🧲 Dynamic Modelling & Control of a Magnetic Levitation System – MATLAB & Simulink

📖 Introduction

This project demonstrates the modeling, analysis, and control of a magnetic levitation (maglev) system, where a ferromagnetic ball is suspended under an electromagnet.

The goal is to maintain the ball’s position at a desired reference point by regulating the input voltage to the coil.
Due to the system’s nonlinear dynamics and open-loop instability, it provides a rich case study for modern control system design.

The project includes:

• Nonlinear state-space modeling and linearization
• Stability, controllability, and observability analysis
• Transfer function derivation
• PID controller design & tuning
• Nonlinear simulations in MATLAB/Simulink with 3D visualization

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🔬 Methodology

1. System Modeling

• Derived a nonlinear state-space model based on Newton’s laws and electrical circuit dynamics.
• Considered system states: ball position, velocity, and coil current.
• Linearized the system around equilibrium points for analysis.

2. Control Design

• Implemented P, PD, and PID controllers for stabilization.
• Tuned parameters to minimize overshoot, settling time, and steady-state error.
• Verified stability using step response analysis and eigenvalue evaluation.

3. Simulation

• Built a nonlinear Simulink model of the maglev system.
• Implemented PID control using MATLAB’s built-in blocks.
• Simulated ball levitation with 3D visualization of motion.

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🗂️ Project Structure

├── 📄 2022MC45.prj # MATLAB project file
├── 📄 maglev_nonlinear.slx # Nonlinear Simulink model
├── 📄 maglev.wrl # 3D visualization model
├── 📄 maglev.x3d # 3D simulation data
├── 📄 AppendixA.m # MATLAB code for analysis
├── 📄 CEA_Report_2022_MC_45.pdf # Full project report
├── 📄 ReadMe.txt # Extra notes
└── 📄 README.md # Project documentation

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📌 Key Insights

• Demonstrates how nonlinear systems can be modeled and controlled using classical and modern techniques.
• Shows the importance of PID tuning in stabilizing unstable systems.
• Highlights the use of MATLAB & Simulink for real-world control engineering problems.