https://github.com/sai-srivardhan-reddy-lingala/pid_controller-aocs-1-
PID Controller for a Higher-Order System
https://github.com/sai-srivardhan-reddy-lingala/pid_controller-aocs-1-
Last synced: 2 months ago
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PID Controller for a Higher-Order System
- Host: GitHub
- URL: https://github.com/sai-srivardhan-reddy-lingala/pid_controller-aocs-1-
- Owner: SAI-SRIVARDHAN-REDDY-LINGALA
- Created: 2025-02-08T17:36:58.000Z (3 months ago)
- Default Branch: main
- Last Pushed: 2025-02-08T17:42:33.000Z (3 months ago)
- Last Synced: 2025-02-08T18:29:58.020Z (3 months ago)
- Language: Python
- Size: 0 Bytes
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# PID Controller for a Higher-Order System (AOCS-1) FOR STUDENT SATELLITE PROGRAM IIT KHARAGPUR
Got it! Here's an updated `README.md` that includes both files (`PID_3rdOrder_controller.py` and `PID_TUNNING.py`) for better organization.
---
# **PID Controller for a Higher-Order System (AOCS-1)**
## **Introduction**
This project implements a **PID controller** for a **third-order system**, incorporating real-world constraints such as:
- **Actuator Saturation:** Limits on control effort to prevent excessive input.
- **Sensor Noise:** Random inaccuracies in measurements to simulate real-world conditions.
- **Noise Filtering:** A **low-pass filter** is used to smooth noisy sensor readings.
The objective is to analyze **PID control trade-offs** in complex environments and optimize system performance using numerical methods.
---
## **System Model**
The system under consideration has the **third-order transfer function**:
G(s) = 1/{s^3 + 3s^2 + 5s + 1}
A **PID controller** is designed and optimized using:
1. **Nelder-Mead Optimization** – A derivative-free approach for refining PID gains.
2. **Genetic Algorithm (GA)** – An evolutionary approach to find globally optimal PID parameters.
---
## **Project Structure 📂**
```
📦 PID_CONTROLLER-AOCS-1
│── 📜 README.md # Project documentation
│── 📜 LICENSE # License file
│── 📜 PID_3rdOrder_controller.py # Implements PID control on the system
│── 📜 PID_TUNNING.py # Optimizes PID parameters using GA and Nelder-Mead
│── 📂 results # Folder for simulation results (plots, logs)
│── 📂 docs # Additional project documentation
```
---
## **Features 🚀**
✔️ **Real-world constraints:** Actuator limits, sensor noise, and filtering.
✔️ **Step response analysis:** Evaluating stability, overshoot, and settling time.
✔️ **Root locus & Bode plot analysis:** Understanding system dynamics.
✔️ **PID tuning via numerical methods:** Nelder-Mead & Genetic Algorithm.
✔️ **State-space simulation:** Advanced system modeling and analysis.
---
## **Installation 📦**
Ensure you have Python installed and install the required dependencies using:
```bash
pip install numpy matplotlib control scipy
```
---
## **Usage 🔧**
### **1️⃣ Run the PID Controller Simulation**
```bash
python PID_3rdOrder_controller.py
```
- Simulates the PID response for a **third-order system**.
- Implements **actuator saturation, sensor noise, and filtering**.
- Plots **step response, root locus, and Bode plot**.
### **2️⃣ Run the PID Tuning Optimization**
```bash
python PID_TUNNING.py
```
- Uses **Nelder-Mead** and **Genetic Algorithm** to optimize PID parameters.
- Compares different PID variants (**PID, PI-D, I-PD**).
- Saves optimized values for further use.
---
## **Results & Analysis 📊**
### 📌 **PID Trade-offs:**
- **High Kp** → Faster response but higher overshoot.
- **High Ki** → Reduces steady-state error but may cause instability.
- **High Kd** → Improves damping but increases control effort.
### 📌 **Noise Handling**
- **Sensor noise** with standard deviation **σ = 0.05** is added to simulate inaccuracies.
- **Low-pass filtering** ensures smooth sensor readings.
### 📌 **Simulation Insights**
- **Step Response Analysis**: The optimized PID controller achieves fast response with minimal overshoot.
- **Noise-Added Simulation**: The PID controller effectively handles measurement noise.
- **Degrees of Freedom Tuning**: Different PID variants (PID, PI-D, I-PD) were analyzed, and PID provided the best balance.
---
## **System Analysis 🏛️**
### 🔹 **Root Locus**
- The system's stability is analyzed using **root locus plots**.
### 🔹 **Bode Plot**
- The **frequency response** is studied to assess system robustness.
### 🔹 **State-Space Representation**
- The system is also modeled using **state-space equations** for dynamic response analysis.
---
## **Visualization 🎨**
The project generates the following plots:
📍 **Step Response**: System response with optimized PID parameters.
📍 **Root Locus Plot**: Stability analysis of the open-loop system.
📍 **Bode Plot**: Frequency response characteristics.
📍 **Comparison of PID Variants**: Evaluating **PID, PI-D, and I-PD controllers**.
---
## **Future Enhancements 🚀**
🔹 Adaptive control strategies (LQR, Kalman Filters).
🔹 AI-based PID tuning methods (Reinforcement Learning).
🔹 Integration with real-world hardware (e.g., Arduino, Raspberry Pi).
---
## **Contributing 🤝**
Contributions are welcome! Feel free to:
- **Fork the repo**
- **Create a pull request**
- **Report issues or suggest improvements**
---
## **License 📜**
This project is licensed under the **MIT License** – see the [LICENSE](LICENSE) file for details.
---
This `README.md` ensures a **clear structure** and makes it easy for anyone exploring your repository. Let me know if you want any modifications! 🚀