# Variable Structure-Based Control for Dynamic Temperature Setpoint Regulation in Hospital Extreme Healthcare Zones

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- For the case of intensive care units (ICU) and OTs in a hospital environment, dynamic setpoints for the zone temperature are incorporated.
- The model will be processed on the dynamic temperature setpoints of operation rooms (ORs) inside the hospital. This is because, in ORs, both patients and healthcare workers desire different temperature environments depending on the patient’s condition and the requirements of the surgical and treatment procedures.
- To achieve the dynamic setpoints’ variability, a detailed mathematical model of the zone temperature is considered in the formulation of the controller.
- The major influencing parameters of the internal zone temperature, i.e., outside air temperature, solar irradiation, wind speed, and heat generated from internal appliances are incorporated into the design of the controller.
- For the dynamic regulation of the HVAC temperature, two nonlinear controllers, DISMC and ITSMC, have been proposed.
- Asymptotic stability of the system has been ensured for both nonlinear controllers.

## 2. Hospital Case Study

## 3. Thermal Mathematical Model

#### 3.1. External Walls

#### 3.2. Solar Contributions

#### 3.3. Ventilation

#### 3.4. Windows

#### 3.5. Humans and Applications

## 4. Robust Controller Design

#### 4.1. Double Integral Sliding Mode Controller Design

#### 4.2. Integral Terminal Sliding Mode Controller Design

## 5. Simulation and Results

#### 5.1. Environmental Conditions

#### 5.2. Dynamic Setpoint

#### 5.3. Johnson Temperature Controller

#### 5.4. Implementation of DISMC Temperature Controller

#### 5.5. Implementation of ITSMC Temperature Controller

#### 5.6. Comparative Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

List of Abbreviations | |

S | Sliding manifold |

$ANN$ | Artificial neural network |

$DISMC$ | Double integral sliding mode control |

$EUI$ | Energy use intensity |

$HVAC$ | Heating, ventilation, and air conditioning |

$ICT$ | Islamabad Capital Territory |

$IEA$ | International Energy Agency |

$ITSMC$ | Integral terminal sliding mode control |

$JCI$ | Joint Commission International |

$JTC$ | Johnson temperature controller |

$MIMO$ | Multi input multi output |

$MPC$ | Model predictive control |

$OR$ | Operation room |

$OT$ | Operation theater |

$S/V$ | Surface-to-volume |

$SIH$ | Shifa International Hospital |

$SMC$ | Sliding mode control |

$SSE$ | Steady-state error |

V | Lyapunov candidate function |

$ZN$ | Ziegler–Nichols |

List of Symbols | |

${R}_{win.j}$ | Window resistance (KW${}^{-1}$) |

${a}_{1},{a}_{2},{a}_{3}$ | Sliding coefficients |

${e}_{1},{e}_{2},{e}_{3},{e}_{5}$ | Errors |

${T}_{O{R}_{ref}}$ | OR temperature reference (°C) |

$\alpha $ | Unit between 0 and 1 |

${\dot{q}}_{wi.j}$ | The flow of heat flux from the internal layer towards the wall node (W) |

${\dot{v}}_{a}$ | Volume of air conditioned per minute (m${}^{3}$/min) |

${\dot{x}}_{hs},{\dot{x}}_{cs}$ | Heating/cooling input thermal power (W) |

${\dot{x}}_{is}$ | Internal free heat gain due to person and equipment (W) |

${\dot{x}}_{sg}$ | Thermal energy contribution due to solar radiation |

${\dot{x}}_{v}$ | Heat transfer through the windows due to ventilation (W) |

${\dot{x}}_{we.j}$ | The flow of heat flux from the external layer towards the wall node (W) |

${\dot{x}}_{win}$ | Flow of heat charge across the window (W) |

${\dot{x}}_{wl}$ | Heat transfer to the wall (W) |

${\kappa}_{2}$ | Design parameter of sliding manifold |

${\lambda}_{2}$ | Positive constant |

$\varphi $ | Small number used to reduce chattering |

${\psi}_{fl}$ | Absorption coefficient |

${\psi}_{w.j}$ | Wall absorbance coefficient |

${\rho}_{v},{c}_{a}$ | The density (kg m${}^{-3}$) and specific heat of the air (kJ/kg · K) |

