Üçüncü derece zaman gecikmeli sistemler için PI denetleyicilerin analitik tasarımı

Year 2020, Volume: 26 Issue: 5, 893 - 898, 23.10.2020

Bilal Şenol

Abstract

Bu yayında üçüncü derece ve zaman gecikmesi içeren sistem modellerinin kararlılığı, performansı ve dayanıklılığı için analitik bir oransal integral denetleyici tasarım yöntemi sunulmuştur. Denetleyici tasarımı, ideal bir sistemin frekans tepkilerini ele alarak denetlenmek istenen sistemin arzu edilen kazanç ve faz özelliklerini sağlaması üzerinde yoğunlaşmıştır. Sözü edilen özellikleri sağlayan oransal integral denetleyici parametrelerini veren denklemler adım adım oluşturulmuştur. Bu denklemler, söz konusu sistemler için genelleştirilmiş eşitlikleri içermektedir. Araştırmacı, bu yöntem sayesinde üçüncü derece zaman gecikmeli sistemler için istenen kazanç kesim frekansı ve faz payı değerlerini sağlayabilmektedir. Bu sayede, Bode grafiği nispeten ayarlanabilmekte ve sistemin performansı ve dayanıklılığı artırılabilmektedir. Aynı zamanda önerilen denklemlerle sistem kararlığı da elde edilebilmektedir. Yayında sunulan yöntemle elde edilen denklemler iki farklı model üzerinde uygulanmıştır. Tüm sonuçlar grafiksel olarak ve tablolarla gösterilmiştir.

Keywords

PI denetleyici, TOPTD model, Kazanç ve faz özellikleri

References

• [1] Camcıoğlu Ş, Özyurt B, Doğan İC, Hapoğlu H. “Application of response surface methodology as a new PID tuning method in an electrocoagulation process control case”. Water Science & Technology, 76(12), 3410-3427, 2017.
• [2] Álvarez de Miguel S, Mollocana Lara JG, García Cena CE, Romero M, García de María JM, González-Aguilar J, “Identification model and PI and PID controller design for a novel electric air heater”. Automatika, 58(1), 55-68, 2017.
• [3] Sung SW, Je CH, Lee J, Lee, DH. “Improved system identification method for Hammerstein-Wiener processes”. Korean Journal of Chemical Engineering, 25(4), 631-636, 2008.
• [4] Rivas-Perez R, Castillo-Garcia F, Sotomayor-Moriano J, Feliu-Batlle V. “Design of a fractional order PI controller for steam pressure in the steam drum of a bagasse fired boiler”. IFAC Proceedings, 47(3), 1337-1342, 2014.
• [5] Malwatkar GM, Sonawane SH, Waghmare LM. “Tuning PID controllers for higher-order oscillatory systems with improved performance”. ISA Transactions, 48(3), 347-353, 2009.
• [6] León de la Barra BA, Jin L, Kim YC, Mossberg M. “Identification of first-order time-delay systems using two different pulse inputs”. Proceedings of the 17th IFAC World Congress, Seoul, Korea, 6-11 July, 2008.
• [7] Vivek S, Chidambaram M. “An improved relay auto tuning of PID controllers for critically damped SOPTD systems”. Chemical Engineering Communications, 199(11), 1437-1462, 2012.
• [8] Park HC, Lee J. “Step and pulse response methods for identification of wiener processes”. American Institute of Chemical Engineers Journal, 52(2), 668-677, 2006.
• [9] Cheon YJ, Jeon CH, Lee, J, Sung SW. “Improved fourier transform to estimate frequency responses”. Korean Journal of Chemical Engineering, 26(4), 925-929, 2009.
• [10] Darwish NM. “PID controller design in the frequency domain for time-delay systems using direct method”. Transactions of the Institute of Measurement and Control, 40(3), 940-950, 2018.
• [11] Alabi SB, Ikpatt FE. “Computer-aided simplification of high-order linear models”. Indian Chemical Engineer, 51(2), 129-155, 2009.
• [12] Sam YM, Osman JHS, Ruddin M, Ghani A. “A class of proportional-integral sliding mode control with application to active suspension system”. Systems & Control Letters, 51(3-4), 217-223, 2004.
• [13] Bhatti SA, Malik SA, Daraz A. "Comparison of P-I and I-P controller by using Ziegler-Nichols tuning method for speed control of DC motor". 2016 International Conference on Intelligent Systems Engineering, Islamabad, India, 15-17 January, 2016.
• [14] Sönmez S, Ayasun S. "Stability region in the parameter space of PI controller for a single-area load frequency control system with time delay". IEEE Transactions on Power Systems, 31(1), 829-830, 2016.
• [15] Khooban MH, Niknam T, Sha-Sadeghi M. "Speed control of electrical vehicles: a time-varying proportional-integral controller-based type-2 fuzzy logic". IET Science, Measurement & Technology, 10(3), 185-192, 2016.
• [16] Vishnu MJ, Karthika S. “Comparison of speed control of PMSM using adaptive fuzzy logic controller and PI controller”. Journal of Power Electronics & Power Systems, 8(3), 24-30, 2018.
• [17] Karthika S, Vishnu MJ. “Comparative study of torque ripple minimization of PMSM using PI and proportional resonant (PI-RES) controller”. Journal of Power Electronics & Power Systems, 8(3), 17-23, 2018.
• [18] Shafie Z, Shenton AT. “Frequency domain design of PID controllers for stable and unstable systems with time delay”. Automatica, 33(12), 2223-2232, 1997.
• [19] Tan N, Kaya I, Celaleddin Y, Atherton DP. “Computation of stabilizing PI and PID controllers using the stability boundary locus”. Energy Conversion and Management, 47, 3045-3058, 2006.
• [20] Hamamci SE, Tan N. “Design of PI controllers for achieving time and frequency domain specifications simultaneously”. ISA Transactions, 45(4), 529-543, 2006.
• [21] 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.
• [22] Şenol B, Demiroğlu U. “Fractional order proportional derivative control for first order plus time delay plants: achieving phase and gain specifications simultaneously”. Transactions of the Institute of Measurement and Control, 41(15), 4358-4369, 2019.
• [23] Wang C, Jin Y, Chen YQ. “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, Shanghai, China, 15-18 December 2009.
• [24] Wang C, Luo Y, Chen YQ. “Fractional order proportional integral (FOPI) and [proportional integral] (FO[PI]) controller designs for first order plus time delay (FOPTD) systems”. Chinese Control and Decision Conference, Guilin, China, 17-19 June 2009.