Coefficient Diagram Method Based Decentralized Controller for Fractional Order TITO Systems

Yıl 2022, , 198 - 208, 30.04.2022

Furkan Nur Deniz , Miray Günay

https://doi.org/10.17694/bajece.984815

Öz

Fractional calculus has gained increasing attention from researchers because of providing accurate modelling and flexible controller design in control applications. More research to design controllers for Fractional Order Two-Input Two-Output (FOTITO) systems, which inherently have certain difficulties, is needed when the studies about these control applications are considered. In this study, Coefficient Diagram Method (CDM) based decentralized controllers are designed for FOTITO systems. For this, integer order approximate models of FOTITO systems are obtained and decoupled into two subsystems by using simplified and inverted decoupling configurations. Obtained high-order approximate subsystem transfer functions are reduced by a model reduction method to facilitate CDM-based decentralized controller design. Then, CDM-based decentralized controllers are designed for each subsystem, which enables to obtain the controllers of the FOTITO system. Simulation results for two different FOTITO systems, one of which is a time delay fractional order system, are demonstrated that the proposed approach exhibits successful performance.

Anahtar Kelimeler

Coefficient Diagram Method, Decentralized Controller, Fractional Order Systems

Kaynakça

• [1] B. Halvarsson, “Interaction Analysis in Multivariable Control Systems,” PhD Thesis, Uppsala University, 2010.
• [2] M. A. Üstüner, “Çok Değişkenli Sistemlerde Etkileşimin Yok Edilmesi : Proses Kontrol Sistemi Uygulaması,” Master Thesis, Celal Bayar University, 2016.
• [3] E. Gagnon, A. Pomerleau, and A. Desbiens, “Simplified, ideal or inverted decoupling?,” ISA Trans., vol. 37, no. 4, pp. 265–276, 1998.
• [4] F. Vázquez and F. Morilla, “Tuning decentralized pid controllers for MIMO systems with decouplers,” IFAC Proc. Vol., vol. 15, no. 1, pp. 349–354, 2002.
• [5] T. Nguyen, L. Vu, and M. Lee, “Design of Extended Simplified Decoupling for Multivariable Processes with Multiple Time Delays,” 2011, pp. 1822–1827.
• [6] K. Weischedel and T. J. McAvoy, “Feasibility of Decoupling in Conventionally Controlled Distillation Columns,” Ind. Eng. Chem. Fundam., vol. 19, no. 4, pp. 379–384, 1980.
• [7] C. Rajapandiyan and M. Chidambaram, “Controller design for MIMO processes based on simple decoupled equivalent transfer functions and simplified decoupler,” Ind. Eng. Chem. Res., vol. 51, no. 38, pp. 12398–12410, 2012.
• [8] M. G. Bulut and F. N. Deniz, “Computation of Stabilizing Decentralized PI Controllers for TITO Systems with Simplified and Inverted Decoupling,” 2020 7th Int. Conf. Electr. Electron. Eng. ICEEE 2020, vol. 7, pp. 294–298, 2020.
• [9] M. G. Bulut and F. N. Deniz, “Computation of Stabilizing Decentralized PI Controllers for Fractional Order TITO ( FOTITO ) Systems,” IEEE 11th Annu. Comput. Commun. Work. Conf. CCWC 2021, vol. 11, no. 1, pp. 1274–1280, 2021.
• [10] L. Liu, S. Tian, D. Xue, T. Zhang, Y. Q. Chen, and S. Zhang, “A Review of Industrial MIMO Decoupling Control,” Int. J. Control. Autom. Syst., vol. 17, no. 5, pp. 1246–1254, 2019.
• [11] A. Numsomran, T. Wongkhum, T. Suksri, P. Nilas, and J. Chaoraingern, “Design of Decoupled Controller for TITO System using Characteristic Ratio Assignment,” 2007, vol. 12, no. 3, pp. 957–962.
• [12] S. Tavakoli, I. Griffin, and P. J. Fleming, “Tuning of decentralised PI (PID) controllers for TITO processes,” pp. 1069–1080, 2006.
• [13] G. Kumar, “Control of TITO Process using Internal Model Control Technique,” vol. 8, no. 16, pp. 87–92, 2020.
• [14] C. Hwang and Y. C. Cheng, “A numerical algorithm for stability testing of fractional delay systems,” Automatica, vol. 42, no. 5, pp. 825–831, 2006.
• [15] D. Li, X. He, T. Song, and Q. Jin, “Fractional Order IMC Controller Design for Two-input-two-output Fractional Order System,” Int. J. Control. Autom. Syst., vol. 17, no. 4, pp. 936–947, 2019.
• [16] Z. Li and Y. Q. Chen, Ideal, simplified and inverted decoupling of fractional order TITO processes, vol. 19, no. 3. IFAC, 2014.
• [17] E. O. Mahdouani, M. Ben Hariz, and F. Bouani, “Design of fractional order controllers for TITO systems,” 2019 Int. Conf. Signal, Control Commun. SCC 2019, pp. 179–184, 2019.
