PID-Controlled Thermal System Simulation

This project simulates a PID controlled heating system commonly found in industrial or telecom hardware.

It includes:

• A simple first order thermal plant
• A digital PID controller with anti windup
• Actuator saturation and ramp rate limits
• Noisy sensor measurements and digital filtering
• Multiple experiments commonly used in control engineering

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System Overview

Thermal Plant

The plant is a simple first order model:

dT/dt = -(T - T_ambient) / tau + K * u

where:

• T is the temperature
• T_ambient is ambient temperature (20 °C)
• tau is the thermal time constant
• K is the heater gain
• u in [0, 1] is the heater power command

Gaussian noise is added to simulate imperfect temperature sensing.

PID Controller (with anti windup)

The controller computes:

u = Kp * e + Ki * integral(e) + Kd * de/dt

with:

• Integral clamping to prevent windup
• Conditional integration when the actuator is saturated
• Output clamped to [0, 1] to represent a real heater

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Block Diagram

+----------------------------+
|        PID Controller      |
|  (Kp, Ki, Kd, anti windup) |    heater_power (0..1)
setpoint ----->(+)-------------->-------------------+
             ^                                   |
             |                                   v
             |   +-----------------------------+      measured
             |   |   Thermal System (Plant)    |      temperature
             +---|  First order model + noise  |<-----------+
                 +-----------------------------+

With filtering enabled:

  measured temp
        |
        v
 +-------------+      filtered temp
 |   Filter    |--------------------> PID
 | moving avg  |
 +-------------+

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Example Results

Baseline PID Closed Loop

Step Response: 30°C -> 50°C -> 40°C

Noisy Sensor with Moving Average Filtering

P vs PI vs PID Comparison

Actuator Ramp Rate Limiting

Ziegler–Nichols Tuning Demonstration

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How to Run the Simulations

From the project root:

python main.py
python step_response.py
python filtered_control.py
python compare_pid_modes.py
python ramp_limited_heater.py
python ziegler_nichols_demo.py
python interactive_pid_tuning.py
python realtime_animation.py

Project Structure

pid-control-simulation/
├── controller/
│   ├── __init__.py
│   └── pid.py
├── system/
│   ├── __init__.py
│   └── system_model.py
├── utils/
│   ├── __init__.py
│   └── filtering.py
├── tests/
│   ├── __init__.py
│   └── test_pid.py
├── images/                    # auto generated plots
├── main.py
├── step_response.py
├── filtered_control.py
├── compare_pid_modes.py
├── ramp_limited_heater.py
├── ziegler_nichols_demo.py
├── interactive_pid_tuning.py
└── realtime_animation.py

Running Tests

pytest

Relevance to Embedded / Firmware Roles

This project demonstrates:

• Closed-loop control of a physical system (thermal plant) using PID
• Handling actuator saturation and anti-windup logic
• Working with noisy sensor data and digital filtering
• Designing and comparing different controller modes (P / PI / PID)
• Building clear visualizations and tools to analyze controller stability

This maps directly to embedded firmware work on real hardware: temperature controllers, power modules, optical / RF modules, and other DSP-assisted systems.