Bulanık Bilişsel Harita Tabanlı PD Kontrolörler Kullanılarak Ters Sarkaç Sisteminin Stabilizasyonu

Yıl 2020, Ejosat Özel Sayı 2020 (HORA), 156 - 164, 15.08.2020

Aykut Denizci Cenk Ulu

https://doi.org/10.31590/ejosat.779601

Öz

Yumuşak hesaplama yöntemleri doğrusal olmayan sistemlerin modellenmesi ve kontrolünde sıklıkla kullanılan yöntemlerdir. Buna karşın, yumuşak hesaplama yöntemlerinden biri olan bulanık bilişsel harita yöntemi, kontrol uygulamalarında ana kontrolör olarak nadiren kullanılmaktadır. Bu çalışmada bulanık bilişsel harita tabanlı PD kontrolör yapısı önerilmiş ve bu yöntem doğrusal olmayan, kararsız ve eksik tahrikli bir sistem olan ters sarkaç sisteminin stabilizasyonu için kullanılmıştır. Önerilen kontrolör hata ve hatanın değişimi olmak üzere iki adet giriş değişkenine sahiptir. Önerilen PD kontrolör yapısında, kesin değerlere sahip girişler bulanık bilişsel harita hesaplama sürecinde değerlendirilebilmek için bulanıklaştırılmaktadır. Ardından bulanıklaştırılmış bu girişler ile kontrolör çıkışı arasındaki nedensel ilişkiler ağırlıklandırma parametreleri kullanılarak tanımlanmaktadır. Son olarak ise bir aktivasyon fonksiyonu kullanarak sisteme uygulanacak kesin çıkış değeri elde edilmektedir. Bulanıklaştırma işlemi için kullanılan üyelik fonksiyonlarının yapıları ve ayrıca aktivasyon fonksiyonun yapısı, önerilen bulanık bilişsel harita tabanlı PD kontrolörün doğrusal olmayan karakteristiğini belirlemektedir. Önerilen kontrolör bir çıkış kazancı ve iki ağırlık parametresi olmak üzere üç adet ayar parametresine sahiptir. Önerilen bulanık bilişsel harita tabanlı PD kontrolörün etkinliğini ve dayanıklılığını göstermek için ters sarkaç sistemi üzerinden benzetim çalışmaları gerçekleştirilmiştir. Ayrıca önerilen PD kontrolörün performansı geleneksel yapıdaki PD kontrolör performansı ile karşılaştırılmıştır. Tüm kontrolör parametreleri genetik algoritma kullanılarak belirlenmiştir. Karşılaştırma sonuçları göstermiştir ki önerilen bilişsel harita tabanlı PD kontrolör geleneksel PD kontrolörden daha iyi bir kontrol performans göstermektedir.

Anahtar Kelimeler

Bulanık bilişsel harita, Üyelik fonksiyonu, Doğrusal olmayan sistem, Ters sarkaç, PD kontrol, Stabilizasyon

Stabilization of Inverted Pendulum System Using Fuzzy Cognitive Map Based PD Controllers

Öz

Soft computing techniques are frequently used in modeling and control applications of nonlinear systems. However, the fuzzy cognitive map method, which is one of the soft computing techniques, is rarely used in control applications as a main controller. In this study, a fuzzy cognitive map based PD controller structure is introduced and used for the stabilization of an inverted pendulum system which is a nonlinear, unstable, and under-actuated system. The proposed controller has two inputs which are the error and the change of error. In the proposed PD controller structure, the crisp input values are fuzzified to be handled in a fuzzy cognitive map process. Then, causal relationships between fuzzified inputs and a control output are defined by using weight parameters. Finally, the crisp control output value which will be applied to the system is obtained by using an activation function. The types of membership functions used for the fuzzification process and the activation function determine the nonlinear characteristics of the proposed fuzzy cognitive map based PD controller. The proposed controller has three tuning parameters which are one output gain and two weight parameters. To show the effectiveness and robustness of the proposed fuzzy cognitive map based PD controller, simulation studies are performed on an inverted pendulum system. Additionally, the performance of the proposed controller is compared with a PD controller. All controller parameters are determined by using a genetic algorithm. Comparison results indicate that the proposed fuzzy cognitive map based PD controller shows better control performance than the classical PD controller.

