Robust Output Feedback Control Design for Nonlinear Coupled-tank System using Linear Matrix Inequalities

Year 2023, Volume: 15 Issue: 1, 125 - 138, 31.01.2023

Jaffar Seyyedesmaeili Abdullah Başçi

https://doi.org/10.29137/umagd.1147466

Abstract

In this experimental study, the Robust Output Feedback controller (ROF) is designed based on the H_∞ theory and implemented to the level control of the coupled tank system. As many chemical processes have complicated and nonlinear characteristics, this robust methodology is proposed to tackle them. Hence, the vertical coupled tank system is selected as one of the popular case study systems to simulate the large-scale chemical processes to illustrate the effectiveness of the proposed ROF controller. Linear Matrix Inequalities (LMIs) methodology is selected as the main mathematical method of the design procedure. To illustrate the best performance and robustness of the ROF controller, the simulation and experimental results are compared to the Feedforward Proportional Integrator, one of the most common controllers in the industries. Two different liquid level control scenarios are considered in this comparison and the obtained results show the expected performance of the ROF controller guaranteeing the design objectives.

Keywords

Coupled-tank, robust control, LMIs, fluid level, output feedback

References

• Arun, N. K., & Mohan, B. M. (2017). Modeling, stability analysis, and computational aspects of some simplest nonlinear fuzzy two-term controllers derived via center of area/gravity defuzzification. ISA transactions, 70, 16-29.
• Åström, K. J., & Hägglund, T. (2004). Revisiting the Ziegler–Nichols step response method for PID control. Journal of process control, 14(6), 635-650.
• Ayten, K. K., & Dumlu, A. (2021). Implementation of a PID Type Sliding-Mode Controller Design Based on Fractional Order Calculus for Industrial Process System. Elektronika ir Elektrotechnika, 27(6), 4-10.
• Başçi, A., & Derdiyok, A. (2016). Implementation of an adaptive fuzzy compensator for coupled tank liquid level control system. Measurement, 91, 12-18.
• Dutta, S., Seal, S., & Sengupta, A. (2014, September). Real-time linear quadratic versus sliding mode liquid level control of a coupled tank system. In 2014 International Conference on Devices, Circuits, and Communications (ICDCCom) (pp. 1-6). IEEE.
• Engules, D., Hot, M., & Alikoc, B. (2015, June). Level control of a coupled-tank system via eigenvalue assignment and LQG control. In 2015 23rd Mediterranean Conference on Control and Automation (MED) (pp. 1198-1203). IEEE.
• Esmaeili, J. S., & Başçi, A. (2019, July). LMI-based H 2 Control of Vertical Nonlinear Coupled-tank System. In 2019 International Conference on Control, Automation and Diagnosis (ICCAD) (pp. 1-7). IEEE.
• Esmaeili, J. S., Akbari, A., & Karimi, H. R. (2015). Load-dependent LPV/H2 output-feedback control of semi-active suspension systems equipped with MR damper. International Journal of Vehicle Design, 68(1-3), 119-140.
• Fu, Y., Chen, W., & Fu, J. (2021). A New Optimal Tracking Controller of Linear Strongly Coupled Systems and Its Applications. IEEE Transactions on Circuits and Systems II: Express Briefs, 69(3), 1387-1391.
• Gahinet, P., Nemirovskii, A., Laub, A. J., & Chilali, M. (1994, December). The LMI control toolbox. In Proceedings of 1994 33rd IEEE Conference on Decision and Control (Vol. 3, pp. 2038-2041). IEEE.
• Jaafar, H. I., Hussien, S. Y. S., Selamat, N. A., Aras, M. S. M., & Rashid, M. Z. A. (2014). Development of PID controller for controlling the desired level of coupled tank system. International Journal of Innovative Technology and Exploring Engineering, 3(9), 32-36.
• Khalil, I. S., Doyle, J. C., & Glover, K. (1996). Robust and optimal control. Prentice-Hall.
• Nail, B., Bekhiti, B., Bdirina, K., Kouzou, A., & Hafaifa, A. (2015, May). Sliding mode control and optimal GPC algorithm for coupled tanks. In 2015 3rd International Conference on Control, Engineering & Information Technology (CEIT) (pp. 1-6). IEEE.
• Owa, K. O., Sharma, S. K., & Sutton, R. (2013). Optimized multivariable nonlinear predictive control for coupled tank applications.
• Prusty, S. B., Seshagiri, S., Pati, U. C., & Mahapatra, K. K. (2016, January). Sliding mode control of coupled tanks using conditional integrators. In 2016 Indian Control Conference (ICC) (pp. 146-151). IEEE.
• Quanser manufacturer, https://www.quanser.com
• Saad, M., Albagul, A., & Abueejela, Y. (2014). Performance comparison between PI and MRAC for coupled-tank system. Journal of Automation and Control Engineering Vol, 2(3).
• Scherer, C., & Weiland, S. (2000). Linear matrix inequalities in control. Lecture Notes, Dutch Institute for Systems and Control, Delft, The Netherlands, 3(2).
• Selamat, N. A., Daud, F. S., Jaafar, H. I., & Shamsudin, N. H. (2015, March). Comparison of LQR and PID controller tuning using PSO for Coupled Tank System. In 2015 IEEE 11th International Colloquium on Signal Processing & Its Applications (CSPA) (pp. 46-51). IEEE.
• Skogestad, S., & Postlethwaite, I. (2007). Multivariable feedback control: analysis and design (Vol. 2). New York: Wiley.
• Souran, D. M., Abbasi, S. H., & Shabaninia, F. (2013). Comparative study between tank’s water level control using PID and fuzzy logic controller. In Soft computing applications (pp. 141-153). Springer, Berlin, Heidelberg.
• Teng, T. K., Shieh, J. S., & Chen, C. S. (2003). Genetic algorithms applied in online autotuning PID parameters of a liquid-level control system. Transactions of the Institute of Measurement and Control, 25(5), 433-450.
• Veronesi, M., & Visioli, A. (2013, July). Automatic feedforward tuning for PID control loops. In 2013 European Control Conference (ECC) (pp. 3919-3924). IEEE.
• Ziegler, J. G., & Nichols, N. B. (1942). Optimum settings for automatic controllers. trans. ASME, 64(11).