Interactive Pole-Zero and Step Response Plot

A MATLAB GUI for visualizing pole-zero plots and step responses of second-order systems with adjustable damping ratio and natural frequency.

The "Interactive Pole-Zero and Step Response Plot" is a MATLAB GUI tool designed for educational and analysis purposes, allowing users to explore the behavior of underdamped second-order systems. This interactive application provides a visual representation of pole-zero plots and step responses, making it a valuable resource for students, educators, and engineers interested in control systems and signal processing.

Key Features:

- Interactive Sliders: Adjust the damping ratio (\(\zeta\)) and natural frequency (\(\omega_n\)) using intuitive sliders to see real-time changes in the system's poles and step response.

- Pole-Zero Plot: Visualize the system's poles in the complex plane, with annotations showing the real and imaginary parts. The plot dynamically updates as you adjust the parameters.

- Step Response Plot: Observe the system's time-domain response to a step input, providing insights into its transient behavior and stability.

- Educational Annotations: The tool includes annotations such as pole coordinates and angles (\(\theta\)) to enhance understanding of the system dynamics.

Usage Instructions:

1. Run the `interactive_pole_step_plot` function in MATLAB.

2. Use the sliders to adjust the damping ratio and natural frequency.

3. Observe the changes in the pole-zero plot and step response plot.

4. Explore different parameter settings to see their effect on system behavior.