Research Article
BibTex RIS Cite

Optimizing PI Controller for Stability and Overshoot in Step Response Using GA and PSO Techniques, A Comparative Study

Year 2025, Volume: 9 Issue: 1, 12 - 23, 30.06.2025

Bilal Şenol , Uğur Demiroğlu

https://doi.org/10.47897/bilmes.1578027

Abstract

In this paper, we present a comprehensive and in-depth investigation on the optimization of Proportional-Integral (PI) controller tuning for achieving stability and desired overshoot in the step response. The main objective of this study is to compare the effectiveness of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) techniques in finding the optimal parameters for the PI controller. The PI controller is a widely used control algorithm that plays a crucial role in many industrial processes. Its tuning greatly affects the system's performance, particularly in terms of stability and overshoot. Therefore, finding the optimal tuning parameters is of utmost importance. To address this optimization problem, we propose the utilization of two popular metaheuristic algorithms, GA and PSO. These algorithms are known for their ability to efficiently search through large solution spaces and find near-optimal solutions. By applying these algorithms to the PI controller tuning problem, we aim to determine which technique yields better results in terms of stability and overshoot tuning. In our comparative study, we provide a detailed explanation of both GA and PSO algorithms, focusing on their working principles and mathematical formulations. We also describe how these algorithms can be applied to the PI controller tuning problem. Furthermore, we highlight the key differences between GA and PSO, shedding light on their strengths and weaknesses. To assess the performance of GA and PSO, we conduct several experiments using different benchmark functions and step response models. We measure the stability and overshoot metrics for various parameter settings obtained through GA and PSO. By thoroughly analyzing the obtained results, we draw meaningful conclusions regarding the effectiveness of each technique. Our findings demonstrate that both GA and PSO exhibit promising results in optimizing PI controller tuning. These observations provide valuable insights and guidelines for choosing the appropriate algorithm based on specific control requirements. In conclusion, this comparative study is thought to contribute to the field of control systems engineering by offering a comprehensive analysis of GA and PSO techniques in the context of PI controller tuning. By highlighting their strengths and weaknesses, it is aimed to provide researchers and practitioners with valuable information for making informed decisions when optimizing control parameters for stability and overshoot reduction purposes.

Keywords

PI Controller Overshoot Step Response Stability Genetic Algorithm Particle Swarm Optimization

