README.md

🎛️ Advanced Control System Analyzer

An interactive web-based tool for analyzing and visualizing control system responses. Built to help engineering students understand fundamental control system concepts through visual demonstrations.

📚 Overview

This tool provides interactive analysis of control systems including:

• Time Domain Analysis - Step, Ramp, Impulse, Parabolic, and Sinusoidal responses
• Frequency Domain Analysis - Bode plots, Nyquist plots, Polar plots
• Root Locus Analysis - Visualize pole movement as gain varies
• Stability Analysis - Routh-Hurwitz criterion and Hurwitz determinants

✨ Features

Time Response Analysis

Feature	Description
First-Order Systems	G(s) = K / (τs + 1)
Second-Order Systems	G(s) = Kωn² / (s² + 2ζωns + ωn²)
Higher-Order Systems	Custom numerator/denominator polynomials
Input Types	Step, Ramp, Parabolic, Impulse, Sinusoidal

Calculated Parameters

Time Domain:

• Delay Time (Td) - Time to reach 50% of final value
• Rise Time (Tr) - Time from 10% to 90% of final value
• Peak Time (Tp) - Time to reach maximum overshoot
• Settling Time (Ts) - Time to stay within 2% of final value
• Maximum Overshoot (Mp) - Percentage overshoot
• Steady-State Error (Ess) - Difference between input and output

Frequency Domain:

• Gain Margin (GM) - Extra gain before instability
• Phase Margin (PM) - Extra phase lag before instability
• Gain Crossover Frequency (ωgc)
• Phase Crossover Frequency (ωpc)
• Bandwidth (ωb)
• Resonant Peak (Mr)
• Corner Frequencies

Stability Analysis

• Routh-Hurwitz Array - Visual table with sign change detection
• Hurwitz Matrix - Principal minors calculation
• Pole-Zero Map - Visual representation of system poles and zeros
• BIBO Stability - Bounded-Input Bounded-Output analysis

🚀 Getting Started

Prerequisites

• A modern web browser (Chrome, Firefox, Safari, Edge)
• https://raw.githubusercontent.com/KushalPitaliya/Control_system_analyzer/main/js/ui/Control-system-analyzer-v3.2.zip v18+ (for development)

Quick Start

1. Clone the repository:

   git clone https://raw.githubusercontent.com/KushalPitaliya/Control_system_analyzer/main/js/ui/Control-system-analyzer-v3.2.zip
   cd Control_system_analyzer

2. Install dependencies:

   npm install

3. Start development server:

   npm run dev

4. Open in browser:

   http://localhost:5173
   

Alternative: Open Directly

Simply open https://raw.githubusercontent.com/KushalPitaliya/Control_system_analyzer/main/js/ui/Control-system-analyzer-v3.2.zip in your browser — no server required!

🧪 Testing

Run the comprehensive test suite:

# Run all tests
npm test

# Run with coverage
npm run test:coverage

# Interactive test UI
npm run test:ui

24 unit tests covering:

• Complex number operations
• Polynomial utilities
• Root finding algorithms
• Helper functions

📖 Usage Guide

Time Response Analysis

1. Select System Order: First-Order, Second-Order, or Higher-Order
2. Enter system parameters:
   • First-Order: Gain (K), Time Constant (τ)
   • Second-Order: Gain (K), Natural Frequency (ωn), Damping Ratio (ζ)
   • Higher-Order: K, Numerator coefficients, Denominator coefficients
3. Select Input Type: Step, Ramp, Parabolic, Impulse, or Sinusoidal
4. Click "Analyze Time Response"

Frequency Response Analysis

1. Select System Order and enter parameters
2. Choose Plot Type:
   • Bode Plot - Magnitude and Phase vs Frequency
   • Nyquist Plot - Polar plot of G(jω)
   • Polar Plot - Similar to Nyquist
   • Root Locus - Pole movement vs Gain
3. Set frequency range (default: 0.1 to 100 rad/s)
4. Click "Analyze Frequency / Root Locus"

Stability Criteria

1. Enter the characteristic polynomial coefficients
2. Click "Generate Stability Tables"
3. View:
   • Routh Array with sign change analysis
   • Hurwitz Matrix with principal minors

