Step Response Error Analysis
Why Step Response Error Matters
A step response diagram shows how a system reacts after a sudden input change. The curve can reveal speed, stability, damping, and accuracy. This calculator turns diagram readings into useful error metrics. It accepts reference values, measured output values, peak data, settling data, and optional sample points. The result helps students, analysts, and control engineers compare a plotted response with the desired behavior.
Reading the Main Error
The main error is the difference between the input step and the measured output. A positive error means the response is still below the target. A negative error means the response is above the target. Percent error scales that difference by the step amplitude. This makes several diagrams easier to compare. Steady state error uses the final output. It shows whether the system reaches the requested value after transients fade.
Transient Metrics
Transient metrics add more context. Overshoot measures how far the response rises above the target. Undershoot measures how far it falls below the starting level. Rise time estimates how quickly the curve moves from a lower threshold to a higher threshold. Settling time records when the response remains inside a chosen tolerance band. These values describe the shape of the step response, not just one point.
Sample Based Accuracy
Sample based error is useful when you digitize a diagram. Enter comma separated time points and output points. The calculator estimates integral absolute error, integral squared error, and time weighted absolute error. Trapezoidal integration is used between neighboring samples. Dense and evenly spaced samples usually give better estimates. Always use consistent time and output units.
Practical Use
Use this calculator when checking lab plots, simulated control systems, or textbook diagrams. Read values from the axes carefully. Enter the input step, the final response, and the selected point. Add peak and settling readings when available. Then review the result table. Export the report as CSV or PDF for records. The formulas section explains each metric, so results stay transparent and easy to verify. For best accuracy, mark the diagram with a cursor or grid. Use the same baseline for every reading. Avoid rounded values when possible. If the final value is uncertain, enter the best observed average after oscillations settle. Compare several tolerance bands when judging borderline responses. Keep notes with each saved report.