References

  • G. Cui, J. Yu and Q. G. Wang, “Finite-time adaptive fuzzy control for MIMO nonlinear systems with input saturation via improved command-filtered backstepping,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 52, no. 2, pp. 980-989, 2020.
  • Y. Ji, X. Jiang and L. Wan, “Hierarchical least squares parameter estimation algorithm for two-input Hammerstein finite impulse response systems, Journal of the Franklin Institute, vol. 357, no. 8, pp. 5019-5032, 2020.
  • Y. Ji and Z. Kang, “Three‐stage forgetting factor stochastic gradient parameter estimation methods for a class of nonlinear systems,” International Journal of Robust and Nonlinear Control, vol. 31, no. 3, pp. 971-987, 2021.
  • B. Obrenovic, J. Du, D. Godinic, D. Tsoy, M. A. S. Khan, and I. Jakhongirov, “Sustaining enterprise operations and productivity during the COVID-19 pandemic:“Enterprise Effectiveness and Sustainability Model,” Sustainability, vol. 12, no. 15, p. 5981, 2020.
  • M. Kamalahmadi, M. Shekarian, and M. Mellat Parast, “The impact of flexibility and redundancy on improving supply chain resilience to disruptions,” International Journal of Production Research, vol. 60, no. 6, pp. 1992-2020, 2022.
  • Z. Yu, A. Razzaq, A. Rehman, A. Shah, K. Jameel and R. S. Mor, “Disruption in global supply chain and socio-economic shocks: a lesson from COVID-19 for sustainable production and consumption,” Operations Management Research, pp. 1-16, 2021.
  • M. Kosmecki, R. Rink, A. Wakszyńska, R. Ciavarella, M. Di Somma, C. N. Papadimitriou, and G. Graditi, “A methodology for provision of frequency stability in operation planning of low inertia power systems,” Energies, vol. 14, no. 3, p. 737, 2021.
  • M. Hu, W. Hua, G. Ma, S. Xu, and W. Zeng, “Improved current dynamics of proportional-integral-resonant controller for a dual three-phase FSPM machine,” IEEE Transactions on Industrial Electronics, vol. 68, no. 12, pp. 11719-11730, 2020.
  • J. Park, H. Kim, K. Hwang, and S. Lim, “Deep reinforcement learning based dynamic proportional-integral (PI) gain auto-tuning method for a robot driver system,” IEEE Access, vol. 10, pp. 31043-31057, 2022.
  • A. W. Khawaja, N. A. M. Kamari, M. A. A. M. Zainuri, S. Abd Halim, M. A. Zulkifley, S. Ansari, and A. S. Malik, “Angle stability improvement using optimised proportional integral derivative with filter controller,” Heliyon, 2024.
  • S. M. Y. Younus, U. Kutbay, J. Rahebi, and F. Hardalaç, “Hybrid gray wolf optimization–proportional integral based speed controllers for brush-less dc motor,” Energies, vol. 16, no. 4, p. 1640, 2023.
  • D. F. Zambrano-Gutierrez, J. M. Cruz-Duarte, J. G. Avina-Cervantes, J. C. Ortiz-Bayliss, J. J. Yanez-Borjas, and I. Amaya, “Automatic design of metaheuristics for practical engineering applications,” IEEE Access, vol. 11, pp. 7262-7276, 2023.
  • E. Bogar and S. Beyhan, “Adolescent Identity Search Algorithm (AISA): A novel metaheuristic approach for solving optimization problems,” Applied Soft Computing, vol. 95, p. 106503, 2020.
  • A. A. Ameen, “Metaheuristic Optimization Algorithms in Applied Science and Engineering Applications,” Doktoral Thesis, 2024.
  • A. Mojtahedi, M. Dadashzadeh and M. Kouhi, “Developing a predictive method based on the vibration behavior of a naval ship hull model using hybrid fuzzy meta-heuristic algorithms,” Ocean Engineering, vol. 311, p. 118994, 2024.
  • O. Rodríguez-Abreo, J. M. Garcia-Guendulain, "Genetic algorithm-based tuning of backstepping controller for a quadrotor-type unmanned aerial vehicle," Electronics, 2020. mdpi.com
  • Y. Tian, Y. Zhang, Y. Su, and X. Zhang, "Balancing objective optimization and constraint satisfaction in constrained evolutionary multiobjective optimization," in IEEE Transactions on ..., 2021. researchgate.net
  • G. D’Angelo, and F. Palmieri, “GGA: A modified genetic algorithm with gradient-based local search for solving constrained optimization problems,” Information Sciences, vol. 547, pp. 136-162, 2021.
  • A. Sohail, “Genetic algorithms in the fields of artificial intelligence and data sciences,” Annals of Data Science, vol. 10, no. 4, pp. 1007-1018, 2023.
  • A. G. Gad, "Particle swarm optimization algorithm and its applications: a systematic review," Archives of computational methods in engineering, 2022. springer.com
