Calculator Inputs
Enter reference and actual sampled values. Separate numbers with commas, spaces, or new lines.
Formula Used
Tracking error at sample i: ei = ri − yi, where r is the reference and y is the actual output.
Mean signed error: Bias = Σei / n
Mean absolute error: MAE = Σ|ei| / n
Root mean square error: RMSE = √(Σei2 / n)
Integral absolute error: IAE = Σ|ei|Δt
Integral squared error: ISE = Σei2Δt
Integral time absolute error: ITAE = Σti|ei|Δt
Normalized RMSE: NRMSE% = (RMSE / full scale) × 100. If no full scale is entered, the calculator uses the reference span.
Steady-state error: The calculator averages the final selected window of samples to show the ending tracking behavior.
How to Use This Calculator
1. Enter a system name so reports stay labeled clearly.
2. Add the engineering units used by your sensor or actuator.
3. Enter the sample interval used while capturing the response.
4. Provide a tolerance band to measure compliance percentage.
5. Enter full scale if you want a custom normalized RMSE.
6. Set the steady-state window size for the final averaging period.
7. Paste reference values and actual values using matching sample counts.
8. Click the calculate button to place results above the form.
9. Use the CSV or PDF buttons to export the report.
Example Data Table
This example represents a command step and a measured response from a servo axis.
| Sample | Time (s) | Reference (mm) | Actual (mm) | Error (mm) |
|---|---|---|---|---|
| 1 | 0.0 | 10.00 | 9.20 | 0.80 |
| 2 | 0.1 | 10.00 | 9.50 | 0.50 |
| 3 | 0.2 | 10.00 | 9.70 | 0.30 |
| 4 | 0.3 | 10.00 | 9.90 | 0.10 |
| 5 | 0.4 | 10.00 | 10.10 | -0.10 |
Frequently Asked Questions
1. What does tracking error mean in engineering?
Tracking error is the difference between a commanded reference and the measured response. It shows how closely a control system follows the intended path, position, speed, temperature, pressure, or other target variable.
2. Why are both MAE and RMSE shown?
MAE gives the average absolute mismatch. RMSE gives more weight to larger deviations. Using both helps you judge normal performance and determine whether rare spikes are causing most of the control problem.
3. When should I use a tolerance band?
Use a tolerance band when a process or machine has an acceptable error limit. The calculator then reports how many samples stayed within that permitted band during the test period.
4. What is steady-state error here?
Steady-state error is calculated from the final chosen group of samples. It helps show the ending offset after most transients have settled, which is useful during tuning and acceptance testing.
5. Why does the calculator ask for full scale?
Full scale is used to normalize RMSE into a percentage. This makes error easier to compare between systems with different units or command magnitudes, especially during benchmarking.
6. Can I paste values from spreadsheets or log files?
Yes. You can paste comma-separated, space-separated, or line-by-line numbers. The only requirement is that reference and actual series must have the same number of samples.
7. What does ITAE tell me?
ITAE penalizes errors that continue later in time. It is helpful when you care more about persistent lag, drift, or settling issues than about short early transients.
8. Is this calculator useful for robotics and motion control?
Yes. It works well for servo axes, robotic joints, positioning stages, drives, thermal loops, and many process-control signals whenever you need to compare commanded behavior against measured output.