Skip to main content
Springer Nature Link
Log in

Novel practically finite-time constrained control of thermoelectric coolers with model-updated approach

  • Published:
International Journal of Dynamics and Control Aims and scope Submit manuscript

Abstract

Precise temperature control in thermoelectric coolers faces significant challenges due to nonlinear dynamics, parameter uncertainties, external disturbances, and input constraints. This study presents a nonlinear model-updating scheme that provides an enriched dynamic model for a novel finite-time controller with input constraints. The proposed methodology compensates for perturbations in a reduced-order model through estimation and incorporation of complementary correction terms. This ensures precise alignment between the mathematical model and physical system behavior. The approach leverages temperature measurements from both sides of the thermoelectric element to estimate perturbations in real time. Using the enhanced model, a novel nonlinear finite-time controller is developed to track the reference temperature by the element in the presence of input constraints. The controller adaptively adjusts to the actual system, achieving high reliability through the improved model. Mathematical analyses prove the practical finite-time convergence of the tracking error to a compact set under input saturation. Experimental validation on a fabricated thermoelectric platform demonstrates the enhanced effectiveness of the controller in temperature tracking. Superior accuracy and robustness are demonstrated in comparative analyses against prevalent control strategies, even under uncertainties, external disturbances and input saturation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+
from €37.37 /Month
  • Starting from 10 chapters or articles per month
  • Access and download chapters and articles from more than 300k books and 2,500 journals
  • Cancel anytime
View plans

Buy Now

Price includes VAT (Norway)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Explore related subjects

Discover the latest articles, books and news in related subjects, suggested using machine learning.

Data availability

No datasets were generated or analyzed during the current study.

Code Availability

The custom code that supports the findings of this study is available from the corresponding author upon reasonable request via email: sa_rafatnia@sut.ac.ir.

References

  1. Wang L, Chu T, Yuan S, Zou P, Zhai W, Zheng X, Xia M (2025) Advances and future perspectives in thermoelectric cooling technology. Energy Conv Manag 332:119621

    Article  Google Scholar 

  2. Luo D, Wu Z, Zhang Z, Chen H, Geng L, Ji Z, Zhang P (2025) Transient thermal analysis of a thermoelectric-based battery thermal management system at high temperatures. Energy 318:134833

    Article  Google Scholar 

  3. Gao Y, Zhu S, Gao J, Miao L, Xu F, Sun L (2024) Wearable thermoelectric cooler encapsulated with low thermal conductivity filler and honeycomb structure for high cooling effect. Mater Today Phys 46:101491

    Article  Google Scholar 

  4. Liu H, Shen L, Li Y, Zhao X, Li G, Liu Z, Yang H (2025) Investigation of a novel separately-configured thermoelectric cooler: a pathway toward the building integrated thermoelectric air conditioning. Adv Appl Energy 18:100218

    Article  Google Scholar 

  5. Khan Y, Khan TA, Ilyas M (2024) Design and experimentation of Peltier-based thermoelectric cooling vaccine carrier box. J Artif Intell Comput 2(1):23–28

    Article  Google Scholar 

  6. Arikusu YS, Bayhan N (2024) Design of a novel PID controller based on machine learning algorithm for a micro-thermoelectric cooler of the polymerase chain reaction device. IEEE Access 12:61959–61977

    Article  Google Scholar 

  7. Jian M, Zhu S, Du W, Yang L, Zhang J (2025) Design of a temperature control system for transient thermal measurement utilizing the backpropagation PID algorithm. Int J Therm Sci 210:109654

    Article  Google Scholar 

  8. Najafi H, Woodbury KA (2013) Optimization of a cooling system based on Peltier effect for photovoltaic cells. Sol Energy 91:152–160

    Article  Google Scholar 

  9. Wang Y, Liu J, Yu J (2025) Lyapunov-derived fuzzy temperature control for thermoelectric cooling system using dynamic updating law. Appl Therm Eng 258:124600

