İkinci derece zaman gecikmeli modeller için kesir dereceli oransal-integral denetleyici tasarımında analitik yaklaşım

Yıl 2022, Cilt: 37 Sayı: 1, 121 - 136, 10.11.2021

Bilal Şenol Uğur Demiroğlu Radek Matušů

https://doi.org/10.17341/gazimmfd.879929

Cited By: 1

Öz

Bu yayın, ikinci derece zaman gecikmeli modellerin kararlılık ve dayanıklı performansı için kesir dereceli oransal-integral denetleyicinin adım adım tasarımına odaklanmaktadır. Analitik olarak elde edilmiş denklemler genelleştirilmiştir ve söz konusu modeller için kullanılabilir. Yöntemin ana hedefi, Bode çizimindeki kazanç ve faz kesim frekansları arasında kalan faz eğrisini düzleştirmektir. Bu şekilde, kazanç değişimlerine karşı dayanıklılık sağlanacaktır. Bunun yanısıra, tüm sistemin kararlılığı temin edilecektir. Tasarım aşamasında, literatürde var olan çalışmaların aksine sadece kazanç kesim frekansı değil, kazanç ve faz kesim frekanslarının her ikisi de ele alınmıştır. Ayrıca, faz düzleştirme işlemi faz türevinin sıfıra eşitlenmesi ile sağlanmamıştır. Bu yayın, probleme farklı bir bakış açısı getirmektedir. İki farklı denetleyici hesaplanmıştır. İlk denetleyici, istenen kazanç kesim frekansı ve faz payı özelliklerini sağlamaktadır. İkinci ise faz kesim frekansı ve kazanç payını temin etmektedir. Daha sonra bu denetleyiciler bağlanmıştır ve her iki durumu da sağlayan tek bir denetleyici elde edilmiştir. Önerilen denklemler, literatürden iki farklı model üzerine uygulanmış ve sonuçlar grafiksel olarak verilmiştir.

Anahtar Kelimeler

SOPTD model, FOPI denetleyici, analitik tasarım, frekans özellikleri, BODE’nin ideal çevrimi

Analytical approach on the design of fractional order proportional-integral controller for second order plus time delay models

Öz

Anahtar Kelimeler

SOPTD plant, FOPI controller, analytical design, frequency properties, BODE’s ideal loop