  • H. Maghfiroh, M. Nizam, M. Anwar, and A. Ma’Arif, “Improved LQR control using PSO optimization and Kalman filter estimator,” IEEE Access, vol. 10, pp. 18330-18337, 2022.
  • M. N. Muftah, A. A. M. Faudzi, S. Sahlan, and M. Shouran, “Modeling and fuzzy FOPID controller tuned by PSO for pneumatic positioning system,” Energies, vol. 15, no. 10, p. 3757, 2022.
  • Basilio, J. C., and Matos, S. R. (2002). Design of PI and PID controllers with transient performance specification. IEEE Transactions on education, 45(4), 364-370.
  • A. Jamison Hill, “Towards Real Time Optimal Auto-tuning of PID Controllers,” Doctoral Thesis, 2013.
  • Salimi, H., Zakipour, A., and Asadi, M. (2022). A novel analytical approach for time-response shaping of the pi controller in field oriented control of the permanent magnet synchronous motors. Journal of Electrical and Computer Engineering Innovations (JECEI), 10(2), 463-476.
  • M. Saiful Islam Aziz, “Improved gravitational search algorithm for proportional integral derivative controller tuning in process control system”, Doctoral Thesis, 2016.
  • Kristiansson, B., and Lennartson, B. (2006). Robust tuning of PI and PID controllers: using derivative action despite sensor noise. IEEE Control Systems Magazine, 26(1), 55-69.
  • I. De Jesus Diaz Rodriguez, “Modern Design of Classical Controllers,” 2017.
  • R. Pagilla, P. Cimino and D. Knittel, ”Design of fixed structure controllers for web tension control,” 2007.
  • Z. Chen, Y. S. Hao, Z. Su and L. Sun, “Data-driven iterative tuning based active disturbance rejection control for FOPTD model,” ISA transactions, vol. 128, pp. 593-605., 2022.
  • H. Meneses, O. Arrieta, F. Padula, A. Visioli and R. Vilanova, “Fopi/fopid tuning rule based on a fractional order model for the process,” Fractal and Fractional, vol. 6, no. 9, p. 478, 2022.
  • P. Ghorai, “Online Parameters Estimation of Time-Delayed Dynamics of Processes for Industrial Use, “ International Journal of Industrial Engineering, vol. 29, no. 4, 2022.
  • T. George and V. Ganesan, “Optimal tuning of PID controller in time delay system: A review on various optimization techniques,” Chemical Product and Process Modeling, vol. 17, no. 1, pp. 1-28, 2022.
  • L. Abdullah, Z. Jamaludin, T. H. Chiew, N. A. Rafan and M. Y. Yuhazri, “Extensive Tracking Performance Analysis of Classical feedback control for XY Stage ballscrew drive system,” Applied Mechanics and Materials, vol. 229, pp. 750-755, 2012.
  • U. Agrawal, P. Etingov and R. Huang, “Advanced Performance Metrics and Sensitivity Analysis for Model Validation and Calibration,” Authorea Preprint, 2023.
  • M. Gen and L. Lin, “Genetic algorithms and their applications,” In Springer handbook of engineering statistics (pp. 635-674). London: Springer London, 2023.
  • Z. Z. Wang and A. Sobey, “A comparative review between Genetic Algorithm use in composite optimisation and the state-of-the-art in evolutionary computation,” Composite Structures, vol.233, 2020.
  • H. R. R. Zaman and F. S. Gharehchopogh, F. S. (2022). An improved particle swarm optimization with backtracking search optimization algorithm for solving continuous optimization problems,” Engineering with Computers, vol. 38, no. 4, pp. 2797-2831 2022.
  • Z. Yu, Z. Si, X. Li, D. Wang and H. Song, “A novel hybrid particle swarm optimization algorithm for path planning of UAVs,” IEEE Internet of Things Journal, vol. 9, no. 22, pp. 22547-22558, 2022
  • A. G. Gad, “Particle swarm optimization algorithm and its applications: a systematic review,” Archives of computational methods in engineering, vol. 29, no. 5, pp. 2531-2561, 2022.
  • H. Zhao, H. Yao, Y. Jiao, T. Lou, andY. Wang, “An Improved Beetle Antennae Search Algorithm Based on Inertia Weight and Attenuation Factor,” Mathematical Problems in Engineering, vol. 1, 2022.
  • J. Chrouta, F. Farhani, F. and A. Zaafouri, “A modified multi swarm particle swarm optimization algorithm using an adaptive factor selection strategy,” Transactions of the Institute of Measurement and Control, vol. 0, no. 0, 2021.
  • B. Durmuş, “Opposite Based Crow Search Algorithm for Solving Optimization Problem,” International Scientific and Vocational Studies Journal, vol. 5, no. 2, pp. 164-170, 2021.
  • B. Şenol and U. Demiroğlu, “Analytical Design of PI Controllers for First Order plus Time Delay Systems,” International Scientific and Vocational Studies Journal, vol. 2, no. 2, pp. 40–47, 2018.