    Article  Google Scholar 

  10. Kherkhar A, Chiba Y, Tlemcani A, Mamur H (2022) Thermal investigation of a thermoelectric cooler based on Arduino and PID control approach. Case Stud Therm Eng 36:102249

    Article  Google Scholar 

  11. Rezk H, Harrag A (2021) A robust type-2 fuzzy logic-based maximum power point tracking approach for thermoelectric generation systems. Int J Energy Res 45(12):18066–18080

    Article  Google Scholar 

  12. Mironova A, Mercorelli P, Zedler A (2018) Thermal disturbances attenuation using a Lyapunov controller for an ice-clamping device actuated by thermoelectric coolers. Therm Sci Eng Prog 6:290–299

    Article  Google Scholar 

  13. Gavrikov A, Kostin G, Aschemann H, Rauh A (2020) Modeling and control of a thermoelectric structure with a Peltier element subject to external disturbances. IFAC-PapersOnLine 53(2):7771–7776

    Article  Google Scholar 

  14. Fallmann M, Losch M, Poks A, Kozek M (2023) Energy-efficient hybrid model predictive control of mobile refrigeration systems. Appl Therm Eng 235:121347

    Article  Google Scholar 

  15. Cui X, Hu T (2023) Robust predictive thermal management strategy for lithium-ion battery based on thermoelectric cooler. Appl Therm Eng 221:119833

    Article  Google Scholar 

  16. Evers E, Slenders R, van Gils R, de Jager B, Oomen T (2021) Thermoelectric modules in mechatronic systems: temperature-dependent modeling and control. Mechatronics 79:102647

    Article  Google Scholar 

  17. Choi HS, Yun S, Whang KI (2007) Development of a temperature-controlled car-seat system utilizing thermoelectric device. Appl Therm Eng 27(17–18):2841–2849

    Article  Google Scholar 

  18. Rafatnia S (2025) Adaptive fixed-time terminal sliding mode control of a Peltier cell fused with a fuzzy fixed-time perturbation estimator. J Process Control 148:103391

    Article  Google Scholar 

  19. Zhu C, Lu F, Zhang H, Mi CC (2018) Robust predictive battery thermal management strategy for connected and automated hybrid electric vehicles based on thermoelectric parameter uncertainty. IEEE J Emerg Sel Top Power Electron 6(4):1796–1805

    Article  Google Scholar 

  20. Zhang C, Li K, Deng J (2016) Real-time estimation of battery internal temperature based on a simplified thermoelectric model. J Power Sources 302:146–154

    Article  Google Scholar 

  21. van Rossum F, Haus B, Mercorelli P, Zedler A (2021) Cascaded Kalman filters for a sliding mode control in a Peltier structure for an innovative manufacturing system. In: IECON 2021 47th annual conference of the IEEE industrial electronics society. IEEE, pp 1–6. https://doi.org/10.1109/IECON48115.2021.9589741

  22. van Rossum F, Haus B, Mercorelli P, Aschemann H (2023) Input–output linearization of a thermoelectric cooler for an ice clamping system using a dual extended Kalman filter. In: 2023 27th International conference on methods and models in automation and robotics (MMAR). IEEE, pp 199–204. https://doi.org/10.1109/MMAR58394.2023.10242590

  23. Mirzaeinejad H, Mirzaei M, Rafatnia S (2018) A novel technique for optimal integration of active steering and differential braking with estimation to improve vehicle directional stability. ISA Trans 80:513–527

    Article  Google Scholar 

  24. Rafatnia S, Nourmohammadi H, Keighobadi J (2019) Fuzzy-adaptive constrained data fusion algorithm for indirect centralized integrated SINS/GNSS navigation system. Gps Solut 23(3):62

    Article  Google Scholar 

  25. Abdolkarimi ES, Mosavi MR, Rafatnia S, Martin D (2021) A hybrid data fusion approach to AI-assisted indirect centralized integrated SINS/GNSS navigation system during GNSS outage. IEEE Access 9:100827–100838

    Article  Google Scholar 

  26. Yu W, Yu X, Wang H (2023) Sliding modes: from asymptoticity, to finite time and fixed time. Sci China Inf Sci 66(9):190205

