Since fractional dynamic system models can represent real-life systems more accurately, interest in fractional order system models and fraction order control has increased. This study presents fractional order PI controller design according to minimum angle pole placement method in v-field that was used for stability analysis of fraction order system models, and the effects of different target minimum angle values on the robust control performance of these designs are considered. For this purpose, fractional order PI controller designs were carried out for selected three different target angle values according to minimum angle pole placement in v-domain. Here, genetic algorithm is used to place the minimum angle system poles to the specified target angles and thus fractional order PI controller coefficients were optimized. In this study, two illustrative design examples are demonstrated, and fractional order PI control system designs, which place minimum angle system poles to selected target points in the stability region, are obtained in these examples. The robust stability performance of the PI controller designs obtained for different target angle configurations were examined by changing gain coefficient of plant functions. According to findings obtained, the target angle regions that provide robust control performance, have been investigated.
Alagoz, B.B. (2018). Fractional order linear time invariant system stabilization by brute-force search, Transactions of the Institute of Measurement and Control, 40(5), 1447–1456. Doi: 10.1177/0142331216685391
Alagoz, B.B. , Yeroglu, C. , Senol B. , and Ates, A. (2015). Probabilistic robust stabilization of fractional order systems with interval uncertainty, ISA Transactions, 57, 101-110. Doi: 10.1016/j.isatra.2015.01.003
Alagoz, B.B., Alisoy, G., Alagoz, S., Alisoy, H. (2017). A note on applications of time-domain solution of Cole permittivity models. Optik, 139, 272-282. Doi: 10.1016/j.ijleo.2017.04.010
Chen, Y.Q. , Ahn, H.S. and Podlubny, I. (2006). Robust stability check of fractional order linear time invariant systems with interval uncertainties, Signal Processing, 86, 2611-2618. Doi: 10.1109/ICMA.2005.1626549
Chen, Y.Q. , Hu, C.H. and Moore, K.L. (2003). Relay feedback tuning of robust PID controllers with iso-damping Property, in 42nd IEEE Conference on Decision and Control, Maui, Hawaii.
Chen Y.Q., Moore K.L., (2005). Relay feedback tuning of robust PID controllers with iso-damping property, EEE Transactions on Systems, Man, and Cybernetics Part B, 35, 23-31. Doi: 10.1109/TSMCB.2004.837950
Chen, Y.Q. , Petras, I. and Xue, D. (2009). Fractional Order Control - A Tutorial, American Control Conference, Missouri, USA, 1397-1411. Doi: 10.1109/ACC.2009.5160719
Cole, K.S., Cole, R.H. (1941). Dispersion and absorption in dielectrics - I. alternating current characteristics, Journal of Chemical Physics, 9, 341-351. Doi: 10.1063/1.1750906
El-Sayed, A.M. (1996). Fractional-order diffusion-wave equation. International Journal of Theoretical Physics, 35(2), 311-322.
Hamamci, S.E. (2007). An algorithm for stabilization of fractional-order time delay systems using fractional-order PID controllers, Automatic Control, IEEE Transactions on, 52, 1964-1969. Doi: 10.1109/TAC.2007.906243
Mainardi, F. (1996). Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Chaos, Solitons & Fractals, 7(9), 1461-1477. Doi: 10.1016/0960-0779(95)00125-5
Matignon, D. (1996). Stability results on fractional differential equations to control processing, in: Processings, Computational Engineering in Systems and Application Multiconference, IMACS, IEEE-SMC, 2, 963-968.
Monje, C.A. , Vinagre, B.M., Feliu, V. , Chen, Y.Q. (2008).Tuning and auto-tuning of fractional order controllers for industry applications, Control. Eng. Pract. , 16( 7), 798-812. Doi: 10.1016/j.conengprac.2007.08.006
Oustaloup, A. , Mathieu, B. (1999). La commande CRONE: du scalaire au multivariable, HERMES, Paris.
Petras, I. (2009). Stability of Fractional-order systems with rational orders: A Survey, Fractional Calculus and Applied Analysis, 12, 269-298.Podlubny, I. (1999). Fractional-order systems and -controllers, IEEE Trans. Automatic Control, 44(1), 208-214.
