This study proposes an analytical design method of a
Proportional Integral controller for the stability and performance of first
order plus time delay systems. The method proposed in the study achieves
general computation equations for such systems. Inspired from Bode’s ideal
loop, gain crossover frequency and phase margin specifications are considered
for the system. Then, these specifications are used to obtain the parameters of
the proportional integral 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.
[1] Pandey, S. and Majhi, S., “Identification and control of unstable FOPTD processes with improved transients”, Electronics Letters, vol. 53 (5), pp. 312-314, 2017.
[2] Ferheen A. and Chidambaram, M., “Design of robust PID controller for an interval plant”, Trends in Industrial Measurement and Automation, Chennai, pp. 1-7. 2017.
[3] Vasičkaninová, A. and Bakošová, M., “Robust controller design for a heat exchanger using ℋ2, ℋ∞, ℋ2/ℋ∞, and μ-synthesis approaches”, Acta Chimica Slovaca, vol. 9 (2), pp. 184-193, 2016.
[4] Lee, J., Lee. Y., Yang, D.R. and Edgar, T.F., “Simple Proportional Integral Controller Tuning Rules for FOPTD and HOPTD Models Based on Matching Two Asymptotes”, Industrial & Engineering Chemistry Research, vol. 57 (8), pp. 2905-2916, 2018.
[5] Liu, H., Li, D., Xi, J., and Zhong, Y., “Robust attitude controller design for miniature quadrotors”, International Journal of Robust and Nonlinear Control, vol, 26, pp. 681–696, 2016.
[6] Tajaddodianfar, F., Moheimani, S.O.R., Owen, J. and Randall, J.N., “A self-tuning controller for high-performance scanning tunneling microscopy”, IEEE Conference on Control Technology and Applications (CCTA), Mauna Lani, pp. 106-110. 2017.
[7] Wang, J., Zong, Q., Su, R. and Tian, B., “Continuous high order sliding mode controller design for a flexible air-breathing hypersonic vehicle”, ISA Transactions, vol. 53 (3), pp. 690-698, 2014.
[8] Madhuranthakam, C.R., Elkamel, A. and Budman, H., “Optimal tuning of PID controllers for FOPTD, SOPTD and SOPTD with lead processes”, Chemical Engineering and Processing: Process Intensification, vol. 47 (2), pp. 251-264, 2008.
[9] Rashid, A.R.M., Siddikhan, P.M., Selvakumar, C. and Suresh, M., “The performance analysis of PID controller with setpoint filter and anti integral Windup for a FOPDT thermal process”, Third International Conference on Sensing, Signal Processing and Security (ICSSS), Chennai, India, pp. 440-443, 2017.
[10] Cvejn, J., “PID control of FOPDT plants with dominant dead time based on the modulus optimum criterion”, Archives of Control Sciences, vol. 26 (1), pp. 5-17, 2016.
[11] Onat, C., Hamamci, S.E. and Obuz, S., “”A Practical PI Tuning Approach For Time Delay Systems”, IFAC Proceedings, vol. 45 (14), pp. 102-107, 2012.
[12] Kar, B. and Roy, P.J., “A Comparative Study Between Cascaded FOPI–FOPD and IOPI–IOPD Controllers Applied to a Level Control Problem in a Coupled Tank System”, Control Autom. Electr. Syst., vol. 29 (3), pp. 340-349, 2018.
[13] Miao, Z., Han, T., Dang, J. and Ju, M., “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.
[14] Wang, C., Ying, L. and Chen, Y.Q., "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, Guilin, pp. 329-334. 2009.
Analytical Design of PI Controllers for First Order plus Time Delay Systems
This study proposes an analytical design method of a
Proportional Integral controller for the stability and performance of first
order plus time delay systems. The method proposed in the study achieves
general computation equations for such systems. Inspired from Bode’s ideal
loop, gain crossover frequency and phase margin specifications are considered
for the system. Then, these specifications are used to obtain the parameters of
the proportional integral 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.
[1] Pandey, S. and Majhi, S., “Identification and control of unstable FOPTD processes with improved transients”, Electronics Letters, vol. 53 (5), pp. 312-314, 2017.
[2] Ferheen A. and Chidambaram, M., “Design of robust PID controller for an interval plant”, Trends in Industrial Measurement and Automation, Chennai, pp. 1-7. 2017.
[3] Vasičkaninová, A. and Bakošová, M., “Robust controller design for a heat exchanger using ℋ2, ℋ∞, ℋ2/ℋ∞, and μ-synthesis approaches”, Acta Chimica Slovaca, vol. 9 (2), pp. 184-193, 2016.