${\tau}_{win.j}$ | Transmittance coefficient of the window glass (Wm${}^{2}$ K${}^{-1}$) |

${C}_{OR}$ | Total capacitance of OR (JK${}^{-1}$) |

${c}_{vv}$ | Specific heat of air ventilated from the system (kJ/kg · K) |

${C}_{w.j}$ | Total thermal capacitance of the wall (JK${}^{-1}$) |

${f}_{j}$ | Function of shadow on the window |

${I}_{jn}$ | Amount of solar irradiation (Wm${}^{2}$) |

${M}_{v}$ | Mass of air ventilated from the system (g/mol) |

${S}_{w.j}$ | Total opaque surface area of wall (m${}^{2}$) |

${S}_{win.j}$ | Total transparent surface area of the window (m${}^{2}$) |

${T}_{OR}$ | OR Internal air temperature (°C) |

${T}_{v}$ | Temperature of ventilation system (°C) |

${T}_{w.j}$ | Temperature of wall internal node (°C) |

${U}_{v}$ | Overall heat transfer coefficient (Wm${}^{2}$ K${}^{-1}$) |

## Appendix A

## References

- Ding, Y.; Zhang, Q.; Yuan, T.; Yang, K. Model input selection for building heating load prediction: A case study for an office building in Tianjin. Energy Build.
**2018**, 159, 254–270. [Google Scholar] [CrossRef] - Hietaharju, P.; Ruusunen, M.; Leiviskä, K. A dynamic model for indoor temperature prediction in buildings. Energies
**2018**, 11, 1477. [Google Scholar] [CrossRef] - Perera, D.W.U.; Pfeiffer, C.F.; Skeie, N.O. Modelling the heat dynamics of a residential building unit: Application to Norwegian buildings. Model. Identif. Control J.
**2014**, 35, 43–57. [Google Scholar] [CrossRef] - Rousselot, M. Energy efficiency trends in buildings. Odyssee-Mure
**2018**, 4, 1–4. [Google Scholar] - Costa, A.; Keane, M.M.; Torrens, J.I.; Corry, E. Building operation and energy performance: Monitoring, analysis and optimisation toolkit. Appl. Energy
**2013**, 101, 310–316. [Google Scholar] [CrossRef] - Adegbenro, A.; Short, M.; Angione, C. An integrated approach to adaptive control and supervisory optimisation of HVAC control systems for demand response applications. Energies
**2021**, 14, 2078. [Google Scholar] [CrossRef] - Pedersen, L. Use of different methodologies for thermal load and energy estimations in buildings including meteorological and sociological input parameters. Renew. Sustain. Energy Rev.
**2007**, 11, 998–1007. [Google Scholar] [CrossRef] - Fateh, A.; Borelli, D.; Spoladore, A.; Devia, F. A state-space analysis of a single zone building considering solar radiation, internal radiation, and PCM effects. Appl. Sci.
**2019**, 9, 832. [Google Scholar] [CrossRef] - Malinowski, A.; Muzychak, A. Mathematical modeling of the building thermal state taking into account the heat and energy impact of the environment. In Proceedings of the IOP Conference Series: Materials Science and Engineering, Yekaterinburg, Russia, 13–16 November 2017; IOP Publishing: Bristol, UK, 2018; Volume 415, p. 012047. [Google Scholar]
- Amara, F.; Agbossou, K.; Cardenas, A.; Dubé, Y.; Kelouwani, S. Comparison and simulation of building thermal models for effective energy management. Smart Grid Renew. Energy
**2015**, 6, 95. [Google Scholar] [CrossRef] - Ljung, L. System Identification: Theory for the User; Pearson: London, UK, 1998; pp. 163–173. [Google Scholar]
- Lebrun, J. Simulation of a HVAC system with the help of an engineering equation solver. In Proceedings of the Seventh International IBPSA Conference, Rio de Janeiro, Brazil, 13–15 August 2001; pp. 13–15. [Google Scholar]
