Full State Feedback Control with Observer for Multi Variable Temperature Regulation in Vapour Compression Refrigeration Systems

References

[1] D. Coulomb, "The role of refrigeration in the global economy," International Institute of Refrigeration (IIR), 29th Informatory Note on Refrigeration Technologies, pp. 1-14, 2015.

[2] R. Reid, "Food preservation and temperature oscillation in domestic refrigerators," International Journal of Food Engineering, vol. 5, no. 2, pp. 12-21, 1999.

[3] M. Di Felice, L. Peroddi, A. Leva, and A. Boer, "Adaptive temperature control of a household refrigerator," in Proc. 2009 American Control Conference, St. Louis, MO, USA, pp. 889-894.

[4] N. H. A. Hamid, M. M. Kamal, and F. H. Yahaya, "Application of PID controller in controlling refrigerator temperature," in Proc. 5th Int. Colloquium on Signal Processing and Its Applications (CSPA), 2009, pp. 22-27.

[5] H. Moradi, H. Setayesh, and A. Alasty, "PID- Fuzzy control of air handling units in the presence of uncertainty," International Journal of Thermal Sciences, vol. 109, pp. 123-135, 2016.

[6] E. P. B. Filho, F. E. M. Garcia, and O. S. H. Mendoza, "Application of adaptive control in a refrigeration system to improve performance," Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 33, no. 2, pp. 176- 182, 2011.

[7] R. B. Ali, M. A. Jaballah, E. Ardhi, and A. Mami, "Design and FPGA-implementation of a PID controller for temperature control in a refrigeration system," Indian Journal of Science and Technology, vol. 11, no. 16, pp. 1-14, 2018.

[8] T. S. S. Dantas, I. C. Franco, A. M. F. Fileti, and F. V. Silva, "Dynamic linear modelling of a refrigeration process with electronic expansion valve actuator," International Journal of Refrigeration, vol. 75, no. 3, pp. 11-21, 2017.

[9] K. Ogata, Modern Control Engineering, 5th ed. Upper Saddle River, NJ, USA: Prentice-Hall, 2010.

[10] C. T. Chen, Linear System Theory and Design, 4th ed. New York, NY, USA: Oxford University Press, 2013.

[11] G. D. Librado, E. E. R. Vazquez, L. A. M. Santiyanes, J. H. P. Vazquez, and C. A. N. Martin, "Transient analysis of a single-stage vapor compression refrigeration system using lumped parameter approaches," International Journal on Advances in Systems and Measurements, vol. 11, nos. 3-4, pp. 352-362, 2018.

[12] E. Aridhi, M. Abbes, and A. Mami, "Temperature control in a cavity of refrigeration using PI controller and predictive control," in Proc. 15th Int. Conf. on Sciences and Techniques of Automatic Control and Computer Engineering (STA), Hammamet, Tunisia, 2014, pp. 123-128.

[13] J. Arfaoui, E. Feki, and A. Mami, "PID and fuzzy logic optimized controller for temperature control in a cavity of refrigeration," in Proc. International Renewable Energy Congress (IREC), 2015, pp. 1-6.

[14] J. E. Schmitz, F. V. Da Silva, L. C. N. Filho, and V. S. Junior, "Fuzzy-PID controller applied to a refrigeration system," International Journal of Air-Conditioning and Refrigeration, vol. 20, no. 2, pp. 65-71, 2012.

[15] X. Qin, Y. Wang, J. Zhang, and L. Zhang, "Fruit fly optimisation algorithm-based PID control of refrigeration system temperature," Energies, vol. 11, no. 8, pp. 1-15, 2018.

[16] G. Reynoso-Meza, J. Sanchis, X. Blasco, and S. Garcia-Nieto, "Multi-objective optimisation design for a proportional-integral-derivative controller of a one-stage refrigeration cycle," Applied Thermal Engineering, vol. 130, pp. 939- 949, 2018.

[17] Z. Lei and Y. Zhou, "A kind of nonlinear PID controller for refrigeration systems based on vapour compression," in Proc. 3rd IFAC Conference on Advances in Proportional- Integral-Derivative Control, Ghent, Belgium, 2018, pp. 716-721.

[18] M. Dehghan, N. Mansouri-Moghaddam, and P. Derakhshan, "Model predictive control using RIOTS for one-stage refrigeration cycle," Applied Thermal Engineering, vol. 135, pp. 62- 72, 2018.

[19] J. J. Carreno-Zagarra, R. Villamizar, and J. C. Moreno, "Active disturbance rejection and PID control of a one-stage refrigeration cycle," in Proc. 3rd IFAC Conference on Advances in PID Control, Ghent, Belgium, 2018, pp. 444-449.

[20] F. Zhang, H. Li, and Z. Wang, "Decentralized linear active disturbance rejection control for a benchmark refrigeration system," ISA Transactions, vol. 82, pp. 248-258, 2018.

[21] C. Huff, L. Jin, T. M. Theunissen, and A. Visioli, "Data-driven control design using prediction error identification for vapour-compression refrigeration," Control Engineering Practice, vol. 78, pp. 100-112, 2018.