Anahtar Kelimeler

Fuzzy cognitive map, Membership function, Nonlinear system, Inverted pendulum, PD control, Stabilization

Kaynakça

• Er, M., Deng, C., & Wang, N. (2018). A Novel Fuzzy Logic Control Method for Multi-Agent Systems with Actuator Faults. 2018 IEEE International Conference On Fuzzy Systems (FUZZ-IEEE), 1-7.
• Amuthameena, S., & Monisa, S. (2017). Design of fuzzy logic controller for a non-linear system. 2017 IEEE International Conference On Electrical, Instrumentation And Communication Engineering (ICEICE), 1-7.
• Azizi, M., Ejlali, R., Mousavi Ghasemi, S., & Talatahari, S. (2019). Upgraded Whale Optimization Algorithm for fuzzy logic based vibration control of nonlinear steel structure. Engineering Structures, 192, 53-70.
• Zhang, X., Ma, X., Zhu, H., & Liu, H. (2017). Neural network controller design for uncertain nonlinear systems based on backstepping control algorithm. 2017 29Th Chinese Control And Decision Conference (CCDC), 1623-1627.
• Zhang, Y., Tao, G., & Chen, M. (2016). Adaptive Neural Network Based Control of Noncanonical Nonlinear Systems. IEEE Transactions On Neural Networks And Learning Systems, 27(9), 1864-1877.
• Slama, S., Errachdi, A., & Benrejeb, M. (2018). Model reference adaptive control for MIMO nonlinear systems using RBF neural networks. 2018 International Conference On Advanced Systems And Electric Technologies (IC_ASET), 346-351.
• Kosko, B. (1986). Fuzzy cognitive maps. International Journal Of Man-Machine Studies, 24(1), 65-75. Papageorgiou, E., & Salmeron, J. (2013). A Review of Fuzzy Cognitive Maps Research During the Last Decade. IEEE Transactions On Fuzzy Systems, 21(1), 66-79.
• Arruda, L., Mendonca, M., Neves, F., Chrun, I., & Papageorgiou, E. (2018). Artificial Life Environment Modeled by Dynamic Fuzzy Cognitive Maps. IEEE Transactions On Cognitive And Developmental Systems, 10(1), 88-101.
• Salmeron, J. (2009). Supporting Decision Makers with Fuzzy Cognitive Maps. Research-Technology Management, 52(3), 53-59.
• Najafi, A., Amirkhani, A., Papageorgiou, E., & Mosavi, M. (2017). Medical decision making based on fuzzy cognitive map and a generalization linguistic weighted power mean for computing with words. 2017 IEEE International Conference On Fuzzy Systems (FUZZ-IEEE), 1-6.
• Yaman, D., & Polat, S. (2009). A fuzzy cognitive map approach for effect-based operations: An illustrative case. Information Sciences, 179(4), 382-403.
• Hajek, P., & Prochazka, O. (2016). Interval-valued fuzzy cognitive maps for supporting business decisions. 2016 IEEE International Conference On Fuzzy Systems (FUZZ-IEEE), 531-536.
• Sudhagar, C. (2019). Role of Fuzzy Cognitive Maps in Smart Education System. 2019 4Th MEC International Conference On Big Data And Smart City (ICBDSC), 1-6.
• Papageorgiou, E. (2011). Review study on fuzzy cognitive maps and their applications during the last decade. 2011 IEEE International Conference On Fuzzy Systems (FUZZ-IEEE 2011).
• Groumpos, P., & Stylios, C. (2000). Modelling supervisory control systems using fuzzy cognitive maps. Chaos, Solitons & Fractals, 11(1-3), 329-336.
• Stylios, C., & Groumpos, P. (2004). Modeling Complex Systems Using Fuzzy Cognitive Maps. IEEE Transactions On Systems, Man, And Cybernetics - Part A: Systems And Humans, 34(1), 155-162.
• Stylios, C., & Groumpos, P. (1999). Fuzzy Cognitive Maps: a model for intelligent supervisory control systems. Computers In Industry, 39(3), 229-238.
• Amirkhani, A., Shirzadeh, M., Papageorgiou, E., & Mosavi, M. (2016). Visual-based quadrotor control by means of fuzzy cognitive maps. ISA Transactions, 60, 128-142.