Kaynakça

• Podlubny, I., Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers, IEEE Transactions on Automatic Control., 44, 208–214, 1999.
• Petras, I., Stability of Fractional-Order Systems with Rational Orders, Fractional Calculus and Applied Analysis., 12, 269–298, 2008.
• Karcı, A., Kesir Dereceli Türevin Yeni Yaklaşımının Özellikleri, Journal of the Faculty of Engineering and Architecture of Gazi University., 30, 2015.
• Valdes-Parada, F. J., Alberto Ochoa-Tapia, J., Alvarez-Ramirez, J., Effective medium equations for fractional Fick’s law in porous media, Physica A: Statistical Mechanics and its Applications., 373, 2007.
• Arena, P., Caponetto, R., Fortuna, L., Porto, D., Nonlinear Noninteger Order Circuits and Systems — An Introduction, WORLD SCIENTIFIC, 2000.
• Silva, M. F., Machado, J. A. T., Lopes, A. M., Fractional Order Control of a Hexapod Robot, Nonlinear Dynamics., 38, 2004.
• Vinagre, B. M., Chen, Y. Q., Petráš, I., Two direct Tustin discretization methods for fractional-order differentiator/integrator, Journal of the Franklin Institute., 340, 2003.
• Tavazoei, M. S., Haeri, M., A necessary condition for double scroll attractor existence in fractional-order systems, Physics Letters A., 367, 2007.
• Senol, B., Ates, A., Baykant Alagoz, B., Yeroglu, C., A numerical investigation for robust stability of fractional-order uncertain systems, ISA Transactions., 53, 2014.
• Senol, B., Yeroglu, C., Tan, N., Analysis of fractional order polynomials using Hermite-Biehler theorem, ICFDA’14 International Conference on Fractional Differentiation and Its Applications 2014, 1–5, 2014.
• Wang, J., Zong, Q., Su, R., Tian, B., Continuous high order sliding mode controller design for a flexible air-breathing hypersonic vehicle, ISA Transactions., 53, 690–698, 2014.
• Tajaddodianfar, F., Reza Moheimani, S. O., Owen, J., Randall, J. N., A self-tuning controller for high-performance scanning tunneling microscopy, 1st Annual IEEE Conference on Control Technology and Applications, CCTA 2017, 106–110, Institute of Electrical and Electronics Engineers Inc., 2017.
• Liu, H., Li, D., Xi, J., Zhong, Y., Robust attitude controller design for miniature quadrotors, International Journal of Robust and Nonlinear Control., 26, 681–696, 2016.
• Rashid, A. R. M., Siddikhan, P. M., Selvakumar, C., Suresh, M., The performance analysis of PID controller with setpoint filter and anti integral Windup for a FOPDT thermal process, Proceedings of 2017 3rd IEEE International Conference on Sensing, Signal Processing and Security, ICSSS 2017, 440–443, Institute of Electrical and Electronics Engineers Inc., 2017.
• Madhuranthakam, C. R., Elkamel, A., Budman, H., Optimal tuning of PID controllers for FOPTD, SOPTD and SOPTD with lead processes, Chemical Engineering and Processing: Process Intensification., 47, 251–264, 2008.
• Cvejn, J., PID control of FOPDT plants with dominant dead time based on the modulus optimum criterion, Archives of Control Sciences., 26, 5–17, 2016.
• Hekimoğlu, B., Çekirge optimizasyon algoritması kullanılarak çok makinalı güç sistemi için gürbüz kesir dereceli PID kararlı kılıcısı tasarımı, Journal of the Faculty of Engineering and Architecture of Gazi University., 35, 2019.
• Tufenkci, S., Senol, B., Alagoz, B. B., Disturbance Rejection Fractional Order PID Controller Design in v-domain by Particle Swarm Optimization, 2019 International Artificial Intelligence and Data Processing Symposium (IDAP), 1–6, 2019.
• Das, S., Pan, I., Das, S., Multi-objective LQR with optimum weight selection to design FOPID controllers for delayed fractional order processes, ISA Transactions., 58, 35–49, 2015.
• Song, X., Chen, Y. Q., Tejado, I., Vinagre, B. M., Multivariable fractional order PID controller design via LMI approach, IFAC Proceedings Volumes (IFAC-PapersOnline), 13960–13965, IFAC Secretariat, 2011.
• Zhao, C., Xue, D., Chen, Y. Q., A fractional order PID tuning algorithm for a class of fractional order plants, IEEE International Conference on Mechatronics and Automation, ICMA 2005, 216–221, 2005.
• Ayasun, S., Sönmez, Ş., Kesir dereceli PI denetleyici içeren zaman gecikmeli bir bölgeli yük frekans kontrol sisteminin kazanç ve faz payı tabanlı kararlılık analizi, Journal of the Faculty of Engineering and Architecture of Gazi University., 2018, 2018.
• Miao, Z., Han, T., Dang, J., Ju, M., FOPI/PI controller parameters optimization using PSO with different performance criteria, Proceedings of the 2017 IEEE 2nd Information Technology, Networking, Electronic and Automation Control Conference, ITNEC 2017, 250–255, Institute of Electrical and Electronics Engineers Inc., 2018.
• Kar, B., Roy, P., A Comparative Study Between Cascaded FOPI–FOPD and IOPI–IOPD Controllers Applied to a Level Control Problem in a Coupled Tank System, Journal of Control, Automation and Electrical Systems., 29, 340–349, 2018.
• Baruah, G., Majhi, S., Mahanta, C., Design of FOPI Controller for Time Delay Systems and Its Experimental Validation, International Journal of Automation and Computing., 16, 310–328, 2019.
• Şenol, B., Demiroğlu, U., Frequency frame approach on loop shaping of first order plus time delay systems using fractional order PI controller, ISA Transactions., 86, 192–200, 2019.
• Jamal, A., Syahputra, R., Heat Exchanger Control Based on Artificial Intelligence Approach, 2016.
• Dhanya Ram, V., Sankar Rao, C., Identification and Control of an Unstable SOPTD system with positive zero, Computer Aided Chemical Engineering, 757–762, Elsevier B.V., 2018.
• Srivastava, S., Pandit, V. S., A scheme to control the speed of a DC motor with time delay using LQR-PID controller, 2015 International Conference on Industrial Instrumentation and Control, ICIC 2015, 294–299, Institute of Electrical and Electronics Engineers Inc., 2015.
• Kapoor, S., Chaturvedi, M., Juneja, P. K., Design of FOPID controller with various optimization algorithms for a SOPDT model, 2017 International Conference on Emerging Trends in Computing and Communication Technologies, ICETCCT 2017, 1–4, Institute of Electrical and Electronics Engineers Inc., 2018.
• Ramakrishnan, V., Chidambaram, M., Estimation of a SOPTD transfer function model using a single asymmetrical relay feedback test, Computers and Chemical Engineering., 27, 1779–1784, 2003.
• Mesa, F., Marin, L. M., A CABRI plot generator to describe frequency and domain properties of SOPTD responses, EUROCON 2005 - The International Conference on Computer as a Tool, 278–281, 2005.
• Şenol, B., Demiroğlu, U., Matušů, R., Fractional order proportional derivative control for time delay plant of the second order: The frequency frame, Journal of the Franklin Institute., 357, 2020.
• Wang, C., Ying Luo, Chen, Y., Fractional order proportional integral (FOPI) and [proportional integral] (FO[PI]) controller designs for first order plus time delay (FOPTD) systems, 2009 Chinese Control and Decision Conference, 329–334, 2009.
• Wang, C., Jin, Y., Chen, Y., Auto-tuning of FOPI and FO[PI] controllers with iso-damping property, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 7309–7314, 2009.
• Chen, Y., Moore, K. L., Vinagre, B. M., Podlubny, I., Robust PID Controller Autotuning With An Iso-Damping Property Through A Phase Shaper, A. Le Mehaute, J. A. Tenreiro Machado, J. C. Trigeassou, J. Sabatier (Eds.), Fractional Differentiation and its Applications, 687–706, Ubooks Verlag, Neusäß, 2005.
• Pommier-Budinger, V., Janat, Y., Nelson-Gruel, D., Lanusse, P., Oustaloup, A., Fractional robust control with ISO-damping property, Proceedings of the American Control Conference, 4954–4959, 2008.
• Saha, S., Das, S., Ghosh, R., Goswami, B., Balasubramanian, R., Chandra, A. K., Das, S., Gupta, A., Fractional order phase shaper design with Bode’s integral for iso-damped control system, ISA Transactions., 49, 196–206, 2010.
• Rajapandiyan, C., Chidambaram, M., Closed-loop identification of second-order plus time delay (SOPTD) model of multivariable systems by optimization method, Industrial and Engineering Chemistry Research., 51, 9620–9633, 2012.
• Das, S., Saha, S., Das, S., Gupta, A., On the selection of tuning methodology of FOPID controllers for the control of higher order processes, ISA Transactions., 50, 376–388, 2011.