Thermoelectric Module Control Based on Fractional-Order Disturbance Estimation State Observers

https://doi.org/10.58571/CNCA.AMCA.2024.057

Resumen: This article presents a fractional-order control strategy based on an uncertainty estimator applied to thermoelectric modules. It is known that thermoelectric modules are nonlinear systems characterized by a polynomial-type nonlinear control input. The proposed control law does not require the linearization of the nonlinear control input, this is achieved through the use of a state observer that estimates certain components of the nonlinear system’s state, enabling the control law to counteract these elements and drive the system toward a desired state. To validate the theoretical results, experiments are conducted by implementing the control law on a platform comprising a buck-type DC/DC converter that powers a Peltier cell.

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Montesinos García, J.J., Barahona Avalos, J.L., Lugo González, E. & Linares Flores, J. (2024). Thermoelectric Module Control Based on Fractional-Order Disturbance Estimation State Observers. Memorias del Congreso Nacional de Control Automático 2024, pp. 332-337. https://doi.org/10.58571/CNCA.AMCA.2024.057

Palabras clave

State observer, Observer-based control, Fractional-order systems, Disturbance estimation, Thermoelectric Module

• Barahona-Avalos, J.L., Juárez-Abad, J.A., Galván-Cruz, G., and Linares-Flores, J. (2021). Control mediante rechazo activo de perturbaciones de la temperatura de un módulo termoeléctrico. Revista Iberoamericana de Automática e Informática Industrial, 19(1), 48–60.
• Dang, V.T., Nguyen, D.B.H., Tran, T.D.T., Le, D.T., and Nguyen, T.L. (2023). Model-free hierarchical control with fractional-order sliding surface for multisection web machines. International Journal of Adaptive Control and Signal Processing, 37(2), 497–518.
• Duarte-Mermoud, M.A., Aguila-Camacho, N., Gallegos, J.A., and Castro-Linares, R. (2015). Using general quadratic lyapunov functions to prove lyapunov uniform stability for fractional order systems. Communications in Nonlinear Science and Numerical Simulation, 22(1-3), 650–659.
• Freeborn, T.J. (2013). A survey of fractional-order circuit models for biology and biomedicine. IEEE Journal on emerging and selected topics in circuits and systems, 3(3), 416–424.
• Hilfer, R. (2000). Applications of fractional calculus in physics. World scientific.
• Hu, X., Song, Q., Ge, M., and Li, R. (2020). Fractionalorder adaptive fault-tolerant control for a class of general nonlinear systems. Nonlinear Dynamics, 101, 379–392.
• Kungwalrut, P., Numsomran, A., Chaiyasith, P., Chaoraingern, J., and Tipsuwanporn, V. (2017). A pi λ d µ controller design for peltier-thermoelectric cooling system. In 2017 17th International Conference on Control, Automation and Systems (ICCAS), 766–770. IEEE.
• Laskin, N. (2000). Fractional market dynamics. Physica A: Statistical Mechanics and its Applications, 287(3-4), 482–492.
• Li, Y., Chen, Y., and Podlubny, I. (2010). Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized mittag–leffler stability. Computers & Mathematics with Applications, 59(5), 1810–1821.
• Lineykin, S. and Ben-Yaakov, S. (2005). Analysis of thermoelectric coolers by a spice-compatible equivalentcircuit model. IEEE Power Electronics Letters, 3(2), 63–66.
• Lineykin, S. and Ben-Yaakov, S. (2007). Modeling and analysis of thermoelectric modules. IEEE Transactions on Industry Applications, 43(2), 505–512.
• Liu, H., Li, S., Li, G., and Wang, H. (2018). Adaptive controller design for a class of uncertain fractionalorder nonlinear systems: an adaptive fuzzy approach. International Journal of Fuzzy Systems, 20, 366–379.
• Maamir, F., Guiatni, M., El Hachemi, H.M.S.M., and Ali, D. (2015). Auto-tuning of fractional-order pi controller using particle swarm optimization for thermal device. In 2015 4th International Conference on Electrical Engineering (ICEE), 1–6. IEEE.
• Macias, M. and Sierociuk, D. (2012). Fractional order calculus for modeling and fractional pid control of the heating process. In Proceedings of the 13th International Carpathian Control Conference (ICCC), 452– 457. IEEE.
• Podlubny, I., Dorcak, L., and Kostial, I. (1999). On fractional derivatives, fractional-order dynamic system and pid-controllers. In Proceedings of the 36th 1997 IEEE Conference on Decision and Control, Phoenix, AZ, USA, 7–10. Citeseer.
• Viola, J., Oziablo, P., and Chen, Y. (2020a). A portable and affordable networked temperature distribution control platform for education and research. IFACPapersOnLine, 53(2), 17530–17535.
• Viola, J., Rodriguez, C., and Chen, Y. (2020b). Phelp: Pixel heating experiment learning platform for education and research on iai-based smart control engineering. In 2020 2nd International Conference on Industrial Artificial Intelligence (IAI), 1–6. IEEE.
• Zhou, X.J., Gao, Q., Abdullah, O., and Magin, R.L. (2010). Studies of anomalous diffusion in the human brain using fractional order calculus. Magnetic resonance in medicine, 63(3), 562–569.
• Zouari, F., Ibeas, A., Boulkroune, A., Jinde, C., and Arefi, M.M. (2021). Neural network controller design for fractional-order systems with input nonlinearities and asymmetric time-varying pseudo-state constraints. Chaos, Solitons & Fractals, 144, 110742.