Precision DC Motor Control: PID Tuning, State-Space & Metaheuristic Optimization

This project represents a comprehensive engineering study on the mathematical modeling and automated control of DC motors. It transitions from classical control theory (Ziegler-Nichols) to advanced state-space representations and AI-driven optimization using Genetic Algorithms (GA).

🚀 Project Highlights (Based on Research Paper)

• Mathematical Modeling: Derived differential equations for the electrical and mechanical subsystems of a DC motor.
• State-Space Representation: Developed the state-space model to analyze internal system variables.
• Advanced PID Features: Implemented a Filter Coefficient (N) in the derivative term to suppress high-frequency noise amplification.
• Stability Analysis: Comprehensive validation using Bode Diagrams and Nyquist Plots to ensure robust stability margins.

🛠️ System Architecture & Methodology

The project utilizes a high-fidelity plant model developed in MATLAB/Simulink.

1. Plant Modeling

We defined the motor dynamics using the following parameters (as derived in the paper):

• Electrical: Resistance ($R$), Inductance ($L$), Back-EMF constant ($K_e$).
• Mechanical: Inertia ($J$), Friction ($b$), Torque constant ($K_t$).

2. Control Strategies

Method	Description
Ziegler-Nichols	Open-loop step response analysis using the tangent method at the inflection point.
Genetic Algorithm (GA)	Metaheuristic search for optimal $K_p$, $K_i$, $K_d$ by minimizing a multi-objective cost function.
State-Space Control	Analysis of the system through state variables for more complex control requirements.

🧬 Genetic Algorithm (GA) Details

The optimization process targets the minimization of a weighted cost function $J$ to achieve a balance between speed and stability: $$J = \alpha \cdot Overshoot + \beta \cdot SettlingTime + \gamma \cdot SteadyStateError + Penalty$$

• Settling Time Optimization: Heavily weighted ($\beta = 0.5$) to ensure rapid system response.
• Constraint Handling: A penalty factor is applied if the system exceeds the 2-second stability threshold.

📉 Stability & Frequency Analysis

As detailed in the research paper, the system's stability was verified through frequency response methods. The Bode Plot analysis ensures that the phase and gain margins are sufficient to handle load variations without oscillation.

📂 File Structure

• functions/: Contains the Simulink models (.slx) and the GA fitness function.
• scripts/: MATLAB scripts for Z-N parameters and performance extraction.
• docs/: (Recommended) Place the komandim det kursi.docx or a PDF version here for full theoretical reference.

🚀 How to Run

1. Open MATLAB and add the project folders to your path.
2. Run pid_optimizationGA.m to execute the AI-driven tuning.
3. Observe the output in the Scope block of the Simulink model for real-time visualization of the speed regulation.

🎓 Academic Credit

This project was developed as part of the "Computer Control" course at the Polytechnic University of Tirana (FTI). Contributors: Samuel Koçi and classmates. Supervisor: Prof. Miranda Hariza.