- Kato, K.; Sakawa, M.; Ishimaru, K.; Ushiro, S.; Shibano, T. Heat load prediction through recurrent neural network in district heating and cooling systems. In Proceedings of the 2008 IEEE International Conference on Systems, Man and Cybernetics, Singapore, 12–15 October 2008; pp. 1401–1406. [Google Scholar]
- Heiselberg, P.K. The Energy Performance Assessment of nZEBs: Limitations of the Quasi-Steady State Approach. In Proceedings of the CLIMA 2016—12th REHVA World Congress, Aalborg, Denmark, 22–25 May 2016. [Google Scholar]
- Mahdavi, A.; Tahmasebi, F.; Kayalar, M. Prediction of plug loads in office buildings: Simplified and probabilistic methods. Energy Build.
**2016**, 129, 322–329. [Google Scholar] [CrossRef] - Paolini, R.; Zani, A.; MeshkinKiya, M.; Castaldo, V.L.; Pisello, A.L.; Antretter, F.; Poli, T.; Cotana, F. The hygrothermal performance of residential buildings at urban and rural sites: Sensible and latent energy loads and indoor environmental conditions. Energy Build.
**2017**, 152, 792–803. [Google Scholar] [CrossRef] - Yang, L.; Lam, J.C.; Tsang, C.L. Energy performance of building envelopes in different climate zones in China. Appl. Energy
**2008**, 85, 800–817. [Google Scholar] [CrossRef] - Handbook-Fundamentals, A.; Edition, S. Inc.; See Page 14.14 for Summary Description of RP-1171 Work on Uncertainty in Design Temperatures; American Society of Heating, Refrigerating and Air-Conditioning Engineers: Atlanta, GA, USA, 2009. [Google Scholar]
- De Rosa, M.; Bianco, V.; Scarpa, F.; Tagliafico, L.A. Heating and cooling building energy demand evaluation; a simplified model and a modified degree days approach. Appl. Energy
**2014**, 128, 217–229. [Google Scholar] [CrossRef] - Kramer, R.; Van Schijndel, J.; Schellen, H. Simplified thermal and hygric building models: A literature review. Front. Archit. Res.
**2012**, 1, 318–325. [Google Scholar] [CrossRef] - Crawley, D.B.; Hand, J.W.; Kummert, M.; Griffith, B.T. Contrasting the capabilities of building energy performance simulation programs. Build. Environ.
**2008**, 43, 661–673. [Google Scholar] [CrossRef] - Naidu, D.S.; Rieger, C.G. Advanced control strategies for heating, ventilation, air-conditioning, and refrigeration systems—An overview: Part I: Hard control. Hvac&R Res.
**2011**, 17, 2–21. [Google Scholar] - Tashtoush, B.; Molhim, M.; Al-Rousan, M. Dynamic model of an HVAC system for control analysis. Energy
**2005**, 30, 1729–1745. [Google Scholar] [CrossRef] - Anderson, M.; Buehner, M.; Young, P.; Hittle, D.; Anderson, C.; Tu, J.; Hodgson, D. MIMO robust control for HVAC systems. IEEE Trans. Control Syst. Technol.
**2008**, 16, 475–483. [Google Scholar] [CrossRef] - Avci, M.; Erkoc, M.; Rahmani, A.; Asfour, S. Model predictive HVAC load control in buildings using real-time electricity pricing. Energy Build.
**2013**, 60, 199–209. [Google Scholar] [CrossRef] - West, S.R.; Ward, J.K.; Wall, J. Trial results from a model predictive control and optimisation system for commercial building HVAC. Energy Build.
**2014**, 72, 271–279. [Google Scholar] [CrossRef] - Širokỳ, J.; Oldewurtel, F.; Cigler, J.; Prívara, S. Experimental analysis of model predictive control for an energy efficient building heating system. Appl. Energy
**2011**, 88, 3079–3087. [Google Scholar] [CrossRef] - Afram, A.; Janabi-Sharifi, F. Theory and applications of HVAC control systems–A review of model predictive control (MPC). Build. Environ.
**2014**, 72, 343–355. [Google Scholar] [CrossRef] - Kreider, J.; Claridge, D.; Curtiss, P.; Dodier, R.; Haberl, J.; Krarti, M. Building energy use prediction and system identification using recurrent neural networks. J. Sol. Energy Eng. Aug.
