Servo Positioning Accuracy & Settling Time Feasibility Calculator
Calculate estimated settling time, positioning error and accuracy ratio using move distance, target time, bandwidth, damping and encoder resolution.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Control configuration
Motion requirements
Servo dynamics
Measurement & noise
Results
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Method, application and limitations
Review the calculation method, intended application and engineering assumptions before using the result in a design decision.
Formula and calculation method
Estimated settling time formula:
ttarget,s = ttarget / 1000
ωn = 2π · fbw
tsettling = 4 / (ζ · ωn)
For cascaded control:
tsettling = 0.85 · 4 / (ζ · ωn)
tsettling,ms = tsettling · 1000
Positioning error formula:
eq = 0.5 / N
ed = x / (2π · fbw · ttarget,s)
en = (η / 100) · (1 / N)
e = √(eq2 + ed2 + en2)
Accuracy ratio formula:
accuracy ratio = e / etarget
where:
- tsettling — estimated settling time (ms)
- e — positioning error (m)
- e / etarget — accuracy ratio (-)
- x — move distance (m)
- ttarget — target time (ms)
- ttarget,s — target time converted to seconds (s)
- etarget — target accuracy (m)
- fbw — control bandwidth (Hz)
- ωn — natural angular frequency (rad/s)
- ζ — damping ratio (-)
- N — encoder resolution (1/m)
- η — noise level (%)
- eq — quantization error (m)
- ed — dynamic error (m)
- en — noise-induced error (m)
When to use this calculator
When to use this calculator:
- Check whether a servo axis can settle within the required target time for a defined move distance.
- Estimate positioning error from encoder quantization, motion dynamics and measurement noise.
- Compare estimated positioning error against the required target accuracy.
- Evaluate whether position loop or cascaded control gives enough settling margin.
- Identify whether accuracy is limited mainly by encoder resolution, dynamic response or noise.
How to interpret the result
Estimated settling time is defined as the calculated time required for the servo response to settle based on damping ratio and control bandwidth. Cascaded control reduces the estimated settling time by applying a 0.85 multiplier.
Positioning error is defined as the combined error from encoder resolution, motion dynamics and noise. It depends on move distance, target time, control bandwidth, encoder resolution and noise level.
Accuracy ratio is defined as positioning error divided by target accuracy. A ratio above 1.0 means the estimated positioning error is greater than the allowed target accuracy.
- Safe — used when accuracy ratio is not above 0.8, settling time ratio is not above 0.8, bandwidth ratio is at least 1.0, resolution ratio is not above 0.5, and overshoot is not above 20%.
- Warning — used when accuracy ratio is above 0.8, settling time ratio is above 0.8, bandwidth ratio is below 1.0, resolution ratio is above 0.5, or overshoot is above 20%.
- Unsafe — used when accuracy ratio is above 1.0, settling time ratio is above 1.0, or bandwidth ratio is below 0.7.
- Invalid — used when required inputs are outside valid calculation limits, such as non-positive move distance, non-positive target time, non-positive target accuracy, non-positive control bandwidth, invalid damping ratio, non-positive encoder resolution or noise level outside 0% to 100%.
Increasing damping ratio or control bandwidth decreases estimated settling time. Increasing move distance increases dynamic positioning error. Increasing target time, control bandwidth or encoder resolution decreases the calculated error contribution.
Calculation example
Example:
A user wants to verify whether a servo axis can move 0.5 m, settle within 250 ms and keep the positioning error below 0.001 m using cascaded control.
- x — Move distance = 0.5 m
- ttarget — Target time = 250 ms
- etarget — Target accuracy = 0.001 m
- fbw — Control bandwidth = 20 Hz
- ζ — Damping ratio = 0.7
- N — Encoder resolution = 10000 1/m
- η — Noise level = 5%
- Control mode = Cascaded control
Result: estimated settling time = 64.4 ms, positioning error = 0.0159 m, accuracy ratio = 15.9.
Assumptions and limitations
- The selected control mode is either position loop or cascaded control.
- Target time is entered in milliseconds and converted internally to seconds.
- Control bandwidth is converted to angular frequency using 2π · fbw.
- Settling time is estimated using 4 / (ζ · ωn).
- Cascaded control applies a 0.85 multiplier to the estimated settling time.
- Total positioning error is calculated as the root-sum-square of quantization error, dynamic error and noise-induced error.
- Damping ratio must be greater than 0.05 and lower than 2.
- Noise level must stay within the 0% to 100% range.