Control System Analyzer

A web-based tool for analyzing and visualizing control system transfer functions, providing comprehensive analysis including time domain response, frequency domain characteristics, and stability analysis.

🌐 Live Demo

Visit the application: https://nguyenle15325.github.io/Control-system-analyzer/

📋 Features

Transfer Function Analysis

• Input Methods: Enter transfer functions in standard form with numerator and denominator polynomials
• System Representation: Supports continuous-time linear time-invariant (LTI) systems
• Multiple Formats: Compatible with various transfer function representations

Time Domain Analysis

• Step Response: Visualize system response to unit step input
• Impulse Response: Analyze system behavior for impulse excitation
• Performance Metrics:
  • Rise time
  • Settling time
  • Peak overshoot
  • Steady-state error
  • Time constant

Frequency Domain Analysis

• Bode Plot: Magnitude and phase plots across frequency spectrum
• Nyquist Plot: Complex plane representation for stability analysis
• Gain and Phase Margins: Critical stability indicators
• Resonant Peak and Bandwidth: Frequency response characteristics

Stability Analysis

• Pole-Zero Map: Visualize system poles and zeros in the s-plane
• Stability Determination: Automatic stability assessment based on pole locations
• Root Locus: (If available) Track pole locations as gain varies

Interactive Visualizations

• Dynamic Plots: Real-time graph updates as parameters change
• Zoom and Pan: Explore plots in detail
• Export Options: Save plots and results for reports and documentation

🚀 Getting Started

Access the Tool

Simply navigate to the live application in your web browser. No installation required!

Basic Usage

1. Enter Transfer Function

   • Input numerator coefficients (e.g., 1, 2, 3 for s² + 2s + 3)
   • Input denominator coefficients (e.g., 1, 4, 5, 6 for s³ + 4s² + 5s + 6)

2. Select Analysis Type

   • Choose from time domain, frequency domain, or stability analysis
   • Select specific plots (step response, Bode, pole-zero, etc.)

3. View Results

   • Interactive plots display automatically
   • Performance metrics and stability information shown
   • Export or save results as needed

Example Systems

First-Order System

Numerator: 5
Denominator: 1, 5
Transfer Function: G(s) = 5/(s + 5)

Second-Order System

Numerator: 10
Denominator: 1, 2, 10
Transfer Function: G(s) = 10/(s² + 2s + 10)

Higher-Order System

Numerator: 1, 2
Denominator: 1, 3, 3, 1
Transfer Function: G(s) = (s + 2)/(s³ + 3s² + 3s + 1)

📊 Supported Analyses

Time Domain

• ✅ Step response
• ✅ Impulse response
• ✅ Ramp response (if supported)
• ✅ Custom input response (if supported)

Frequency Domain

• ✅ Bode magnitude plot
• ✅ Bode phase plot
• ✅ Nyquist plot
• ✅ Nichols chart (if supported)

System Characteristics

• ✅ Pole-zero analysis
• ✅ Damping ratio and natural frequency
• ✅ System order and type
• ✅ Stability assessment

🎓 Educational Applications

This tool is ideal for:

• Control Systems Courses: Supplement lectures with interactive demonstrations
• Engineering Students: Homework verification and concept visualization
• Engineers: Quick analysis and system design validation
• Self-Learning: Explore control theory concepts hands-on

📄 License

This project is open source and available under the MIT License.