HVAC Thermal System Modeling & PID Control using MATLAB Simulink

A complete simulation of a room’s thermal behavior using Simscape Thermal along with a PID-controlled HVAC system for temperature regulation. This project demonstrates dynamic modeling, debugging, controller design, and system-level understanding using MATLAB/Simulink.

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Project Overview

This project models a room as a thermal mass exposed to a constant outside temperature via wall conduction.

• The System: An HVAC system, modeled as a Controlled Heat Flow Rate Source, injects or removes heat to regulate room temperature.
• The Control: A PID controller adjusts HVAC power to maintain the room at a target temperature despite disturbances such as heat leakage.
• Key Deliverables:
  • Thermal system modeling
  • Simscape physical connections
  • PID controller design & tuning
  • Simulation and analysis

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System Architecture

Simscape Thermal Components (Physical Layer)

• Thermal Mass: Represents room air + thermal inertia ($C$).
• Conductive Heat Transfer: Models wall heat conduction ($R_{th}$).
• Temperature Source: Represents the constant outdoor temperature.
• Controlled Heat Flow Rate Source: Acts as the HVAC actuator.
• Thermal Reference: Ground node for zero heat flow.
• Temperature Sensor: Measures real-time room temperature.

Simulink Components (Signal Layer)

• PID Controller: Computes the control effort.
• Saturation: Limits HVAC power to realistic values.
• Simulink-PS / PS-Simulink Converters: Interfaces between physical signals and control logic.
• Scopes: For visualizing temperature and heat flow over time.

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Mathematical Model

The system is governed by the First Law of Thermodynamics (Energy Balance):

$$C \frac{dT}{dt} = Q_{\text{HVAC}} + Q_{\text{wall}}$$

Wall Heat Flow (Newton's Law / Conduction)

$$Q_{\text{wall}} = \frac{T_{\text{out}} - T_{\text{room}}}{R_{\text{th}}}$$

HVAC Control Logic (PID)

The HVAC output ($u$) represents $Q_{\text{HVAC}}$: $$u = K_p e + K_i \int e , dt + K_d \frac{de}{dt}$$

Where $e$ is the error signal ($T_{\text{setpoint}} - T_{\text{room}}$).

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PID Tuning

Iterative tuning was performed to achieve stability.

Attempt	Kp	Ki	Kd	Notes
1	200	0.1	0	Slow response, underdamped.
2	500	0.05	0	Stable, minimal overshoot.
3	High	Low	0	Stable but slower convergence.

Final Result: Tuning strategy #2 was selected for smooth and stable control.

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Simulation Highlights

Temperature Behavior

• Initial room temperature starts at approx 293 K.
• System rises to 300–303 K (depending on setpoint).
• PID stabilizes temperature close to setpoint with minimal overshoot.
• Long-duration simulations confirm stable convergence.

HVAC Power Response

• HVAC injects heat ($+Q$) when $T_{room} < T_{set}$.
• HVAC applies cooling ($-Q$) when $T_{room} > T_{set}$.
• Saturation limits prevent unrealistic infinite power spikes.

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Repository Structure

HVAC-Temperature-Control/
│
├── resources/
│   ├── project/
│   │   ├── fjRQtWiSIy7hIIj-Kmk87M7s21k
│   │   ├── NjSPEMsluLUyIpr2u1Js5bVPsOs
│   │   └── root
│   ├── Project.xml
│   └── rootp.xml
│
├── 1.png                         # Simulation result figure
├── 2.png                         # Simulation result figure
├── 3.png                         # Simulation result figure
├── HVAC Room Model.png           # Diagram of the Simulink model
├── HVAC_Project_Report.pdf       # Full project report
├── HVAC_Project.prj              # Simulink Project definition file
├── HVAC.m                        # MATLAB script for parameters/initialization
├── HVAC.slx                      # Main Simulink model file
└── README.md                     # Project documentation

## 📄 License

This project is licensed under the MIT License - see the [LICENSE](LICENSE) file for details.