    Article  MathSciNet  Google Scholar 

  27. Cruz-Ortiz D, Chairez I, Poznyak A (2022) Non-singular terminal sliding-mode control for a manipulator robot using a barrier Lyapunov function. ISA Trans 121:268–283

    Article  Google Scholar 

  28. Wang J, Alattas KA, Bouteraa Y, Mofid O, Mobayen S (2023) Adaptive finite-time backstepping control tracker for quadrotor UAV with model uncertainty and external disturbance. Aerosp Sci Technol 133:108088

    Article  Google Scholar 

  29. Hu X, Chen J, Lv C, Zhang Z, Wang Y (2024) Finite-time trajectory tracking control for unmanned ground vehicle based on finite-time disturbance observer. J Frankl Inst 361(17):107222

    Article  MathSciNet  Google Scholar 

  30. Ghadiri H, Khodadadi H, Hazareh GA (2024) Finite-time integral fast terminal sliding mode control for uncertain quadrotor UAV based on state-dependent Riccati equation observer subjected to disturbances. J Vib Control 30(11–12):2528–2548

    Article  MathSciNet  Google Scholar 

  31. Hui J (2024) Discrete-time integral terminal sliding mode load following controller coupled with disturbance observer for a modular high-temperature gas-cooled reactor. Energy 292:130479

    Article  Google Scholar 

  32. Zhang JX, Ding J, Chai T (2024) Fault-tolerant prescribed performance control of wheeled mobile robots: a mixed-gain adaption approach. IEEE Trans Autom Control 69(8):5500–5507

    Article  MathSciNet  Google Scholar 

  33. Cui X, Jiang S (2024) A novel temperature distribution modeling method for thermoelectric cooler with application to battery thermal management system. Energy 306:132426

    Article  Google Scholar 

  34. Wang L, Chu T, Yuan S, Zou P, Zhai W, Zheng X, Xia M (2025) Advances and future perspectives in thermoelectric cooling technology. Energy Conv Manag 332:119621

    Article  Google Scholar 

  35. Bechlioulis CP, Rovithakis GA (2008) Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance. IEEE Trans Autom Control 53(9):2090–2099

    Article  MathSciNet  Google Scholar 

  36. Zhao D, Tan G (2024) A review of thermoelectric cooling: materials, modeling and applications. Appl Therm Eng 66(1–2):15–24

    Google Scholar 

  37. Zhao D, Tan G (2014) A review of thermoelectric cooling: materials, modeling and applications. Appl Therm Eng 66(1–2):15–24

    Article  Google Scholar 

  38. Rafatnia S, Mirzaei M (2021) Adaptive estimation of vehicle velocity from updated dynamic model for control of anti-lock braking system. IEEE Trans Intell Transp Syst 23(6):5871–5880

    Article  Google Scholar 

  39. Rafatnia S, Mirzaei M (2022) Estimation of reliable vehicle dynamic model using IMU/GNSS data fusion for stability controller design. Mech Syst Signal Proc 168:108593

    Article  Google Scholar 

  40. Shahir MM, Mirzaei M, Farbodi M, Rafatnia S (2024) Estimation of shape memory alloy actuator dynamics to design reduced-order position controller with input saturation. IET Contr Theory Appl 18(10):1301–1313

    Article  MathSciNet  Google Scholar 

  41. Yarinia N, Mirzaei M, Rafatnia S (2024) Construction of an enhanced 2-DOF finite element model for precise control of flexible beam vibration. Int J Dyn Control 12(10):3577–3592

    Article  MathSciNet  Google Scholar 

  42. Samiei SK, Mirzaei M, Rafatnia S, Avval SSP, Yarinia N (2025) Updating reduced-order dynamic model for flexible-joint arm to design adaptive feedback linearization control. Proc Inst Mech Eng Part C J Eng Mech Eng Sci 239(5):1474–1491