[22] C. Piedrahita-Velasquez, O. Alvarez, and H. Alvarez, "Anti-windup control for variable- speed compressor refrigeration systems," Applied Thermal Engineering, vol. 130, pp. 949- 961, 2018.

[23] L. A. Aloo, R. K. Kibe, and J. P. Mwaniki, "Design of state-space feedback control for temperature-controlled food storage applications," International Journal of Engineering Research and Applications, vol. 6, no. 4, pp. 80-88, 2016.

[24] Achebe P.N. and Muoghalu C.N. (2025), “Design of Adaptive PD Controller for Microsatellite Yaw Axis Attitude Control System”, International Journal of Engineering Research and Development (IJERD), Vol. 21, Issue 2, Pp. 225-232.

[25] Achebe, P.N. and Muoghalu, C.N. (2024), “State-Space Modelling and Control of Two- Phase Hybrid Stepping Motor for Robot Grinding Using LQR Controller”, International Journal of Academic Information Systems Research (IJAISR), Vol. 8, Issue 4. Pp. 132-136.

[26] C.N. Muoghalu and P.N. Achebe (2021), “Two- Phase Hybrid Stepping Motor Based Antenna Positioning Control System Using Proportional Integral and Derivative Controller”, Iconic Research and Engineering Controller (IREC), Vol. 4, Issue 10, Pp. 152-157.

[27] Muoghalu C.N. and Achebe P.N. (2025), “Enhancing the Dynamic Response Servo Positioning System using Internal Model Control Based Compensator: A Case Study of HDD” International Journal of Progressive Research in Engineering Management and Science (IJPREMS), Vol. 5, Issue 3, Pp. 236-242.

[28] Muoghalu, C. N., Achebe, P. N. and Oyeka, D.O. (2025), “Investigating the Essence of Compensators in Engineering Systems: A Case Study of Industrial Belt Conveyor System”, International Journal of Research Publication and Reviews (IJRPR), Vol. 6, Issue 5, Pp. 353- 358.

[29] C.N. Muoghalu, M.I. Ndefo and H.I. Ugwu (2021), “Performance Enhancement of Chopper Fed DC Motor Speed Control System Using PID Controller”, Multidisciplinary International Journal of Research and Development (MIJRD), Vol. 1, Issue 2, Pp. 1-8.

[30] Chisom Ifunanya Onyekwelu, C. A. Nwabueze, C. N. Muoghalu and B. O. Ekengwu (2023), “Model Reference Adaptive Control Based PID Controller for Hard Disk Drive Read/Write Head Servo Positioning System”, International Journal of Academic Multidisciplinary Research (IJAMR), Vol.7, Issue 8, Pp. 135-144.

[31] Bonaventure Onyeka Ekengwu, Paulinus Chinanye Eze, Chidiebere Nnaedozie Muoghalu, Christopher Nnaemeka Asiegbu and Patience Nkiruka Achebe (2024), “Design of Robust Centralized PID Optimized LQR Controller for Temperature Control in Single -Stage Refrigeration System”, International Journal of Electrical Engineering and Informatics (IJEEI), Vol. 12, No. 3, Pp. 726-738.

@article{1716088,
      author = {Onunwor, Kelechi O., Muoghalu, C. N., Atuchukwu, A. J., Nnaemeka C. Asiegbu},
      title = {Full State Feedback Control with Observer for Multi Variable Temperature Regulation in Vapour Compression Refrigeration Systems},
      journal = {Iconic Research And Engineering Journals},
      year = {2026},
      volume = {9},
      number = {10},
      pages = {4996-5004},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1716088.pdf},
      abstract = {Achieving tight and reliable temperature regulation across all functional components of a vapour-compression refrigeration system remains a persistent challenge, primarily because classical control strategies struggle to account for the multi-dimensional, nonlinear, and coupled thermal dynamics inherent to such systems. This paper presents the design, analysis, and simulation-based validation of a full state feedback controller augmented with an observer for multi-variable temperature control of a single-stage vapour-compression refrigeration system. The plant model, derived by applying energy conservation principles to each of the four major components — evaporator, compressor, condenser, and expansion valve — is cast in state-space form, and its controllability and observability are analytically confirmed. A pole placement approach is employed to compute the state feedback gain matrix K, a forward path gain Kf is subsequently introduced to enforce zero steady-state tracking, and a Luenberger observer is designed to estimate unmeasured system states, thereby reducing reliance on physical sensors. MATLAB/Simulink simulations are conducted across five progressive design stages, and transient response metrics — rise time, settling time, peak overshoot, and steady-state error — are extracted and benchmarked. The proposed full state feedback controller with forward gain and observer achieves rise times of approximately 1.1 s for the evaporator and compressor and 0.732 s for the condenser and expansion valve, with settling times below 2.0 s, zero peak overshoot, and zero steady-state error. Practical validation with realistic operating temperatures confirms the controller's capacity to track and maintain desired temperatures for efficient cooling.},
      keywords = {Vapour-Compression Refrigeration, Full State Feedback, Pole Placement, Luenberger Observer, Temperature Control.},
      month = {April},
      doi = {https://doi.org/10.64388/IREV9I10-1716088}
  }