🎛️ 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.

License: MIT JavaScript Vite Tests

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

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

• 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

• 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)

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
   

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!

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

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"

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"

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

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)

• 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

• 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

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

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

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

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

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

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

• 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

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

Made with ❤️ for Control Systems Students