Servo Following Error & Bandwidth Requirement Analyzer
Calculate following error estimate using commanded acceleration, equivalent mass, servo bandwidth, position loop gain, and feedforward factor.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Control mode
Motion profile
System parameters
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
Following error estimate formula:
ω = 2 · π · f
Fdyn = m · a
Cservo = K · ω
e = (Fdyn / Cservo) · FF
e / emax = e / emax
ωreq = Fdyn / (K · emax)
freq = ωreq / (2 · π)
where:
- e — Following error estimate (length)
- e / emax — Tracking ratio (-)
- freq — Required bandwidth (frequency)
- ω — Angular servo bandwidth (rad/s)
- f — Servo bandwidth (Hz)
- Fdyn — Dynamic load (N)
- m — Equivalent mass (kg)
- a — Commanded acceleration (m/s²)
- Cservo — Servo capability (-)
- K — Position loop gain (-)
- emax — Max allowed following error (length)
- FF — Feedforward factor (-)
When to use this calculator
When to use this calculator:
- Estimate following error for a commanded acceleration profile before selecting servo loop settings.
- Check whether the estimated tracking error stays below the maximum allowed following error.
- Calculate required servo bandwidth from equivalent mass, commanded acceleration, position loop gain, and allowed error.
- Compare actual servo bandwidth against the bandwidth required for the selected motion profile.
- Evaluate the effect of velocity feedforward on the estimated following error when feedforward mode is enabled.
How to interpret the result
Following error estimate is defined as the estimated position tracking deviation produced by dynamic load relative to servo capability.
The tracking ratio depends on estimated following error and maximum allowed following error. A lower tracking ratio means the estimated tracking error uses less of the allowed error band.
- Safe — tracking ratio is below 0.7.
- Warning — tracking ratio is from 0.7 to 1.0.
- Invalid — tracking ratio is above 1.0, or an input condition is outside the valid range.
Required bandwidth is defined as the servo bandwidth needed to keep the estimated following error at the allowed error limit for the selected mass, acceleration, position loop gain, and maximum allowed following error.
Calculation example
Example:
A user checks whether a servo axis can follow a commanded acceleration profile without exceeding the allowed following error.
- Control mode: Velocity feedforward
- v — Commanded velocity: 0.5 m/s
- a — Commanded acceleration: 2 m/s²
- m — Equivalent mass: 20 kg
- f — Servo bandwidth: 25 Hz
- K — Position loop gain: 80
- emax — Max allowed following error: 0.005 m
- FF — Feedforward factor: 0.5
e = 0.00159 m, e / emax = 0.318, and freq = 0.995 Hz.
Assumptions and limitations
- Dynamic load is calculated as equivalent mass multiplied by commanded acceleration.
- Servo capability is calculated as position loop gain multiplied by angular servo bandwidth.
- Angular servo bandwidth is calculated from servo bandwidth using 2 · π · f.
- In position control mode, the feedforward factor is set to 1.
- In velocity feedforward mode, the feedforward factor must be greater than 0 and less than or equal to 1.