• [18] A. San-Millan, D. Feliu-Talegón, V. Feliu-Batlle, and R. Rivas-Perez, “On the modelling and control of a laboratory prototype of a hydraulic canal based on a TITO fractional-order model,” Entropy, vol. 19, no. 8, 2017.
• [19] F. N. Deniz, B. B. Alagoz, N. Tan, and M. Koseoglu, “Revisiting four approximation methods for fractional order transfer function implementations: Stability preservation, time and frequency response matching analyses,” Annu. Rev. Control, vol. 49, pp. 239–257, 2020.
• [20] D. Xue, Y. Chen, and D. P. Atherton, Linear Feedback Control - Analysis and Design with MATLAB. Society for Industrial and Applied Mathematics, 2007.
• [21] S. Manabe, “Coefficient Diagram Method,” IFAC Proc. Vol., vol. 31, no. 21, pp. 211–222, 1998.
• [22] H. Kayan, “Durum Zaman Gecikmeli Sistemler için Kontrol Sistem Tasarımı,” Master Thesis, Inonu University, 2014.
• [23] M. Yardımcı, “Katsayı Di̇yagram Yöntemi̇ni̇n (KDY) Ölü Zamanlı Si̇stemlere Uygulanması,” Master Thesis, Istanbul Tekni̇k University, 2005.
• [24] S. E. Hamamcı, “Zaman Gecikmeli Kararsız Sistemler için Katsayı Diyagram Metodu ile Kontrolör Tasarımı,” vol. 6, no. 3, pp. 135–142, 2002.
• [25] S. E. Hamamci, “İntegratörlü sistemler için Katsayı Diyagram Metodu ile kontrolör tasarımı,” İTÜ Derg., no. 422, pp. 3–12, 2004.
• [26] S. Manabe, “Application of Coefficient Diagram Method to Dual-Control-Surface Missile,” IFAC Proc. Vol., vol. 34, no. 15, pp. 499–504, 2001.
• [27] S. Manabe, “Application of coefficient diagram method to MIMO design in aerospace,” IFAC Proc. Vol., vol. 15, no. 1, pp. 43–48, 2002.
• [28] S. E. Hamamci and M. Koksal, “Robust controller design for TITO processes with coefficient diagram method,” IEEE Conf. Control Appl. - Proc., vol. 2, no. November, pp. 1431–1436, 2003.
• [29] J. Rajaraman and T. Indiran, “Experimental implementation of cdm based two mode controller for an interacting 2 * 2 distillation process,” no. March, 2018.
• [30] C. Wutthithanyawat and S. Wangnipparnto, “Decentralized PI controller with coefficient diagram method incorporating feedforward controller based on inverted decoupling for two input - Two output system,” Prz. Elektrotechniczny, vol. 96, no. 9, pp. 159–166, 2020.
• [31] C. Wutthithanyawat and S. Wangnippamto, “Design of Decentralized PID Controller with Coefficient Diagram Method Based on Inverted Decoupling for TITO System,” iEECON 2018 - 6th Int. Electr. Eng. Congr., vol. 0, pp. 0–3, 2018.
• [32] Q. G. Wang, B. Huang, and X. Guo, “Auto-tuning of TITO decoupling controllers from step tests,” ISA Trans., vol. 39, no. 4, pp. 407–418, 2000.
• [33] K. V. T. Waller, “Decoupling in distillation,” AIChE Journal, vol. 20, no. 3. pp. 592–594, 1974.
• [34] S. Fragoso, J. Garrido, F. Vázquez, and F. Morilla, “Comparative analysis of decoupling control methodologies and H∞ multivariable robust control for variable-speed, variable-pitch wind turbines: Application to a lab-scale wind turbine,” Sustain., vol. 9, no. 5, 2017.
• [35] M. Araki and H. Taguchi, “Two-degree-of-freedom PID controllers,” Int. J. Control. Autom. Syst., vol. 1, no. 4, pp. 401–411, 2003.
• [36] N. Tan, A. Yüce, A. Özel, and F. N. Deniz, “Kesirli Dereceli Kontrol Sistemlerinde Tamsayı Dereceli Yaklaşım Metotlarının İncelenmesi,” no. January, 2014.
• [37] A. Oustaloup, F. Levron, B. Mathieu, and F. M. Nanot, “Frequency-band complex noninteger differentiator: Characterization and synthesis,” IEEE Trans. Circuits Syst. I Fundam. Theory Appl., vol. 47, no. 1, pp. 25–39, 2000.
• [38] K. Matsuda and H. Fujii, “H∞ optimized wave-absorbing control: Analytical and experimental results,” J. Guid. Control. Dyn., vol. 16, no. 6, pp. 1146–1153, 1993. [39] F. N. Deniz, B. B. Alagoz, N. Tan, and D. P. Atherton, “An integer order approximation method based on stability boundary locus for fractional order derivative/integrator operators,” ISA Trans., vol. 62, pp. 154–163, 2016.
• [40] F. N. Deniz, “Kesir Dereceli Sistemlerde Modelleme ve Kontrol Uygulamaları,” PhD Thesis, Inonu University, 2017.
• [41] “Integer order approximation for fractional order derivative - File Exchange - MATLAB Central.” [Online]. Available: https://nl.mathworks.com/matlabcentral/fileexchange/87357-integer-order-approximation-for-fractional-order-derivative?s_tid=srchtitle. [Accessed: 01-Jun-2021].