**1995**, 117, 161–166. [Google Scholar] [CrossRef] - Kalogirou, S.; Neocleous, C.; Schizas, C. Building heating load estimation using artificial neural networks. In Proceedings of the 17th International Conference on Parallel Architectures and Compilation Techniques, San Francisco, CA, USA, 11–15 October 1997; Volume 8, p. 14. [Google Scholar]
- Lei, J.; Hongli, L.; Cai, W. Model predictive control based on fuzzy linearization technique for HVAC systems temperature control. In Proceedings of the 2006 1ST IEEE Conference on Industrial Electronics and Applications, Singapore, 24–26 May 2006; pp. 1–5. [Google Scholar]
- Wang, J.; An, D.; Lou, C. Application of fuzzy-PID controller in heating ventilating and air-conditioning system. In Proceedings of the 2006 International Conference on Mechatronics and Automation, Luoyang, China, 25–28 June 2006; pp. 2217–2222. [Google Scholar]
- Basin, M.V.; Ramírez, P.C.R. A supertwisting algorithm for systems of dimension more than one. IEEE Trans. Ind. Electron.
**2014**, 61, 6472–6480. [Google Scholar] [CrossRef] - Shah, A.; Huang, D.; Huang, T.; Farid, U. Optimization of buildingSenergy consumption by designing sliding mode control for multizone VAV air conditioning systems. Energies
**2018**, 11, 2911. [Google Scholar] [CrossRef] - Shah, A.; Huang, D.; Chen, Y.; Kang, X.; Qin, N. Robust sliding mode control of air handling unit for energy efficiency enhancement. Energies
**2017**, 10, 1815. [Google Scholar] [CrossRef] - Gonzalez, T.; Moreno, J.A.; Fridman, L. Variable gain super-twisting sliding mode control. IEEE Trans. Autom. Control
**2011**, 57, 2100–2105. [Google Scholar] [CrossRef] - Wang, Z.; Bao, W.; Li, H. Second-order dynamic sliding-mode control for nonminimum phase underactuated hypersonic vehicles. IEEE Trans. Ind. Electron.
**2016**, 64, 3105–3112. [Google Scholar] [CrossRef] - Borowski, M.; Mazur, P.; Kleszcz, S.; Zwolińska, K. Energy monitoring in a heating and cooling system in a building based on the example of the Turówka hotel. Energies
**2020**, 13, 1968. [Google Scholar] [CrossRef] - Coraci, D.; Brandi, S.; Piscitelli, M.S.; Capozzoli, A. Online implementation of a soft actor-critic agent to enhance indoor temperature control and energy efficiency in buildings. Energies
**2021**, 14, 997. [Google Scholar] [CrossRef] - Espejel-Blanco, D.F.; Hoyo-Montaño, J.A.; Arau, J.; Valencia-Palomo, G.; García-Barrientos, A.; Hernández-De-León, H.R.; Camas-Anzueto, J.L. HVAC control system using predicted mean vote index for energy savings in buildings. Buildings
**2022**, 12, 38. [Google Scholar] [CrossRef] - Hu, S.; Chen, J.; Chuah, Y. Energy cost and consumption in a large acute hospital. Int. J. Archit. Sci.
**2004**, 5, 11–19. [Google Scholar] - Khalil, H.K. Nonlinear Systems; Patience Hall: Upper Saddle Revier, NJ, USA, 2002. [Google Scholar]
- Qureshi, M.A.; Ahmad, I.; Munir, M.F. Double integral sliding mode control of continuous gain four quadrant quasi-Z-source converter. IEEE Access
**2018**, 6, 77785–77795. [Google Scholar] [CrossRef] - Pradhan, R.; Subudhi, B. Double integral sliding mode MPPT control of a photovoltaic system. IEEE Trans. Control Syst. Technol.
**2015**, 24, 285–292. [Google Scholar] [CrossRef] - Pakistan Meteorological Department. National Weather Forecasting Centre, Islamabad. Available online: https://nwfc.pmd.gov.pk/new/daily-forecast-en.php (accessed on 5 January 2023).