Optimizing PI Controller for Stability and Overshoot in Step Response Using GA and PSO Techniques, A Comparative Study

Year 2025, Volume: 9 Issue: 1, 12 - 23, 30.06.2025

Bilal Şenol , Uğur Demiroğlu

https://doi.org/10.47897/bilmes.1578027

Abstract

In this paper, we present a comprehensive and in-depth investigation on the optimization of Proportional-Integral (PI) controller tuning for achieving stability and desired overshoot in the step response. The main objective of this study is to compare the effectiveness of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) techniques in finding the optimal parameters for the PI controller. The PI controller is a widely used control algorithm that plays a crucial role in many industrial processes. Its tuning greatly affects the system's performance, particularly in terms of stability and overshoot. Therefore, finding the optimal tuning parameters is of utmost importance. To address this optimization problem, we propose the utilization of two popular metaheuristic algorithms, GA and PSO. These algorithms are known for their ability to efficiently search through large solution spaces and find near-optimal solutions. By applying these algorithms to the PI controller tuning problem, we aim to determine which technique yields better results in terms of stability and overshoot tuning. In our comparative study, we provide a detailed explanation of both GA and PSO algorithms, focusing on their working principles and mathematical formulations. We also describe how these algorithms can be applied to the PI controller tuning problem. Furthermore, we highlight the key differences between GA and PSO, shedding light on their strengths and weaknesses. To assess the performance of GA and PSO, we conduct several experiments using different benchmark functions and step response models. We measure the stability and overshoot metrics for various parameter settings obtained through GA and PSO. By thoroughly analyzing the obtained results, we draw meaningful conclusions regarding the effectiveness of each technique. Our findings demonstrate that both GA and PSO exhibit promising results in optimizing PI controller tuning. These observations provide valuable insights and guidelines for choosing the appropriate algorithm based on specific control requirements. In conclusion, this comparative study is thought to contribute to the field of control systems engineering by offering a comprehensive analysis of GA and PSO techniques in the context of PI controller tuning. By highlighting their strengths and weaknesses, it is aimed to provide researchers and practitioners with valuable information for making informed decisions when optimizing control parameters for stability and overshoot reduction purposes.

Keywords

PI Controller Overshoot Step Response Stability Genetic Algorithm Particle Swarm Optimization