📁 Project Structure

control-system-analyzer/
├── https://raw.githubusercontent.com/KushalPitaliya/Control_system_analyzer/main/js/ui/Control-system-analyzer-v3.2.zip              # Main HTML structure
├── https://raw.githubusercontent.com/KushalPitaliya/Control_system_analyzer/main/js/ui/Control-system-analyzer-v3.2.zip               # Core control system calculations
├── https://raw.githubusercontent.com/KushalPitaliya/Control_system_analyzer/main/js/ui/Control-system-analyzer-v3.2.zip              # Dark theme with glassmorphism
├── https://raw.githubusercontent.com/KushalPitaliya/Control_system_analyzer/main/js/ui/Control-system-analyzer-v3.2.zip            # Dependencies & scripts
├── .gitignore              # Git ignore rules
│
├── js/                     # Modular JavaScript
│   ├── config/
│   │   └── https://raw.githubusercontent.com/KushalPitaliya/Control_system_analyzer/main/js/ui/Control-system-analyzer-v3.2.zip    # Centralized configuration
│   ├── utils/
│   │   ├── https://raw.githubusercontent.com/KushalPitaliya/Control_system_analyzer/main/js/ui/Control-system-analyzer-v3.2.zip # Complex number & polynomial utilities
│   │   ├── https://raw.githubusercontent.com/KushalPitaliya/Control_system_analyzer/main/js/ui/Control-system-analyzer-v3.2.zip  # Root finding algorithms
│   │   └── https://raw.githubusercontent.com/KushalPitaliya/Control_system_analyzer/main/js/ui/Control-system-analyzer-v3.2.zip Export functionality (PNG, SVG, JSON, CSV)
│   └── ui/
│       └── https://raw.githubusercontent.com/KushalPitaliya/Control_system_analyzer/main/js/ui/Control-system-analyzer-v3.2.zip # Enhanced UI components
│
├── css/
│   └── https://raw.githubusercontent.com/KushalPitaliya/Control_system_analyzer/main/js/ui/Control-system-analyzer-v3.2.zip    # Enhanced UI styles
│
└── tests/
    └── https://raw.githubusercontent.com/KushalPitaliya/Control_system_analyzer/main/js/ui/Control-system-analyzer-v3.2.zip Unit tests (24 tests)

🛠️ Technologies Used

• HTML5 - Structure
• CSS3 - Modern dark theme with glassmorphism effects
• JavaScript (ES6+) - Control system calculations & modules
• https://raw.githubusercontent.com/KushalPitaliya/Control_system_analyzer/main/js/ui/Control-system-analyzer-v3.2.zip - Interactive chart plotting
• MathJax - Mathematical formula rendering
• https://raw.githubusercontent.com/KushalPitaliya/Control_system_analyzer/main/js/ui/Control-system-analyzer-v3.2.zip - Complex number operations
• Vite - Build tool & dev server
• Vitest - Unit testing framework

🎓 Control System Concepts

Second-Order System Response Categories

Damping Ratio (ζ)	System Type	Behavior
ζ < 1	Underdamped	Oscillates before settling
ζ = 1	Critically Damped	Fastest settling, no overshoot
ζ > 1	Overdamped	Slow response, no oscillation

Stability Margins

• Gain Margin: How much gain can be increased before instability

  • GM > 0 dB → Stable
  • GM = ∞ → Unconditionally stable for gain

• Phase Margin: How much phase lag can be added before instability

  • PM > 45° → Well-damped response
  • PM > 30° → Acceptable damping
  • PM < 30° → Poor damping, oscillatory

Routh-Hurwitz Stability Criterion

A system is stable if and only if:

1. All coefficients of the characteristic polynomial are positive
2. All elements in the first column of the Routh array are positive
3. No sign changes occur in the first column

📐 Key Formulas

Second-Order Step Response (Underdamped)

c(t) = K[1 - (e^(-ζωnt) / √(1-ζ²)) × sin(ωd×t + φ)]
where φ = atan(√(1-ζ²) / ζ) and ωd = ωn√(1-ζ²)

Time Domain Specifications

Rise Time:     Tr ≈ (π - β) / ωd
Peak Time:     Tp = π / ωd
Settling Time: Ts ≈ 4 / (ζωn)     (2% criterion)
Overshoot:     Mp = e^(-πζ/√(1-ζ²)) × 100%

Stability Margins

Gain Margin:  GM = -20 log₁₀|G(jωpc)|   where ∠G(jωpc) = -180°
Phase Margin: PM = 180° + ∠G(jωgc)       where |G(jωgc)| = 1 (0 dB)

🤝 Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

1. Fork the repository
2. Create your feature branch (git checkout -b feature/AmazingFeature)
3. Commit your changes (git commit -m 'Add some AmazingFeature')
4. Push to the branch (git push origin feature/AmazingFeature)
5. Open a Pull Request

📄 License

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

🙏 Acknowledgments

• Control system formulas based on standard textbooks:
  • Ogata, K. "Modern Control Engineering"
  • Nise, N. "Control Systems Engineering"
  • Dorf, R. & Bishop, R. "Modern Control Systems"
• Built with https://raw.githubusercontent.com/KushalPitaliya/Control_system_analyzer/main/js/ui/Control-system-analyzer-v3.2.zip for interactive charts
• Mathematical rendering by MathJax
• Complex operations by https://raw.githubusercontent.com/KushalPitaliya/Control_system_analyzer/main/js/ui/Control-system-analyzer-v3.2.zip

📞 Support

If you encounter any issues or have questions:

1. Check the existing issues on GitHub
2. Create a new issue with detailed description
3. Include browser console errors if applicable

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Made with ❤️ for Control Systems Students