• Mendonça, M., Neves, F., de Arruda, L., Chrun, I., & Papageorgiou, E. (2016). Embedded Dynamic Fuzzy Cognitive Maps for Controller in Industrial Mixer. Intelligent Decision Technologies 2016, 57, 251-261.
• Farinaz, B., Abdul, R., Khairulmizam, S., & Hossein, E. (2017). Energy saving by applying the fuzzy cognitive map control in controlling the temperature and humidity of room. International Journal Of Physical Sciences, 12(1), 13-23.
• de Souza, L., Prieto Soares, P., Mendonca, M., Mourhir, A., & Papageorgiou, E. (2018). Fuzzy Cognitive Maps and Fuzzy Logic applied in industrial processes control. 2018 IEEE International Conference On Fuzzy Systems (FUZZ-IEEE), 1-8.
• Denizci, A., Karadeniz, S., & Ulu, C. Fuzzy Cognitive Map Based PI Controller Design. International Conference On Intelligent And Fuzzy Systems (INFUS 2020), in press.
• Bettayeb, M., Boussalem, C., Mansouri, R., & Al-Saggaf, U. (2014). Stabilization of an inverted pendulum-cart system by fractional PI-state feedback. ISA Transactions, 53(2), 508-516.
• Boubaker, O. (2013). The Inverted Pendulum Benchmark in Nonlinear Control Theory: A Survey. International Journal Of Advanced Robotic Systems, 10(5), 1-9.
• Chang, W., Hwang, R., & Hsieh, J. (2002). A self-tuning PID control for a class of nonlinear systems based on the Lyapunov approach. Journal Of Process Control, 12(2), 233-242.
• Prasad, L., Tyagi, B., & Gupta, H. (2014). Optimal Control of Nonlinear Inverted Pendulum System Using PID Controller and LQR: Performance Analysis Without and With Disturbance Input. International Journal Of Automation And Computing, 11(6), 661-670.
• Irfan, S., Mehmood, A., Razzaq, M., & Iqbal, J. (2018). Advanced sliding mode control techniques for Inverted Pendulum: Modelling and simulation. Engineering Science And Technology, An International Journal, 21(4), 753-759.
• Mun-Soo Park, & Dongkyoung Chwa. (2009). Swing-Up and Stabilization Control of Inverted-Pendulum Systems via Coupled Sliding-Mode Control Method. IEEE Transactions On Industrial Electronics, 56(9), 3541-3555.
• Siuka, A., & Schöberl, M. (2009). Applications of energy based control methods for the inverted pendulum on a cart. Robotics And Autonomous Systems, 57(10), 1012-1017.
• Messikh, L., Guechi, E., & Benloucif, M. (2017). Critically damped stabilization of inverted-pendulum systems using continuous-time cascade linear model predictive control. Journal Of The Franklin Institute, 354(16), 7241-7265.
• Gawthrop, P., & Wang, L. (2006). Intermittent predictive control of an inverted pendulum. Control Engineering Practice, 14(11), 1347-1356.
• Mishra, S., & Chandra, D. (2014). Stabilization and Tracking Control of Inverted Pendulum Using Fractional Order PID Controllers. Journal Of Engineering, 2014, 1-9.
• Roose, A., Yahya, S., & Al-Rizzo, H. (2017). Fuzzy-logic control of an inverted pendulum on a cart. Computers & Electrical Engineering, 61, 31-47.
• Jianqiang Yi, Yubazaki, N., & Hirota, K. (1999). Upswing and stabilization control of inverted pendulum and cart system by the SIRMs dynamically connected fuzzy inference model. FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315), 400-405.
• Upadhyay, D., Tarun, N., & Nayak, T. (2013). ANN based intelligent controller for inverted pendulum system. 2013 Students Conference On Engineering And Systems (SCES), 1-6.
• Zadeh, L. (1972). A Fuzzy-Set-Theoretic Interpretation of Linguistic Hedges. Journal Of Cybernetics, 2(3), 4-34.