Radwan, A.G. , Soliman, A.M., Elwakil, A.S. and Sedeek, A. (2009). On the stability of linear systems with fractional-order elements, Chaos, Solitons& Fractals, 40, 2317-2328.Doi: 10.1016/j.chaos.2007.10.033
Senol, B. , Ates, A. , Alagoz, B.B. and Yeroglu, C. (2014). A numerical investigation for robust stability of fractional-order uncertain systems, ISA transactions, 53, 189-198. Doi: 10.1016/j.isatra.2013.09.004
Senol, B. and Yeroglu, C. (2012). Robust stability analysis of fractional order uncertain polynomials, In Proceedings of the 5th IFAC Workshop on Fractional Differentiation and its Applications.
Tan, N. , Kaya, I. , Yeroglu, C. and Atherton, D.P. (2006). Computation of stabilizing PI and PID controllers using the stability boundary locus, Energy Conversion and Management, 47, 3045-3058. Doi: 10.1016/j.enconman.2006.03.022
Tan, N. , Ozguven, O.F. and Ozyetkin, M.M. (2009). Robust stability analysis of fractional order interval polynomials, ISA transactions, 48, 166-172. Doi: 10.1016/j.isatra.2009.01.002
Tufenkci, S., Senol, B., Alagoz, B.B. (2018). Stabilization of Fractional Order PID Controllers for Time-Delay Fractional Order Plants by Using Genetic Algorithm. International Conference on Artificial Intelligence and Data Processing IDAP 2018, Malatya, Turkey, 1-4. Doi: 10.1109/IDAP.2018.8620770
Xue, D., Chen, Y.Q. (2002). A comparative introduction of four fractional order controllers. 4th World Congress on Intelligent Control and Automation, 3228-3235. Doi: 10.1109/WCICA.2002.1020131
V-alanında Minimum Açılı Kutup Yerleşimi Yöntemine Göre Kesir Dereceli PI Denetçi Tasarımı ve Dayanıklı Kontrol Performansının Bir İncelenmesi
Kesir dereceli dinamik sistem modelleri gerçek hayatta kullanılan sistemleri daha doğru bir şekilde temsil edilebilmesi nedeni ile kesir dereceli sistem modellerine ve kesir dereceli kontrole olan ilgi artırmıştır. Bu çalışma kesir dereceli sistem modellerinin kararlılık analizi için kullanılan v-alanı içerisinde, minimum açılı kutup yerleştirme yöntemine göre kesir dereceli PI denetçi tasarımlarını sunmaktadır ve farklı hedef açı değerlerinin bu tasarımların dayanıklı kontrol performansına etkileri incelenmektedir. Bu amaçla, kesir dereceli PI denetçi tasarımları seçilen üç farklı hedef açı değeri için v-alanında kutup yerleştirme yöntemine göre gerçekleştirilmiştir Burada, minimum açılı sistem kutuplarının belirlenmiş hedef açılara yerleştirilmesi için genetik algoritma kullanılmış ve böylece kesir dereceli PI denetçi katsayıları optimize edilmiştir. Bu çalışmada iki örnek uygulama gösterilmekte ve bu örnek uygulamalarda kararlılık bölgesi içerisinde seçilen hedef noktalara minimum açılı sistem kutuplarının yerleştiren kesir dereceli PI denetçi tasarımları elde edilmiştir. Elde edilen PI denetçi tasarımları için plant fonksiyonlarının kazanç katsayısı değiştirilerek farklı hedef açı konfigürasyonları için elde edilen kontrol sistemlerinin dayanıklı kontrol performansları incelenmiştir. Elde edilen bulgulara göre dayanıklı kontrol performansı sağlayan hedef açı bölgeleri araştırılmıştır.
Alagoz, B.B. (2018). Fractional order linear time invariant system stabilization by brute-force search, Transactions of the Institute of Measurement and Control, 40(5), 1447–1456. Doi: 10.1177/0142331216685391
Alagoz, B.B. , Yeroglu, C. , Senol B. , and Ates, A. (2015). Probabilistic robust stabilization of fractional order systems with interval uncertainty, ISA Transactions, 57, 101-110. Doi: 10.1016/j.isatra.2015.01.003
Alagoz, B.B., Alisoy, G., Alagoz, S., Alisoy, H. (2017). A note on applications of time-domain solution of Cole permittivity models. Optik, 139, 272-282. Doi: 10.1016/j.ijleo.2017.04.010
Chen, Y.Q. , Ahn, H.S. and Podlubny, I. (2006). Robust stability check of fractional order linear time invariant systems with interval uncertainties, Signal Processing, 86, 2611-2618. Doi: 10.1109/ICMA.2005.1626549
Chen, Y.Q. , Hu, C.H. and Moore, K.L. (2003). Relay feedback tuning of robust PID controllers with iso-damping Property, in 42nd IEEE Conference on Decision and Control, Maui, Hawaii.
