Determination of optimal PID control parameters by response surface methodology

Year 2020, Volume: 4 Issue: 2, 142 - 153, 15.08.2020

Adnan Aldemir , Mohammed Sadralddin Anwer

https://doi.org/10.35860/iarej.711314

Cited By: 3

Abstract

Proportional–Integral–Derivative (PID) controllers are the most widely used systems in industrial applications and in academic research regarding control engineering. In this study, the optimal PID control parameters of a liquid level control system were determined with Response Surface Methodology. Dynamic analysis was carried out on the liquid level control system to prepare the reaction curve. Accordingly, dead time, time constant and process gain values were determined as 16s, 261s and 0.842, respectively. Based on the dynamic analysis, PID parameters were calculated in accordance with the Cohen-Coon, Ziegler-Nichols, Yuwana-Seborg methods, which are the commonly used tuning methods. The Kp, τI, τD parameters were calculated as 30.77, 29.15 and 5.4 with the Cohen-Coon method, as 0.453, 30.0 and 7.5 with the Ziegler-Nichols method and as 1.63, 686.3 and 117.7 with the Yuwana-Seborg method, respectively. The PID control parameters applied for the 40cm, 50cm and 60cm set points and ISE and IAE control performance values after experiments were calculated. The Kp, τI and τD values were selected as the independent parameters, while the ISE and IAE values were chosen as the dependent variables. The numerical values of the responses for the runs in the design matrices were determined with a closed-loop PID controller with the liquid level system block diagram that was designed in MATLAB/Simulink. The simulations proposed by the trial version of Design Expert 7.0 program were performed in order and the IAE and ISE values were calculated after the simulations were processed. In this study, minimum ISE and IAE values were selected to determine the best PID parameters of a liquid level control system. The optimal PID control parameters of the liquid level system required to obtain the lowest ISE and IAE values were determined as 23.14, 28.31 and 11.50 for Kp, τI and τD, respectively. 

Keywords

Dynamic analysis, Liquid level control, Optimum control parameters, PID control, Response surface methodology

References

• 1. Srivastava, S. Pandit, V. S., A PI/PID controller for time delay systems with desired closed loop time responses and guaranteed gain and phase margins. Journal of Process Control, 2016. 37: p.70–77.
• 2. Guangyue, L. Shangqi, L. Pingping, S. Yang, L. Yanyan, L., A new optimization method for steam-liquid level intelligent control model in oil sands steam-assisted gravity drainage (SAGD) process, Petroleum Exploration And Development, 2016. 43(2): p.301–307.
• 3. Ravikishore, C., Praveen Kumar D.T.V. and Padma Sree, R., Enhanced performance of PID controllers for unstable time delay systems using direct synthesis method, Indian Chemical Engineer, 2020. 56(3): p.1-17.
• 4. Huang, C. N., Chung, A., An intelligent design for a PID controller for nonlinear systems. Asian Journal of Control, 2016. 18(2): p.447-455.
• 5. Ziegler J. G. Nichols N. B., Optimum settings for automatic controllers, Transactions of the Asme, 1993. 115(2): p. 220–222.
• 6. Cohen, C., Theoretical consideration of retarded control. Transaction of the Asme, 1953. 75: p.827-834.
• 7. Bequette, B. W., 2003, Process Control: Modeling, Design and Simulation, Prentice Hall Upper Saddle River, NJ.
• 8. Grimholt, C. Skogestad, S., Optimal PI and PID control of first-order plus delay processes and evaluation of the original and improved SIMC rules, Journal of Process Control, 2018. 70: p.36-46.
• 9. Anil, C., Sree, R. P., Design of Optimal PID Controllers for Integrating Systems, Indian Chemical Engineer, 2014. 56(3): p.215-228.
• 10. Camcioglu, S., Ozyurt, B., Doğan, İ. C., Hapoglu H., Application of response surface methodology as a new PID tuning method in an electrocoagulation process control case, Water Science and Technology, 2017. 76(12): p. 3410-3427.
• 11. Gasparovic, C. L. M., Eyng, E., Frare, L. M., Arioli R., Orssatto F., PID tuning by central composite rotational design methodology: a case study of absorption column for biogas purification, International Journal of Innovative Computing, Information and Control, 2018. 14(1): p.15-32.
• 12. Demirtaş, M., Karaoglan, A. D., Optimization of PI parameters for DSP-based permanent magnet brushless motor drive using response surface methodology, Energy Conversion and Management, 2012. 56: p.104-111.
• 13. Gouta, H., Said, S. H., Barhoumi, N., M’Sahli, F., Observer-Based backstepping controller for a state-coupled two-tank system. IETE Journal of Research, 2015. 61(3): p.259-268.
• 14. Başçi, A., Derdiyok, A., Implementation of an adaptive fuzzy compensator for coupled tank liquid level control system, Measurement, 2016. 91: p.12-18.
• 15. Boiko, I., Variable-structure PID controller for level process, Control Engineering Practice, 2013. 21(5): p.700-707.
• 16. Jain, T., Nigam, M. J., Optimization of PD-PI controller using swarm intelligence. International Journal of Computational Cognition, 2008. 6(4): p.55-59.
• 17. Mehta, A. K., Swarnalatha, R., Performance evaluation of conventional PID control tuning techniques for a first order plus dead time blending process. Journal of Engineering Science and Technology. 2018. 13: p.3593-3609.
• 18. Selvaraj, S. P., Nirmalkumar, A., Constrained GA based online PI Controller parameter tuning for stabilization of water level in spherical tank system. International Journal of Mechanical & Mechatronics Engineering, 2015. 15(1): p.19-31.
• 19. Mamat, R., Fleming, P., Method for on-line identification of a first order plus dead-time process model. Electronics Letters. 1995. 31: p.1297 - 1298.
• 20. Wang, D-J., Synthesis of PID controllers for high-order plants with time-delay, Journal of Process Control, 2009. 19(10): p.1763-1768.
• 21. Aldemir, A., Hapoğlu, H., Comparison of PID tuning methods for wireless temperature. Journal of Polytechnic, 2016. 19(1): p.9–19
• 22. Grimholt, C., Skogestad, S., Optimal PI and PID control of first-order plus delay processes and evaluation of the original and improved SIMC rules. Journal of Process Control. 2018. 70: p.36-46.