A position servomechanism compares a commanded position with a measured output position, forms an error, and uses a controller and actuator to influence the output through a closed feedback loop.
Servo Static Error and Proportional-Command Reference
Explore exact static servo-loop arithmetic without inferring closed-loop dynamics or performance.
Equation Used
- Command and measured position use the same angular reference and units.
- The proportional command is unsaturated and has the units implied by the selected gain.
- Encoder scale is uniform over one 360-degree revolution.
- Dynamics, stability, limits, mechanics and safety are excluded.
Encoder count difference is an ideal real-valued angular conversion and does not model device-specific quantization or wrap.
Command, comparison, actuation and feedback
The selected command r enters a summing junction and measured output y returns through the feedback path. Their signed difference e = r − y enters a proportional block, whose selected static output is u = Kpe. NASA actuator documentation describes this command-versus-actual-position comparison and the resulting motor command.
The animation keeps the signal path physically connected and moves the output arm between selected actual and command angles as an illustrative comparison sweep. It is not a simulated transient response.
What the calculator determines
Select command and measured angles, proportional gain and encoder counts per revolution. The calculator reports signed error, absolute error, the unsaturated proportional command, and the equivalent signed count difference.
Static loop arithmetic
e = r − y. Absolute error is |e|. For the selected proportional-only reference, u = Kpe. With CPR counts per 360°, the equivalent count difference is e·CPR/360.
Selected-input arithmetic
At r = 90°, y = 72°, Kp = 0.08 V/degree and CPR = 4,096, signed error is 18°, absolute error 18°, unsaturated proportional command 1.44 V, and equivalent count difference 204.8 counts.
Model boundary
This is an instantaneous arithmetic snapshot. It does not close a plant model or predict convergence, stability, bandwidth, rise time, settling time, overshoot, steady-state error, torque, speed, saturation, current, backlash, compliance, disturbance rejection, sampling, quantization noise or safety.
The count result is a real-valued conversion; a specific encoder interface may quantize, wrap, decode quadrature differently or use a different zero reference.
Questions
Does a larger Kp always improve the servo?
No. Stability and performance depend on plant and loop dynamics absent here.
Does the animation show settling time?
No.
Are fractional encoder counts physically reported?
Not necessarily; the value is an ideal angular conversion before device-specific quantization.
References & Further Reading
- Wikipedia contributors. Servomechanism. Wikipedia
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