[4] Lee, J., Lee. Y., Yang, D.R. and Edgar, T.F., “Simple Proportional Integral Controller Tuning Rules for FOPTD and HOPTD Models Based on Matching Two Asymptotes”, Industrial & Engineering Chemistry Research, vol. 57 (8), pp. 2905-2916, 2018.
[5] Liu, H., Li, D., Xi, J., and Zhong, Y., “Robust attitude controller design for miniature quadrotors”, International Journal of Robust and Nonlinear Control, vol, 26, pp. 681–696, 2016.
[6] Tajaddodianfar, F., Moheimani, S.O.R., Owen, J. and Randall, J.N., “A self-tuning controller for high-performance scanning tunneling microscopy”, IEEE Conference on Control Technology and Applications (CCTA), Mauna Lani, pp. 106-110. 2017.
[7] Wang, J., Zong, Q., Su, R. and Tian, B., “Continuous high order sliding mode controller design for a flexible air-breathing hypersonic vehicle”, ISA Transactions, vol. 53 (3), pp. 690-698, 2014.
[8] Madhuranthakam, C.R., Elkamel, A. and Budman, H., “Optimal tuning of PID controllers for FOPTD, SOPTD and SOPTD with lead processes”, Chemical Engineering and Processing: Process Intensification, vol. 47 (2), pp. 251-264, 2008.
[9] Rashid, A.R.M., Siddikhan, P.M., Selvakumar, C. and Suresh, M., “The performance analysis of PID controller with setpoint filter and anti integral Windup for a FOPDT thermal process”, Third International Conference on Sensing, Signal Processing and Security (ICSSS), Chennai, India, pp. 440-443, 2017.
[10] Cvejn, J., “PID control of FOPDT plants with dominant dead time based on the modulus optimum criterion”, Archives of Control Sciences, vol. 26 (1), pp. 5-17, 2016.
[11] Onat, C., Hamamci, S.E. and Obuz, S., “”A Practical PI Tuning Approach For Time Delay Systems”, IFAC Proceedings, vol. 45 (14), pp. 102-107, 2012.
[12] Kar, B. and Roy, P.J., “A Comparative Study Between Cascaded FOPI–FOPD and IOPI–IOPD Controllers Applied to a Level Control Problem in a Coupled Tank System”, Control Autom. Electr. Syst., vol. 29 (3), pp. 340-349, 2018.
[13] Miao, Z., Han, T., Dang, J. and Ju, M., “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.
[14] Wang, C., Ying, L. and Chen, Y.Q., "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, Guilin, pp. 329-334. 2009.
Şenol, B., & Demiroğlu, U. (2018). Analytical Design of PI Controllers for First Order plus Time Delay Systems. International Scientific and Vocational Studies Journal, 2(2), 40-47.
AMA
Şenol B, Demiroğlu U. Analytical Design of PI Controllers for First Order plus Time Delay Systems. ISVOS. Aralık 2018;2(2):40-47.
Chicago
Şenol, Bilal, ve Uğur Demiroğlu. “Analytical Design of PI Controllers for First Order Plus Time Delay Systems”. International Scientific and Vocational Studies Journal 2, sy. 2 (Aralık 2018): 40-47.
EndNote
Şenol B, Demiroğlu U (01 Aralık 2018) Analytical Design of PI Controllers for First Order plus Time Delay Systems. International Scientific and Vocational Studies Journal 2 2 40–47.
IEEE
B. Şenol ve U. Demiroğlu, “Analytical Design of PI Controllers for First Order plus Time Delay Systems”, ISVOS, c. 2, sy. 2, ss. 40–47, 2018.
ISNAD
Şenol, Bilal - Demiroğlu, Uğur. “Analytical Design of PI Controllers for First Order Plus Time Delay Systems”. International Scientific and Vocational Studies Journal 2/2 (Aralık 2018), 40-47.
JAMA
Şenol B, Demiroğlu U. Analytical Design of PI Controllers for First Order plus Time Delay Systems. ISVOS. 2018;2:40–47.
MLA
Şenol, Bilal ve Uğur Demiroğlu. “Analytical Design of PI Controllers for First Order Plus Time Delay Systems”. International Scientific and Vocational Studies Journal, c. 2, sy. 2, 2018, ss. 40-47.
Vancouver
Şenol B, Demiroğlu U. Analytical Design of PI Controllers for First Order plus Time Delay Systems. ISVOS. 2018;2(2):40-7.