A linear position servomechanism compares a commanded position with measured feedback, forms signed error, and drives an actuator through a closed feedback path. The retained calculator is a static error and sampling-arithmetic reference, not a performance simulation.
Linear Servomechanism Static Error and Sampling Reference
Explore exact selected linear error and sampling arithmetic without inferring servo dynamics or accuracy.
Equation Used
- Command and feedback use the same linear coordinate and millimetre scale.
- Sampling rate is constant over the selected interval.
- The interval count may be fractional for arbitrary inputs, though the provided slider produces whole counts.
- Dynamics, performance, accuracy, loads and safety are excluded.
The selected observation interval is not a measured or predicted settling time.
Connected linear feedback topology
Command and measured carriage position enter a summing junction. A controller drives the actuator, while the position sensor returns the carriage coordinate through the feedback path. The animation moves one physically connected carriage between the two selected coordinates as an illustrative comparison sweep.
What the calculator determines
Select command and feedback positions, sampling rate and a selected observation interval. The calculator reports signed error in millimetres and micrometres, exact sample period, and the number of sample intervals in the selected observation window.
Static error and sampling identities
e = C − F; eµm = 1000e; Ts = 1000/f milliseconds; and N = ft/1000 for t entered in milliseconds.
Selected-input arithmetic
At C = 130 mm, F = 125 mm, f = 8,000 Hz and t = 10 ms, error is 5 mm or 5,000 µm, sample period 0.125 ms and the selected interval contains 80 sample periods.
Model boundary
N is only a time-base count; it is not a settling-update prediction. The model does not include controller law, plant dynamics, stability, bandwidth, delay, jitter, resolution, quantization, saturation, accuracy, load, friction, compliance, backlash, disturbance rejection or safety.
Questions
Does the interval count predict settling?
No.
Does zero selected error prove accuracy?
No.
Is the carriage motion a time response?
No; it is an illustrative coordinate sweep.
References & Further Reading
- Wikipedia contributors. Servomechanism. Wikipedia
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