Chen Y.Q., Moore K.L., (2005). Relay feedback tuning of robust PID controllers with iso-damping property, EEE Transactions on Systems, Man, and Cybernetics Part B, 35, 23-31. Doi: 10.1109/TSMCB.2004.837950
Chen, Y.Q. , Petras, I. and Xue, D. (2009). Fractional Order Control - A Tutorial, American Control Conference, Missouri, USA, 1397-1411. Doi: 10.1109/ACC.2009.5160719
Cole, K.S., Cole, R.H. (1941). Dispersion and absorption in dielectrics - I. alternating current characteristics, Journal of Chemical Physics, 9, 341-351. Doi: 10.1063/1.1750906
El-Sayed, A.M. (1996). Fractional-order diffusion-wave equation. International Journal of Theoretical Physics, 35(2), 311-322.
Hamamci, S.E. (2007). An algorithm for stabilization of fractional-order time delay systems using fractional-order PID controllers, Automatic Control, IEEE Transactions on, 52, 1964-1969. Doi: 10.1109/TAC.2007.906243
Mainardi, F. (1996). Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Chaos, Solitons & Fractals, 7(9), 1461-1477. Doi: 10.1016/0960-0779(95)00125-5
Matignon, D. (1996). Stability results on fractional differential equations to control processing, in: Processings, Computational Engineering in Systems and Application Multiconference, IMACS, IEEE-SMC, 2, 963-968.
Monje, C.A. , Vinagre, B.M., Feliu, V. , Chen, Y.Q. (2008).Tuning and auto-tuning of fractional order controllers for industry applications, Control. Eng. Pract. , 16( 7), 798-812. Doi: 10.1016/j.conengprac.2007.08.006
Oustaloup, A. , Mathieu, B. (1999). La commande CRONE: du scalaire au multivariable, HERMES, Paris.
Petras, I. (2009). Stability of Fractional-order systems with rational orders: A Survey, Fractional Calculus and Applied Analysis, 12, 269-298.Podlubny, I. (1999). Fractional-order systems and -controllers, IEEE Trans. Automatic Control, 44(1), 208-214.
Radwan, A.G. , Soliman, A.M., Elwakil, A.S. and Sedeek, A. (2009). On the stability of linear systems with fractional-order elements, Chaos, Solitons& Fractals, 40, 2317-2328.Doi: 10.1016/j.chaos.2007.10.033
Senol, B. , Ates, A. , Alagoz, B.B. and Yeroglu, C. (2014). A numerical investigation for robust stability of fractional-order uncertain systems, ISA transactions, 53, 189-198. Doi: 10.1016/j.isatra.2013.09.004
Senol, B. and Yeroglu, C. (2012). Robust stability analysis of fractional order uncertain polynomials, In Proceedings of the 5th IFAC Workshop on Fractional Differentiation and its Applications.
Tan, N. , Kaya, I. , Yeroglu, C. and Atherton, D.P. (2006). Computation of stabilizing PI and PID controllers using the stability boundary locus, Energy Conversion and Management, 47, 3045-3058. Doi: 10.1016/j.enconman.2006.03.022
Tan, N. , Ozguven, O.F. and Ozyetkin, M.M. (2009). Robust stability analysis of fractional order interval polynomials, ISA transactions, 48, 166-172. Doi: 10.1016/j.isatra.2009.01.002
Tufenkci, S., Senol, B., Alagoz, B.B. (2018). Stabilization of Fractional Order PID Controllers for Time-Delay Fractional Order Plants by Using Genetic Algorithm. International Conference on Artificial Intelligence and Data Processing IDAP 2018, Malatya, Turkey, 1-4. Doi: 10.1109/IDAP.2018.8620770
Xue, D., Chen, Y.Q. (2002). A comparative introduction of four fractional order controllers. 4th World Congress on Intelligent Control and Automation, 3228-3235. Doi: 10.1109/WCICA.2002.1020131
Tüfenkçi, S., Şenol, B., & Alagöz, B. B. (2019). V-alanında Minimum Açılı Kutup Yerleşimi Yöntemine Göre Kesir Dereceli PI Denetçi Tasarımı ve Dayanıklı Kontrol Performansının Bir İncelenmesi. Avrupa Bilim Ve Teknoloji Dergisi(17), 9-19.