A Paradigm on the Qualitative Behavior of Dynamical Systems Inspired by Circuit Theory
Öz
In this paper, we consider the qualitative analysis of a liquid mechanical tank system with an electrical model. In the prototype phase, such models are more flexible like the construction process of the first nuclear reactors. The mathematical model of this dynamic system is nonlinear and time-varying. Here, physical principles and engineering specifications will be used to find unique results without any mathematical approximation. The energy function of the system is constructed with intuitive physical principles. The system also will be discussed with and without feedback control laws. Global asymptotic controllability of the equilibrium point of the system will be determined. The literature presents us, the level control works with a few multi-tanks up to six. We generalize those with tanks from a different theoretical perspective. The readymade system and candidate Lyapunov function will not be used here; the study will be conducted by constructing them. The effectiveness of the control mechanism will be determined by both theoretical analysis and simulation. According to the proposed algorithm, the measurement of liquid levels in tanks can be made in volts anywhere in the system, collectively or individually. The algorithm is clear, not large time-consuming and the solution cost is not expensive. Some simulations are also presented that validate our theoretical predictions.
Anahtar Kelimeler
Liquid level control, Lyapunov, Passivity, PD control, Stability
Kaynakça
- Ates, M. (2021). Circuit theory approach to stability and passivity analysis of nonlinear dynamical systems. International Journal of Circuit Theory and Applications, 50(1), 214–225. https://doi.org/10.1002/cta.3159
- Başçi, A., & Derdiyok, A. (2016). Implementation of an adaptive fuzzy compensator for coupled tank liquid level control system. Measurement, 91, 12–18. https://doi.org/10.1016/j.measurement.2016.05.026
- Biswas, P. P., Srivastava, R., Ray, S., & Samanta, A. N. (2009). Sliding mode control of quadruple tank process. Mechatronics, 19(4), 548–561. https://doi.org/10.1016/j.mechatronics.2009.01.001
- Eduardo, D. S. (1998). Mathematical control theory Deterministic finite dimensional systems. Second edition, Springer-Verlag New York, pp.218–230.
- Edwards, C. H., & Penney, D. E. (2018). Elementary differential equations with boundary value problems (Classic version, 6th ed.). Pearson. ISBN: 9780134995410
- Iplikci, S. (2010). A support vector machine based control application to the experimental three-tank system. ISA Transactions, 49(3), 376–386. https://doi.org/10.1016/j.isatra.2010.03.013
- Kämpjärvi, P., & Jämsä-Jounela, S. L. (2003). Level control strategies for flotation cells. Minerals Engineering, 16(11), 1061–1068. https://doi.org/10.1016/j.mineng.2003.06.004
- Raff, T., Huber, S., Nagy, Z. K., & Allgower, F. (2006, October). Nonlinear model predictive control of a four tank system: An experimental stability study. IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control. https://doi.org/10.1109/CACSD-CCA-ISIC.2006.4776652
- Sankar, G. S., Kumar, S. M., Narasimhan, S., & Bhallamudi, S. M. (2015). Optimal control of water distribution networks with storage facilities. Journal of Process Control, 32, 127–137. https://doi.org/10.1016/j.jprocont.2015.04.007
- Sbarbaro, D., & Ortega, R. (2005, December). Averaging level control of multiple tanks: a passivity based approach. Proceedings of the 44th IEEE Conference on Decision and Control. Sevilla, Spain. https://doi.org/10.1109/cdc.2005.1583353