References

  • G. Cui, J. Yu and Q. G. Wang, “Finite-time adaptive fuzzy control for MIMO nonlinear systems with input saturation via improved command-filtered backstepping,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 52, no. 2, pp. 980-989, 2020.
  • Y. Ji, X. Jiang and L. Wan, “Hierarchical least squares parameter estimation algorithm for two-input Hammerstein finite impulse response systems, Journal of the Franklin Institute, vol. 357, no. 8, pp. 5019-5032, 2020.
  • Y. Ji and Z. Kang, “Three‐stage forgetting factor stochastic gradient parameter estimation methods for a class of nonlinear systems,” International Journal of Robust and Nonlinear Control, vol. 31, no. 3, pp. 971-987, 2021.
  • B. Obrenovic, J. Du, D. Godinic, D. Tsoy, M. A. S. Khan, and I. Jakhongirov, “Sustaining enterprise operations and productivity during the COVID-19 pandemic:“Enterprise Effectiveness and Sustainability Model,” Sustainability, vol. 12, no. 15, p. 5981, 2020.
  • M. Kamalahmadi, M. Shekarian, and M. Mellat Parast, “The impact of flexibility and redundancy on improving supply chain resilience to disruptions,” International Journal of Production Research, vol. 60, no. 6, pp. 1992-2020, 2022.
  • Z. Yu, A. Razzaq, A. Rehman, A. Shah, K. Jameel and R. S. Mor, “Disruption in global supply chain and socio-economic shocks: a lesson from COVID-19 for sustainable production and consumption,” Operations Management Research, pp. 1-16, 2021.
  • M. Kosmecki, R. Rink, A. Wakszyńska, R. Ciavarella, M. Di Somma, C. N. Papadimitriou, and G. Graditi, “A methodology for provision of frequency stability in operation planning of low inertia power systems,” Energies, vol. 14, no. 3, p. 737, 2021.
  • M. Hu, W. Hua, G. Ma, S. Xu, and W. Zeng, “Improved current dynamics of proportional-integral-resonant controller for a dual three-phase FSPM machine,” IEEE Transactions on Industrial Electronics, vol. 68, no. 12, pp. 11719-11730, 2020.
  • J. Park, H. Kim, K. Hwang, and S. Lim, “Deep reinforcement learning based dynamic proportional-integral (PI) gain auto-tuning method for a robot driver system,” IEEE Access, vol. 10, pp. 31043-31057, 2022.
  • A. W. Khawaja, N. A. M. Kamari, M. A. A. M. Zainuri, S. Abd Halim, M. A. Zulkifley, S. Ansari, and A. S. Malik, “Angle stability improvement using optimised proportional integral derivative with filter controller,” Heliyon, 2024.
  • S. M. Y. Younus, U. Kutbay, J. Rahebi, and F. Hardalaç, “Hybrid gray wolf optimization–proportional integral based speed controllers for brush-less dc motor,” Energies, vol. 16, no. 4, p. 1640, 2023.
  • D. F. Zambrano-Gutierrez, J. M. Cruz-Duarte, J. G. Avina-Cervantes, J. C. Ortiz-Bayliss, J. J. Yanez-Borjas, and I. Amaya, “Automatic design of metaheuristics for practical engineering applications,” IEEE Access, vol. 11, pp. 7262-7276, 2023.
  • E. Bogar and S. Beyhan, “Adolescent Identity Search Algorithm (AISA): A novel metaheuristic approach for solving optimization problems,” Applied Soft Computing, vol. 95, p. 106503, 2020.
  • A. A. Ameen, “Metaheuristic Optimization Algorithms in Applied Science and Engineering Applications,” Doktoral Thesis, 2024.
  • A. Mojtahedi, M. Dadashzadeh and M. Kouhi, “Developing a predictive method based on the vibration behavior of a naval ship hull model using hybrid fuzzy meta-heuristic algorithms,” Ocean Engineering, vol. 311, p. 118994, 2024.
  • O. Rodríguez-Abreo, J. M. Garcia-Guendulain, "Genetic algorithm-based tuning of backstepping controller for a quadrotor-type unmanned aerial vehicle," Electronics, 2020. mdpi.com
  • Y. Tian, Y. Zhang, Y. Su, and X. Zhang, "Balancing objective optimization and constraint satisfaction in constrained evolutionary multiobjective optimization," in IEEE Transactions on ..., 2021. researchgate.net
  • G. D’Angelo, and F. Palmieri, “GGA: A modified genetic algorithm with gradient-based local search for solving constrained optimization problems,” Information Sciences, vol. 547, pp. 136-162, 2021.
  • A. Sohail, “Genetic algorithms in the fields of artificial intelligence and data sciences,” Annals of Data Science, vol. 10, no. 4, pp. 1007-1018, 2023.
  • A. G. Gad, "Particle swarm optimization algorithm and its applications: a systematic review," Archives of computational methods in engineering, 2022. springer.com