    Article  Google Scholar 

  43. Sisi ZA, Mirzaei M, Rafatnia S, Jamshidi S, Farbodi M (2025) Novel observer-based fault-tolerant tracking control of input-constrained polymerization reactor with statistical analysis. J Process Control 155:103541

    Article  Google Scholar 

  44. Ahmadlou N, Mirzaei M, Rafatnia S (2025) Information fusion-based estimation of model uncertainties and disturbances for constrained predictive control of autonomous wheeled mobile robot. Int J Dyn Control 13(5):192

    Article  MathSciNet  Google Scholar 

  45. Sisi ZA, Mirzaei M, Rafatnia S (2025) Input-saturated control of active suspension system using fuzzy-scheduled estimation of model uncertainties and road disturbances. Int J Robust Nonlinear Control https://doi.org/10.1002/rnc.70180

  46. Samiei SK, Mirzaei M, Rafatnia S (2024) Constrained control of flexible-joint lever arm based on uncertainty estimation with data fusion for correcting measurement errors. Nonlinear Dyn 112(13):11147–11166

    Article  Google Scholar 

  47. Sisi ZA, Mirzaei M, Rafatnia S (2024) New strategy to perturbation estimation and constrained control of vehicle suspension system. Proc Inst Mech Eng Part D J Automob Eng https://doi.org/10.1177/0954407025132426

  48. Rafatnia S, Abdolkarimi ES (2025) An integration algorithm for SINS/GNSS/Airdata navigation system using adaptive super-twisting method+ optimized hybrid GRU-LSTM sequential model. ISA Trans https://doi.org/10.1016/j.isatra.2025.10.024

  49. Abdolkarimi ES, Rafatnia S (2026) Fuzzy fixed-time multi-source fusion with attention-based neural networks for reliable navigation under satellite signal loss. Eng Appl Artif Intell 163:112806

    Article  Google Scholar 

  50. Pak F, Mirzaei M, Rafatnia S, Salmani Pour Avval S (2024) Novel observer-based input-constrained control of nonlinear second-order systems with stability analysis: experiment on lever arm. Iran J Sci Technol Trans Electr Eng 48(3):1111–1128

    Article  Google Scholar 

  51. Gharamaleki RM, Mirzaei M, Rafatnia S, Alizadeh B (2020) An analytical approach to optimal control of nonlinear systems with input constraints. Int J Autom Control 14(2):213–238

    Article  Google Scholar 

  52. Najjari B, Mirzaei M, Tahouni A (2022) Decentralized integration of constrained active steering and torque vectoring systems to energy-efficient stability control of electric vehicles. J Franklin Inst 359(16):8713–8741

    Article  MathSciNet  Google Scholar 

  53. Liu C, Li L, Xia Y, Zhao L (2025) Practically finite-time ADRC for a 3-DOF parallel mechanism of PMAs with couplings. IEEE Trans Circuits Syst I Regul Pap. https://doi.org/10.1109/TCSI.2025.3540911

    Article  Google Scholar 

Download references

Acknowledgements

There is no acknowledgment.

Funding

No funding was received.

Author information

Authors and Affiliations

  1. Sahand University of Technology, Tabriz, Islamic Republic of Iran

    Sadra Rafatnia & Mehdi Mirzaei

Authors
  1. Sadra Rafatnia
    View author publications

    Search author on:PubMed Google Scholar

  2. Mehdi Mirzaei
    View author publications

    Search author on:PubMed Google Scholar

Contributions

Rafatnia and Mirzaei contributed to the study conception and design. Data collection and analysis were performed by Rafatnia and Mirzaei. Mirzaei carried out the formal analysis. The first draft of the manuscript was written by Rafatnia; Mirzaei commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Sadra Rafatnia.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rafatnia, S., Mirzaei, M. Novel practically finite-time constrained control of thermoelectric coolers with model-updated approach. Int. J. Dynam. Control 14, 18 (2026). https://doi.org/10.1007/s40435-025-01956-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Version of record:

  • DOI: https://doi.org/10.1007/s40435-025-01956-4

Keywords

Profiles

  1. Sadra Rafatnia View author profile