Analytical Design of PI Controllers for Second Order plus Time Delay Systems

Yıl 2019, Cilt:7 Sayı:2 (2019) (Özel Sayı), 27 - 37, 30.03.2019

Bilal Şenol

https://doi.org/10.29130/dubited.474280

Öz

Analytical
design scheme of a Proportional Integral controllers for the stability and
performance of second order plus time delay systems is presented in this paper.
The method proposed in the study achieves general computation equations for
mentioned systems. Inspired from the Bode’s ideal transfer function
characteristics, gain crossover frequency and phase margin specifications are
considered for the system. Then, these specifications are used to obtain the
parameters of the controller. Analytically derived formulas by the proposed
method are tested with existing plants in the literature and the results are
illustrated graphically. It is shown that the tuning method satisfies desired gain
crossover frequency and phase margin specifications.

Anahtar Kelimeler

Second Order Plus Time Delay Plant, PI Controller, Bode’s ideal loop

İkinci Derece Zaman Gecikmeli Sistemler için PI Denetleyicilerin Analitik Tasarımı

Öz

Bu
çalışmada ikinci dereceden zaman gecikmeli sistemlerin kararlılığı ve
performansı için oransal integral denetleyicilerin analitik tasarımı
verilmiştir. Çalışmada önerilen yöntem söz konusu sistemler için
genelleştirilmiş hesaplama eşitliklerini elde etmektedir. Bode’nin ideal
transfer fonksiyonunun karakteristiklerinden esinlenerek, kazanç kesim frekansı
ve faz payı şartları göz önüne alınmıştır. Daha sonra, bu şartlar denetleyicinin
prametrelerini elde etmek için kullanılmıştır. Önerilen yöntemle analitik olan
türetilen formüller literatürde var olan sistemler üzerinde test edilmiş ve
sonuçlar grafiksel olarak sergilenmiştir. Parametre ayarlama yönteminin istenen
kazanç kesim frekansı ve faz payı şartlarını sağladığı gösterilmiştir.

Anahtar Kelimeler

İkinci Derece Zaman Gecikmeli Sistem, Oransal Integral Denetleyici, Bode’nin İdeal Çevrim

Kaynakça

• [1] W. K. Ho, C. C. Hang and L. S. Cao, "Tuning of PI controllers based on gain and phase margin specifications," IEEE International Symposium on Industrial Electronics, Xian, China, 1992, pp. 497-502.
• [2] Z. Ibrahim and E. Levi, "A comparative analysis of fuzzy logic and PI speed control in high performance AC drives using experimental approach," IEEE Industry Applications Conference, Rome, Italy, 2000, pp. 1210-1218.
• [3] M. Cheng, Q. Sun and E. Zhou, "New self-tuning fuzzy PI control of a novel doubly salient permanent-magnet motor drive," IEEE Transactions on Industrial Electronics, vol. 53, no. 3, pp. 814-821, 2006.
• [4] Z. Miao, T. Han, J. Dang and M. Ju, “FOPI/PI controller parameters optimization using PSO with different performance criteria,” IEEE 2nd Information Technology, Networking, Electronic and Automation Control Conference (ITNEC), Chengdu, China, 2017, pp. 250-255.
• [5] B. Kar and P. J. Roy, “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, vol. 29, no. 3, pp. 340-349, 2018.
• [6] C. Onat, S. E. Hamamci and S. Obuz, ”A Practical PI Tuning Approach For Time Delay Systems,” IFAC Proceedings, vol. 45, no. 14, pp. 102-107, 2012.
• [7] C. R. Madhuranthakam, A. Elkamel and H. Budman, “Optimal tuning of PID controllers for FOPTD, SOPTD and SOPTD with lead processes,” Chemical Engineering and Processing: Process Intensification, vol. 47, no. 2, pp. 251-264, 2008.
• [8] V. Ramakrishnan and M. Chidambaram, “Estimation of a SOPTD transfer function model using a single asymmetrical relay feedback test,” Computers & Chemical Engineering, vol. 27, no. 12, pp. 1779-1784, 2003.
• [9] C. Rajapandiyan and M. Chidambaram, “Closed-Loop Identification of Second-Order Plus Time Delay (SOPTD) Model of Multivariable Systems by Optimization Method,” Industrial & Engineering Chemistry Research, vol. 51, no. 28, pp. 9620-9633, 2012.
• [10] J. Lee, Y. Lee, D. R. Yang and T. F. Edgar, “Simple Proportional Integral Controller Tuning Rules for FOPTD and HOPTD Models Based on Matching Two Asymptotes,” Industrial & Engineering Chemistry Research, vol. 57, no. 8, pp. 2905-2916, 2018.
• [11] H. Liu, D. Li, J. Xi and Y. Zhong, “Robust attitude controller design for miniature quadrotors,” International Journal of Robust and Nonlinear Control, vol, 26, no. 4, pp. 681–696, 2016.
• [12] F. Tajaddodianfar, S. O. R. Moheimani, J. Owen and J. N. Randall, “A self-tuning controller for high-performance scanning tunneling microscopy,” IEEE Conference on Control Technology and Applications (CCTA), Mauna Lani, USA, 2017, pp. 106-110.
• [13] J. Wang, Q. Zong, R. Su and B. Tian, “Continuous high order sliding mode controller design for a flexible air-breathing hypersonic vehicle,” ISA Transactions, vol. 53, no. 3, pp. 690-698, 2014.