Low-‎computational adaptive MPC algorithmization strategy for over ‎and ‎undershoots ‎instantaneous ‎water ‎heaters stability

Abstract

Tankless gas Hot Water users' ‎comforting perception ‎is severely affected by ‎sudden ‎changes ‎in temperature ‎apart from ‎the ‎desired temperature. The instability of the ‎water ‎temperature ‎with ‎overshoots and ‎undershoots is the ‎most common disadvantage ‎that ‎appears ‎mainly ‎because of the sudden changes in ‎the water flow demanded by ‎users ‎and ‎the ‎response delays inherent to ‎the heating system. ‎Classical ‎controllers for heat ‎cells have ‎difficulties in ‎responding ‎to ‎temperature ‎instability in a timely manner because ‎they do not ‎have the ‎capacity to anticipate ‎the ‎effects ‎of sudden variations in water flow ‎rate. ‎The ‎model ‎predictive control with adaptive function strategy reported ‎the ‎best ‎response ‎in ‎the stabilization of ‎temperature ‎in previous work. Its ‎performance is a ‎result of ‎the ‎predictive nature that allows ‎anticipating and ‎correcting the negative ‎influences ‎of ‎sudden ‎variations in the flow rate in ‎the ‎temperature. The present study aims to employ ‎this ‎strategy a low-computational ‎algorithm that can be embedded in low-cost ‎hardware ‎with ‎the limitation of computational and ‎memory resources. ‎The ‎study’s ‎motivation is to ‎meet ‎the ‎opening of manufacturers by ‎implementing low-cost and optimal-‎performance ‎microcontrollers ‎for ‎water heaters. The algorithm predictions ‎are ‎showing ‎good ‎agreement ‎responses in temperature stabilization.‎

Keywords

• Tankless hot-water stability
• predictive control
• adaptive ‎function
• low-computational ‎microcontroller
• time delay‎

References

1. Aliskan, I. (2018). Adaptive model predictive control for wiener nonlinear systems. Iranian Journal of Science and Technology Transactions of Electrical Engineering, 43, 361–377.
2. Astrom, K. J., & Wittenmark, B. (1997). Computer controlled systems: Theory and design (3rd ed.). Prentice Hall. Bourke, G., Bansal, P., & Raine, R. (2014). Performance of gas tankless (instantaneous) water heaters under various international standards. Applied Energy, 131, 468–478.
3. Costa, V., Ferreira, J., & Guilherme, D. (2016). Modeling and simulation of tankless gas water heaters to reduce temperature overshoots and undershoots. 12th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics (HEFAT 2016), 1404–1409.
4. Ehtiwesh, I. A. S., & Durović, Ž. (2009). Comparative analysis of different control strategies for electro-hydraulic servo systems. World Academy of Science, Engineering and Technology, 32(8), 906–909.
5. Ehtiwesh, I. A. S., Quintã, A. F., & Ferreira, J. A. F. (2021). Predictive control strategies for optimizing temperature stability in instantaneous hot water systems. Science and Technology for the Built Environment, 27(5), 679–690.
6. Haissig, C. M., & Woessner, M. (2000). Adaptive fuzzy algorithm for domestic hot water temperature control of a combi-boiler. HVAC&R Research, 6(2), 117–134.
7. Henze, G. P., Yuill, D. P., & Coward, A. H. (2009). Development of a model predictive controller for tankless water heaters. HVAC & R Research, 15(1), 3–23.
8. Laurencio-Molina, J.C. & Salazar-Garcia, C., 2018. Design of an artificial neural network controller for a tankless water heater by using a low-profile embedded system. In J. L. Crespo-Mariño (Eds.), 2018 IEEE International work conference on bioinspired intelligence, IWOBI 2018 – Proceedings (pp. 1–8). IEEE.

9. Li, P., Vrabie, D., Li, D., Sorin, C., Bengea, S., O’Neill, Z. D., & Mijanovic, S. (2015). Simulation and experimental demonstration of model predictive control in a building HVAC system. Science and Technology for the Built Environment, 21(6), 721–732.
10. MathWorks. (2021). fmincon function. Available from: https://www.mathworks.com/help/optim/ug/ fmincon.html#:~:text=example-,x %3D fmincon(fun %2C x0 %2C A %2C b %2C,lb ≤ x ≤ ub .&text=If x(i) is unbounded,ub(i) %3D Inf.
11. Quintã, A. F., Ehtiwesh, I. A. S., Martins, N., & Ferreira, J. A. F. (2022). Gain scheduling model predictive controller design for tankless gas water heaters with time-varying delay. Applied Thermal Engineering, 213, Article 118669.
12. Quinta, A. F., Oliveira, J. D., Ferreira, J. A. F., Costa, V. A. F., & Martins, N. (2022). Virtual test bench for the design of control strategies for water heaters. Journal of Thermal Science and Engineering Applications, 14(5), 1–11.
13. Santos, T. L. M., Limon, D., Normey-Rico, J. E., & Alamo, T. (2012). On the explicit dead-time compensation for robust model predictive control. Journal of Process Control, 22(1), 236–246.
14. Takács, B., Števek, J., Valo, R., & Kvasnica, M. (2016). Python code generation for explicit MPC in MPT. In: 2016 European control conference (ECC) (pp. 1328–1333). IEEE.
15. Wang, L., Zang, H., & Ning, Y. (2011). The gas water heater control system design based on fuzzy control. 2011 International conference on electric information and control engineering, ICEICE 2011 - Proceedings (pp. 840–843). IEEE.
16. Xu, K., Qiu, X., Li, X., & Xu, Y. (2008). A dynamic neuro-fuzzy controller for gas-fired water heater. In M. Guo (Ed.), Proceedings - 4th International Conference on Natural Computation (pp. 240–244). IEEE.
17. Yuill, D. P., Coward, A. H., & Henze, G. P. (2010). Performance comparison of control methods for tankless water heaters. HVAC & R Research, 16(5), 677–690.