**Figure 1.**General view of OR, HVAC ducts, and corridor of hospital. (

**a**) OR corridor 1; (

**b**) OR corridor 2; (

**c**) OR; (

**d**) HVAC ducts.

**Figure 17.**Comparative analysis of zone temperature in the case of JTC, DISMC, and ITSMC in the first span of time.

**Figure 18.**Comparative analysis of zone temperature in the case of JTC, DISMC, and ITSMC in the second span of time.

**Figure 19.**Comparative analysis of zone temperature in the case of JTC, DISMC, and ITSMC in the third span of time.

**Figure 20.**Comparative analysis of power consumption with the DISMC and ITSMC temperature regulators during the first span of time.

**Figure 21.**Comparative analysis of power consumption with the DISMC and ITSMC temperature regulators during the second span of time.

**Figure 22.**Comparative analysis of power consumption with the DISMC and ITSMC temperature regulators during the third span of time.

**Figure 23.**Comparative analysis of total power consumption by the HVAC during the first phase of observation.

**Figure 24.**Comparative analysis of total power consumption by the HVAC during the second phase of observation.

**Figure 25.**Comparative analysis of total power consumption by the HVAC during the third phase of observation.

Height | m | 4 |

Base | m × m | 11.5824 × 6.7056 |

Number of Floors | - | 1 |

Volume | m${}^{3}$ | 310.6677 |

Surface-to-Volume Ratio (S/V) | m${}^{-1}$ | 0.73 |

Roof Surface | m${}^{2}$ | 77.6669 |

Type of Floor | - | On First Floor |

Vertical Wall Orientation | - | $N-S-E-W$ |

For Each Orientation | ||

Total Opaque Wall Surface Area (East, West) | m${}^{2}$ | 46.3296 |

Total Opaque Wall Surface Area (East, West) | m${}^{2}$ | 26.8224 |

Opaque Wall Surface Area (South) | m${}^{2}$ | 21.8224 |

Window Surface (South) | m${}^{2}$ | 5 |

Thermal Transmittance (W m${}^{-1}$ K${}^{-1})$ | Specific Thermal Capacity (kJ m${}^{-2}$ K${}^{-1}$) | |
---|---|---|

Heavy Wall | ||

Vertical Wall | 0.40 | 622.92 |

Roof | 0.35 | 395.28 |

Floor | 0.42 | 320.65 |

Light Wall | ||

Vertical Wall | 0.40 | 39.47 |

Roof | 0.35 | 298.58 |

Floor | 0.42 | 320.65 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hamza, A.; Uneeb, M.; Ahmad, I.; Saleem, K.; Ali, Z.
Variable Structure-Based Control for Dynamic Temperature Setpoint Regulation in Hospital Extreme Healthcare Zones. *Energies* **2023**, *16*, 4223.
https://doi.org/10.3390/en16104223

**AMA Style**

Hamza A, Uneeb M, Ahmad I, Saleem K, Ali Z.
Variable Structure-Based Control for Dynamic Temperature Setpoint Regulation in Hospital Extreme Healthcare Zones. *Energies*. 2023; 16(10):4223.
https://doi.org/10.3390/en16104223

**Chicago/Turabian Style**

Hamza, Ali, Muhammad Uneeb, Iftikhar Ahmad, Komal Saleem, and Zunaib Ali.
2023. "Variable Structure-Based Control for Dynamic Temperature Setpoint Regulation in Hospital Extreme Healthcare Zones" *Energies* 16, no. 10: 4223.
https://doi.org/10.3390/en16104223