Gökhan YÜKSEK, Ahmet Naci METE, Alkan ALKAYA

PID Parametrelerinin LQR ve GA Tabanlı Optimizasyonu: Sıvı Seviye Kontrol Uygulaması

Bu çalışmada iki farklı metot kullanılarak PID parametre ayarlaması yapılmıştır. İlk olarak Doğrusal Karesel Düzenleyici (LQR) yaklaşımı kullanılarak maliyet fonksiyonu minimize edilmiş ve optimal parametreler elde edilerek LQR tabanlı PID denetleyici tasarlanmıştır. Ardından LQR maliyet fonksiyonunun minimizasyonu için Genetik Algoritma (GA) kullanılmış ve GA tabanlı PID denetleyici tasarlanmıştır. Tasarlanan PID denetleyiciler bir sıvı seviye kontrol sisteminde benzetimsel ve deneysel olarak test edilmiş ve performans karşılaştırmaları yapılmıştır. Deneysel sonuçlar, GA tabanlı PID'nin performansının LQR tabanlı PID'den performans indisleri açısından daha başarılı olduğunu göstermektedir. GA Tabanlı PID için normalize edilmiş ITSE indisi 0.6479 ile daha başarılı performans sergilemiştir.

Anahtar Kelimeler:

Doğrusal Karesel Düzenleyici, PID Ayarlama, Genetik Algoritma

LQR and GA based PID Parameter Optimization: Liquid Level Control Application

In this study, PID parameter tuning was made by using two different methods. Firstly, LQR based PID controller is designed by minimizing the cost function by obtaining Linear Quadratic Regulator (LQR) approach. Then Genetic Algorithm (GA) was used for minimizing the LQR cost function and GA based PID controller was designed. The designed PID controllers have been simulated and experimentally tested in a liquid level control system and performance comparisons have been made. Experimental results show that the performance of the GA based PID is better than LQR based PID in terms of performance indices. Normalized ITSE index of 0.6479 is achieved for better performing GA based PID.

Keywords:

Linear quadratic regulator, PID tuning, genetic algorithm,

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H. N. Koivo and J. T. Tanttu, “Tuning of PID Conrollers: Survey of Siso and Mimo Techniques,” IFAC Proc. Vol., 2017.
A. Ghosh, T. R. Krishnan, and B. Subudhi, “Brief Paper - Robust proportional-integral-derivative compensation of an inverted cart-pendulum system: an experimental study,” IET Control Theory Appl., 2012.
G. Lin and G. Liu, “Tuning PID controller using adaptive genetic algorithms,” in ICCSE 2010 - 5th International Conference on Computer Science and Education, Final Program and Book of Abstracts, 2010.
T. Hägglund and K. J. Åström, “Revisiting The Ziegler-Nichols Tuning Rules For Pi Control,” Asian J. Control, 2008.
W. Chunchen, C. Feng, Z. Guang, Y. Ming, L. Li, and W. Taihu, “Desing of Genetic Algorithm Optimized PID Controller for Gas Mixture System,” in 2017 IEEE 13th International Conference on Electronic Measurement & Instruments, 2017.
B. Nagaraj, S. Subha, and B. Rampriya, “Tuning algorithms for PID controller using soft computing techniques,” Int. J. Comput. Sci. Netw. Secur. IJCSNS, 2008.
D. A. R. Wati and R. Hidayat, “Genetic algorithm-based PID parameters optimization for air heater temperature control,” in Proceedings of 2013 International Conference on Robotics, Biomimetics, Intelligent Computational Systems, ROBIONETICS 2013, 2013.
Z. Cheng and H. Xu, “PID Controller Parameters Optimization Based on Artificial Fish Swarm Algorithm,” Fifth Int. Conf. Intell. Comput. Technol. Autom., 2012.
H. Fang and L. Chen, “Application of an enhanced PSO algorithm to optimal tuning of PID gains,” in 2009 Chinese Control and Decision Conference, CCDC 2009, 2009.
B. Sravan, T. S. Babu, and N. Rajasekar, “Tuning PID Controller for Inverted Pendulum Using Genetic Algorithm,” Adv. Syst. Control Autom., pp. 395–404, 2018.
M. K. Al-Smadi, Y. Hu, and Y. Mahmoud, “LQR-based PID Voltage Controller for Photovoltaic Systems,” 44th Annu. Conf. IEEE Ind. Electron. Soc., pp. 1854–1859, 2018.
O. Saleem and M. Rizwan, “Performance optimization of LQR-based PID controller for DC-DC buck converter via iterative-learning-tuning of state-weighting matrix,” Int. J. Numer. Model. Electron. Networks, Devices Fields, vol. 32, 2019.
T. Wang, Q. Wang, Y. Hou, and D. Chaoyang, “Suboptimal controller design for flexible launch vehicle based on genetic algorithm: selection of the weighting matrices Q and R,” IEEE Int. Conf. Intell. Comput. Intell. Syst., vol. 2, pp. 720–724, 2009.
S. Das, I. Pan, K. Halder, S. Das, and A. Gupta, “LQR based improved discrete PID controller design via optimum selection of weighting matrices using fractional order integral performance index,” Appl. Math. Model., 2013.
S. Saha, S. Das, S. Das, and A. Gupta, “A conformal mapping based fractional order approach for sub-optimal tuning of PID controllers with guaranteed dominant pole placement,” Commun. Nonlinear Sci. Numer. Simul., 2012.
S. Brunton and N. Kutz, Data Driven Science and Engineering. Cambridge University Press, 978-1-108-42209-3, 2019.