglu, “Auto-tuning of PID Controller According to Fractional-order Reference Model Approximation for DC Rotor Control,” Mechatronics, vol. 23, no. 7, pp. 789–797, Oct. 2013, doi: 10.1016/J.MECHATRONICS.2013.05.001.
• R. Beard, “Quadcopter Dynamics and Control Rev, no. 1, p. 1325, 2008, Accessed: Apr. 17, 2023. [Online]. Available: https://scholarsarchive.byu.edu/facpubhttps://scholarsarchive.byu.edu/facpub/1325
• T. Oktay and O. Köse, “Farklı Uçuş Durumları için Quadcopter Dinamik Modeli ve Simulasyonu,” European Journal of Science and Technology, pp. 132–142, Mar. 2019, doi: 10.31590/EJOSAT.507222.
• M. İçen, A. Ateş, and C. Yeroǧlu, “Optimization of LQR Weight Matrix to Control Three Degree of Freedom Quadcopter,” IDAP 2017- International Artificial Intelligence and Data Processing Symposium, Oct. 2017, doi: 10.1109/IDAP.2017.8090164.
• V. E. Ömürlü, U. Büyükşahin, R. Artar, A. Kirli, and M. N. Turgut, “An Experimental Stationary Quadrotor with Variable DOF,” Sadhana- Academy Proceedings in Engineering Sciences, vol. 38, no. 2, pp. 247–264, Apr. 2013, doi: 10.1007/S12046-013-0132-6.
• H. K. Tran and T. N. Nguyen, “Flight Motion Controller Design Using Genetic Algorithm for a Quadcopter,” Measurement and Control (United Kingdom), vol. 51, no. 3–4, pp. 59–64, Apr. 2018, doi: 10.1177/0020294018768744/ASSET/IMAGES/LARGE/10.1177_0020294018768744-FIG7.JPEG.
• A. Reizenstein, “Position and Trajectory Control of a Quadcopter Using PID and LQ Controllers,” 2017, Accessed: Apr. 17, 2023. [Online]. Available: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-139498
• Demiryurek A, “Modelıng and Control of a Quadrotor,” Hacettepe University, Ankara, 2018.
• M. Karakoyun and A. Özkış, “Transfer Fonksiyonları Kullanarak İkili Güve-Alev Optimizasyonu Algoritmalarının Geliştirilmesi ve Performanslarının Karşılaştırılması,” Necmettin Erbakan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, vol. 3, no. 2, pp. 1–10, 2021.
• D. E. Goldberg and J. H. Holland, “Genetic Algorithms and Machine Learning,” Mach Learn, vol. 3, no. 2, pp. 95–99, 1988, doi: 10.1023/A:1022602019183/METRICS.
• J. Kennedy and R. Eberhart, “Particle Swarm Optimization,” Proceedings of ICNN’95- International Conference on Neural Networks, vol. 4, pp. 1942–1948, doi: 10.1109/ICNN.1995.488968.
• S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science (1979), vol. 220, no. 4598, pp. 671–680, May 1983, doi: 10.1126/SCIENCE.220.4598.671.
• S. Mirjalili, S. M. Mirjalili, and A. Lewis, “Grey Wolf Optimizer,” Advances in Engineering Software, vol. 69, pp. 46–61, Mar. 2014, doi: 10.1016/J.ADVENGSOFT.2013.12.007.
• “Linear-Quadratic Regulator (LQR) design- MATLAB lqr.” https://www.mathworks.com/help/control/ref/lti.lqr.html (accessed Apr. 18, 2023).
• “Rise time, settling time, and other step-response characteristics- MATLAB stepinfo.” https://www.mathworks.com/help/control/ref/dynamicsystem.stepinfo.html (accessed Apr. 17, 2023).
• İ. İlhan, “An Improved Simulated Annealing Algorithm with Crossover Operator for Capacitated Vehicle Routing Problem,” Swarm Evol Comput, vol. 64, p. 100911, Jul. 2021, doi: 10.1016/J.SWEVO.2021.100911.
• A. Tabak and İ. İlhan, “An Effective Method Based on Simulated Annealing for Automatic Generation Control of Power Systems,” Appl Soft Comput, vol. 126, p. 109277, Sep. 2022, doi: 10.1016/J.ASOC.2022.109277.
• A. Hassanat, K. Almohammadi, E. Alkafaween, E. Abunawas, A. Hammouri, and V. B. S. Prasath, “Choosing Mutation and Crossover Ratios for Genetic Algorithms—A Review with a New Dynamic Approach,” Information 2019, Vol. 10, Page 390, vol. 10, no. 12, p. 390, Dec. 2019, doi: 10.3390/INFO10120390.
• A. K. Peprah, S. K. Appiah, and S. K. Amponsah, “An Optimal Cooling Schedule Using a Simulated Annealing Based Approach,” Appl Math (Irvine), vol. 08, no. 08, pp. 1195–1210, Aug. 2017, doi: 10.4236/AM.2017.88090.

