Implementation of Advanced PID Control Algorithm for SDOF System

Year 2021, Volume: 2 Issue: 2, 98 - 107, 15.12.2021

Abdullah Turan , Hüseyin Aggümüş

Abstract

The maximum performance to be obtained by applying the Proportion-Integral-Derivative (PID) controller on a system depends on the optimum adjustment of its parameters. This study aims to present a design method for tuning the PID control parameters. In this method, PID controller design is made based on the optimal proportional gain from the system to the desired settling time and overshoot. The infrastructure of the technique is based on obtaining the other PID controller parameters by adjusting the optimum proportional gain (kp), which minimizes the settling time in a stable loop and the error rate of the overshoot. Routh Hurwitz criterion is used to guarantee stability in the control system. The effectiveness of the proposed method is tested as an active control application of the PID controller on a single degree of freedom (SDOF) structural system. The efficiency of the PID controller designed with this method, which does not require the destruction of parameters and does not contains complex mathematical formulations, is proven by its successful suppression of SDOF structural system responses.

Keywords

Active control, PID controller, SDOF system, structural control

References

• K. J. Astrom and T. Hagglund, “Design of PI controllers based on non-convex optimization,’’ Automatica, vol. 34, no. 5, pp. 585-601, 1998.
• J. G. Ziegler and N. B. Nichols, “Optimum settings for automatic controllers,’’ Trans ASME, vol. 64, pp. 759–768, 1942.
• G. H. Cohen and G. A. Coon, “Theoretical consideration of retarded control,” Trans ASME, vol. 75, pp. 827–34, 1953.
• A. D. Paor and M. O’Malley, “Controllers of ziegler-nichols type for unstable process with time delay,” Int.J.Control, vol. 49, pp. 1273–1284, 1989.
• V. Venkatashankar, and M. Chidambaram, “Design of P and PI controllers for unstable first-order plus time delay systems,” Int.J.Control, vol. 60, pp. 137–144, 1994.
• K. J. Astrom and Hagglund, T. “The future of PID control,” Control Engineering Practice, vol. 9, pp. 1163-1175, 2001.
• K. J. Manoj, and M. Chidambaram, “PID controller tuning for unstable systems by optimization method,” Chem.Engg.Comm., vol. 185, pp. 91–113, 2001.
• A. Visioli, “Optimal tuning of PID controllers for integral and unstable processes,” IEE Proc. in Control Theory Appln., vol. 148, pp. 148–180, 2001.
• C. Clement, and M. Chidambaram, “PID control of unstable FOPTD systems,” Chem. Eng. Commun., vol. 162, pp. 63–74, 1997.
• A. Turan, C. Onat and M. Sahin, “Active vibration suppression of a smart beam via PID controller designed through weighted geometric center method,” Proceedings of the 10th Ankara International Aerospace Conference, METU, Ankara, Turkey, September, 2019.
• R. Ali, T. H. Mohamed, Y. S. Qudaih and Y. Mitani, “A new load frequency control approach in an isolated small power systems using coefficient diagram method,” Int J Electr Power Energy Syst vol. 56, pp. 110–116, 2014, https://doi.org/ 10.1016/j.ijepes.2013.11.002.
• A. Mittal, A. Kapoor and T. K. Saxena, “Adaptive tuning of PID controller for a nonlinear constant temperature water bath under set-point disturbances using GANFC,” J. Auto Syst. Eng. vol. 7 pp. 143–63, 2013.
• A. Fereidouni, M. A. S. Masoum and M. Moghbel, “A new adaptive configuration of PID type fuzzy logic controller,” ISA Trans. vol. 56, pp. 222–240, 2015, https://doi.org/ 10.1016/j.isatra.2014.11.010.
• X. Wu, G. Qin, H. Yu, S. Gao, L. Liu and Y. Xue, “Using improved chaotic and swarm to tune PID controller on cooperative adaptive cruise control,” Optik, vol. 127 pp. 3445–3450, 2016, https://doi.org/10.1016/j.ijleo.2015.12.014.
• A. Moharam, M. A. El-Hosseini and H. A. Ali, “Design of optimal PID controller using hybrid differential evolution and particle swarm optimization with an aging leader and challengers,” Appl Soft Comput. vol. 38 pp. 727–37, 2016, https://doi.org/ 10.1016/j.asoc.2015.10.041.
• F. N. Deniz, B. A. Alagoz and N. Tan, “PID Controller Design Based on Second Order Model Approximation by Using Stability Boundary Locus Fitting,” 9th International Conference on Electrical and Electronics Engineering (ELECO), 2015, 10.1109/ELECO.2015.7394585.
• P. Patel and S. Janardhanan, “Near optimal PID controller tuning: Interval arithmetic approach,” IFAC PapersOnLine vol. 53, no. 1, pp. 246–251, 2020, 10.1016/j.ifacol.2020.06.042.
• R. Toscano, “A simple robust PI/PID controller design via numerical optimization approach,” Journal of Process Control, vol. 15, pp. 81-88, 2005.
• H. Aggumus and R. Guclu, “Robust H∞ control of STMDs used in structural systems by hardware in the loop simulation method,” In: Actuators. Multidisciplinary Digital Publishing Institute, pp. 55, 2020.
• H. Aggumus, and S. Cetin, “Experimental investigation of semiactive robust control for structures with magnetorheological dampers,” Journal of Low Frequency Noise, Vibration and Active Control, vol. 37, no. 2, pp. 216-234, 2018.
• R. Guclu and H. Yazici, “Seismic-vibration mitigation of a nonlinear structural system with an ATMD through a fuzzy PID controller,” Nonlinear Dynamics, vol. 58, no. 3, pp. 553-564, 2009.
• R. Guclu, “Sliding mode and PID control of a structural system against earthquake,” Mathematical and Computer Modelling, vol. 44, no. 1-2, pp. 210-217, 2006.