  • H. Maghfiroh, M. Nizam, M. Anwar, and A. Ma’Arif, “Improved LQR control using PSO optimization and Kalman filter estimator,” IEEE Access, vol. 10, pp. 18330-18337, 2022.
  • M. N. Muftah, A. A. M. Faudzi, S. Sahlan, and M. Shouran, “Modeling and fuzzy FOPID controller tuned by PSO for pneumatic positioning system,” Energies, vol. 15, no. 10, p. 3757, 2022.
  • Basilio, J. C., and Matos, S. R. (2002). Design of PI and PID controllers with transient performance specification. IEEE Transactions on education, 45(4), 364-370.
  • A. Jamison Hill, “Towards Real Time Optimal Auto-tuning of PID Controllers,” Doctoral Thesis, 2013.
  • Salimi, H., Zakipour, A., and Asadi, M. (2022). A novel analytical approach for time-response shaping of the pi controller in field oriented control of the permanent magnet synchronous motors. Journal of Electrical and Computer Engineering Innovations (JECEI), 10(2), 463-476.
  • M. Saiful Islam Aziz, “Improved gravitational search algorithm for proportional integral derivative controller tuning in process control system”, Doctoral Thesis, 2016.
  • Kristiansson, B., and Lennartson, B. (2006). Robust tuning of PI and PID controllers: using derivative action despite sensor noise. IEEE Control Systems Magazine, 26(1), 55-69.
  • I. De Jesus Diaz Rodriguez, “Modern Design of Classical Controllers,” 2017.
  • R. Pagilla, P. Cimino and D. Knittel, ”Design of fixed structure controllers for web tension control,” 2007.
  • Z. Chen, Y. S. Hao, Z. Su and L. Sun, “Data-driven iterative tuning based active disturbance rejection control for FOPTD model,” ISA transactions, vol. 128, pp. 593-605., 2022.
  • H. Meneses, O. Arrieta, F. Padula, A. Visioli and R. Vilanova, “Fopi/fopid tuning rule based on a fractional order model for the process,” Fractal and Fractional, vol. 6, no. 9, p. 478, 2022.
  • P. Ghorai, “Online Parameters Estimation of Time-Delayed Dynamics of Processes for Industrial Use, “ International Journal of Industrial Engineering, vol. 29, no. 4, 2022.
  • T. George and V. Ganesan, “Optimal tuning of PID controller in time delay system: A review on various optimization techniques,” Chemical Product and Process Modeling, vol. 17, no. 1, pp. 1-28, 2022.
  • L. Abdullah, Z. Jamaludin, T. H. Chiew, N. A. Rafan and M. Y. Yuhazri, “Extensive Tracking Performance Analysis of Classical feedback control for XY Stage ballscrew drive system,” Applied Mechanics and Materials, vol. 229, pp. 750-755, 2012.
  • U. Agrawal, P. Etingov and R. Huang, “Advanced Performance Metrics and Sensitivity Analysis for Model Validation and Calibration,” Authorea Preprint, 2023.
  • M. Gen and L. Lin, “Genetic algorithms and their applications,” In Springer handbook of engineering statistics (pp. 635-674). London: Springer London, 2023.
  • Z. Z. Wang and A. Sobey, “A comparative review between Genetic Algorithm use in composite optimisation and the state-of-the-art in evolutionary computation,” Composite Structures, vol.233, 2020.
  • H. R. R. Zaman and F. S. Gharehchopogh, F. S. (2022). An improved particle swarm optimization with backtracking search optimization algorithm for solving continuous optimization problems,” Engineering with Computers, vol. 38, no. 4, pp. 2797-2831 2022.
  • Z. Yu, Z. Si, X. Li, D. Wang and H. Song, “A novel hybrid particle swarm optimization algorithm for path planning of UAVs,” IEEE Internet of Things Journal, vol. 9, no. 22, pp. 22547-22558, 2022
  • A. G. Gad, “Particle swarm optimization algorithm and its applications: a systematic review,” Archives of computational methods in engineering, vol. 29, no. 5, pp. 2531-2561, 2022.
  • H. Zhao, H. Yao, Y. Jiao, T. Lou, andY. Wang, “An Improved Beetle Antennae Search Algorithm Based on Inertia Weight and Attenuation Factor,” Mathematical Problems in Engineering, vol. 1, 2022.
  • J. Chrouta, F. Farhani, F. and A. Zaafouri, “A modified multi swarm particle swarm optimization algorithm using an adaptive factor selection strategy,” Transactions of the Institute of Measurement and Control, vol. 0, no. 0, 2021.
  • B. Durmuş, “Opposite Based Crow Search Algorithm for Solving Optimization Problem,” International Scientific and Vocational Studies Journal, vol. 5, no. 2, pp. 164-170, 2021.
  • B. Şenol and U. Demiroğlu, “Analytical Design of PI Controllers for First Order plus Time Delay Systems,” International Scientific and Vocational Studies Journal, vol. 2, no. 2, pp. 40–47, 2018.
There are 44 citations in total.