Yıl 2024, Cilt: 12 Sayı: 2, 494 – 510, 01.06.2024

Yasin Büyüker , İlhan İlhan

https://doi.org/10.36306/konjes.1291710

Öz

Kaynakça

• S. Mohanty and A. Misra, “3 DOF Autonomous Control Analysis of an Quadcopter Using Artificial Neural Network,” Studies in Computational Intelligence, vol. 885, pp. 39–57, 2020, doi: 10.1007/978-3-030-38445-6_4/COVER.
• “3 DOF Hover- Quanser.” https://www.quanser.com/products/3-dof-hover/ (accessed Apr. 17, 2023).
• M. K. Bayrakceken and A. Arisoy, “An Educational Setup for Nonlinear Control Systems: Enhancing the Motivation and Learning in a Targeted Curriculum by Experimental Practices [Focus on Education],” IEEE Control Syst, vol. 33, no. 2, pp. 64–81, Mar. 2013, doi: 10.1109/MCS.2012.2234971.
• Ö. Bayraktar and A. Güldaş, “Quadrotor İtme ve Tork Katsayılarının Optimizasyonu ve Matlab/Simulink ile Simülasyonu,” Politeknik Dergisi, vol. 23, no. 4, pp. 1197–1204, Dec. 2020, doi: 10.2339/POLITEKNIK.636950.
• B. Alagoz, A. Ates, and C. Yeroglu, “Auto-tuning of PID Controller According to Fractional-order Reference Model Approximation for DC Rotor Control,” Mechatronics, vol. 23, no. 7, pp. 789–797, Oct. 2013, doi: 10.1016/J.MECHATRONICS.2013.05.001.
• R. Beard, “Quadcopter Dynamics and Control Rev, no. 1, p. 1325, 2008, Accessed: Apr. 17, 2023. [Online]. Available: https://scholarsarchive.byu.edu/facpubhttps://scholarsarchive.byu.edu/facpub/1325
• T. Oktay and O. Köse, “Farklı Uçuş Durumları için Quadcopter Dinamik Modeli ve Simulasyonu,” European Journal of Science and Technology, pp. 132–142, Mar. 2019, doi: 10.31590/EJOSAT.507222.
• M. İçen, A. Ateş, and C. Yeroǧlu, “Optimization of LQR Weight Matrix to Control Three Degree of Freedom Quadcopter,” IDAP 2017- International Artificial Intelligence and Data Processing Symposium, Oct. 2017, doi: 10.1109/IDAP.2017.8090164.
• V. E. Ömürlü, U. Büyükşahin, R. Artar, A. Kirli, and M. N. Turgut, “An Experimental Stationary Quadrotor with Variable DOF,” Sadhana- Academy Proceedings in Engineering Sciences, vol. 38, no. 2, pp. 247–264, Apr. 2013, doi: 10.1007/S12046-013-0132-6.
• H. K. Tran and T. N. Nguyen, “Flight Motion Controller Design Using Genetic Algorithm for a Quadcopter,” Measurement and Control (United Kingdom), vol. 51, no. 3–4, pp. 59–64, Apr. 2018, doi: 10.1177/0020294018768744/ASSET/IMAGES/LARGE/10.1177_0020294018768744-FIG7.JPEG.
• A. Reizenstein, “Position and Trajectory Control of a Quadcopter Using PID and LQ Controllers,” 2017, Accessed: Apr. 17, 2023. [Online]. Available: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-139498
• Demiryurek A, “Modelıng and Control of a Quadrotor,” Hacettepe University, Ankara, 2018.
• M. Karakoyun and A. Özkış, “Transfer Fonksiyonları Kullanarak İkili Güve-Alev Optimizasyonu Algoritmalarının Geliştirilmesi ve Performanslarının Karşılaştırılması,” Necmettin Erbakan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, vol. 3, no. 2, pp. 1–10, 2021.
• D. E. Goldberg and J. H. Holland, “Genetic Algorithms and Machine Learning,” Mach Learn, vol. 3, no. 2, pp. 95–99, 1988, doi: 10.1023/A:1022602019183/METRICS.
• J. Kennedy and R. Eberhart, “Particle Swarm Optimization,” Proceedings of ICNN’95- International Conference on Neural Networks, vol. 4, pp. 1942–1948, doi: 10.1109/ICNN.1995.488968.
• S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science (1979), vol. 220, no. 4598, pp. 671–680, May 1983, doi: 10.1126/SCIENCE.220.4598.671.
• S. Mirjalili, S. M. Mirjalili, and A. Lewis, “Grey Wolf Optimizer,” Advances in Engineering Software, vol. 69, pp. 46–61, Mar. 2014, doi: 10.1016/J.ADVENGSOFT.2013.12.007.
• “Linear-Quadratic Regulator (LQR) design- MATLAB lqr.” https://www.mathworks.com/help/control/ref/lti.lqr.html (accessed Apr. 18, 2023).
• “Rise time, settling time, and other step-response characteristics- MATLAB stepinfo.” https://www.mathworks.com/help/control/ref/dynamicsystem.stepinfo.html (accessed Apr. 17, 2023).
• İ. İlhan, “An Improved Simulated Annealing Algorithm with Crossover Operator for Capacitated Vehicle Routing Problem,” Swarm Evol Comput, vol. 64, p. 100911, Jul. 2021, doi: 10.1016/J.SWEVO.2021.100911.
• A. Tabak and İ. İlhan, “An Effective Method Based on Simulated Annealing for Automatic Generation Control of Power Systems,” Appl Soft Comput, vol. 126, p. 109277, Sep. 2022, doi: 10.1016/J.ASOC.2022.109277.
• A. Hassanat, K. Almohammadi, E. Alkafaween, E. Abunawas, A. Hammouri, and V. B. S. Prasath, “Choosing Mutation and Crossover Ratios for Genetic Algorithms—A Review with a New Dynamic Approach,” Information 2019, Vol. 10, Page 390, vol. 10, no. 12, p. 390, Dec. 2019, doi: 10.3390/INFO10120390.
• A. K. Peprah, S. K. Appiah, and S. K. Amponsah, “An Optimal Cooling Schedule Using a Simulated Annealing Based Approach,” Appl Math (Irvine), vol. 08, no. 08, pp. 1195–1210, Aug. 2017, doi: 10.4236/AM.2017.88090.

Toplam 23 adet kaynakça vardır.

Ayrıntılar

Kaynak Göster

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