Details

Primary Language English
Subjects Satisfiability and Optimisation
Journal Section Articles
Authors

Bilal Şenol 0000-0002-3734-8807

Uğur Demiroğlu 0000-0002-0000-8411

Publication Date June 30, 2025
Submission Date November 2, 2024
Acceptance Date January 8, 2025
Published in Issue Year 2025 Volume: 9 Issue: 1

Cite

APA Şenol, B., & Demiroğlu, U. (2025). Optimizing PI Controller for Stability and Overshoot in Step Response Using GA and PSO Techniques, A Comparative Study. International Scientific and Vocational Studies Journal, 9(1), 12-23. https://doi.org/10.47897/bilmes.1578027
AMA Şenol B, Demiroğlu U. Optimizing PI Controller for Stability and Overshoot in Step Response Using GA and PSO Techniques, A Comparative Study. ISVOS. June 2025;9(1):12-23. doi:10.47897/bilmes.1578027
Chicago Şenol, Bilal, and Uğur Demiroğlu. “Optimizing PI Controller for Stability and Overshoot in Step Response Using GA and PSO Techniques, A Comparative Study”. International Scientific and Vocational Studies Journal 9, no. 1 (June 2025): 12-23. https://doi.org/10.47897/bilmes.1578027.
EndNote Şenol B, Demiroğlu U (June 1, 2025) Optimizing PI Controller for Stability and Overshoot in Step Response Using GA and PSO Techniques, A Comparative Study. International Scientific and Vocational Studies Journal 9 1 12–23.
IEEE B. Şenol and U. Demiroğlu, “Optimizing PI Controller for Stability and Overshoot in Step Response Using GA and PSO Techniques, A Comparative Study”, ISVOS, vol. 9, no. 1, pp. 12–23, 2025, doi: 10.47897/bilmes.1578027.
ISNAD Şenol, Bilal - Demiroğlu, Uğur. “Optimizing PI Controller for Stability and Overshoot in Step Response Using GA and PSO Techniques, A Comparative Study”. International Scientific and Vocational Studies Journal 9/1 (June 2025), 12-23. https://doi.org/10.47897/bilmes.1578027.
JAMA Şenol B, Demiroğlu U. Optimizing PI Controller for Stability and Overshoot in Step Response Using GA and PSO Techniques, A Comparative Study. ISVOS. 2025;9:12–23.
MLA Şenol, Bilal and Uğur Demiroğlu. “Optimizing PI Controller for Stability and Overshoot in Step Response Using GA and PSO Techniques, A Comparative Study”. International Scientific and Vocational Studies Journal, vol. 9, no. 1, 2025, pp. 12-23, doi:10.47897/bilmes.1578027.
Vancouver Şenol B, Demiroğlu U. Optimizing PI Controller for Stability and Overshoot in Step Response Using GA and PSO Techniques, A Comparative Study. ISVOS. 2025;9(1):12-23.


Creative Commons Lisansı


Creative Commons Atıf 4.0 It is licensed under an International License