Servo Position and Power Budget Calculation Audit

Servo Position and Power Budget Calculation Audit

Ada re-derives this chapter’s own numbers step by step, at full precision

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Ada ADA · CALCULATION AUDIT

Servo Position and Power Budget Calculation Audit

Commanding a servo to 45 degrees inside its 20 ms frame is just a 1.25 ms pulse at 6.25% duty — deceptively cheap, until three MG996R servos moving together pull 7.5 A, roughly 15x what a 0.5 A ESP32 pin can source. This audit rebuilds the pulse, current, torque, and deadband figures and asks whether the feared brownout is really a PWM-frequency problem or simply a current-limit one.

Companion to the chapter Servo Motors — every number here comes from that chapter.

— pulse timing, current, torque, and deadband, ~4 minutes

A servo looks simple because the command is one pulse, but the audit has two ledgers: the mathematics that maps pulse width to angle, and the physics that decides whether the supply, gearing, and linkage can survive the requested motion.

See the relationship before changing it

The figure reads from left to right. The blue card is command angle. The middle card applies this page's rule. The green card is pulse width. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only command angle, so the numeric fixture does not switch without explanation.

Command angle changes pulse width An input card leads through the rule pulse = 1 ms + angle / 180 degrees x 1 ms to the pulse width result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. The pulse encodes position inside the frame; it is not the motor power duty cycle.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 45 degrees.

  2. 2

    Name the relationship. pulse = 1 ms + angle / 180 degrees x 1 ms

  3. 3

    Substitute with units. 1 + 45 / 180 = 1.25 ms

  4. 4

    Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change command angle

Try Predict the direction of pulse = 1 ms + angle / 180 degrees x 1 ms. Test another command angle, then compare pulse width.

45 degrees
Chapter baseline
Pulse width

Observe The pulse encodes position inside the frame; it is not the motor power duty cycle. Reset command angle to 45 and compare pulse width.

Explain The pulse encodes position inside the frame; it is not the motor power duty cycle.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only command angle moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only command angle. It is not a field prediction.

The worked checks

Check Arithmetic from this chapter Review result
Frame timing 50 Hz means T = 1 / 50 = 0.020 s = 20 ms. The pulse-width command is measured inside a 20 ms frame; it is not motor-power duty cycle.
45 degree command t = 1 ms + (45 / 180) x (2 ms - 1 ms) = 1.25 ms; duty = 1.25 / 20 = 6.25%. The angle interpolation uses the stated 1-2 ms, 0-180 degree convention.
Smooth 1 s sweep 50 frames/s x 1 s = 50 commands; 180 degrees / 50 = 3.6 degrees per frame. The motion profile should send small angle changes instead of one large mechanical shock.
Two-second actuation energy (0.5 A x 5 V x 1 s) + (0.1 A x 5 V x 1 s) = 2.5 J + 0.5 J = 3.0 J; 3.0 / 3600 = 0.000833 Wh. The chapter's 0.00083 Wh value comes from full-precision joules before final rounding.
Four MG90S peak current 4 x 0.700 A = 2.8 A; with ESP32 Wi-Fi current, 2.8 A + 0.240 A = 3.04 A. A 3 A rail is only adequate if movement is staggered; simultaneous stall needs more margin.
MG996R three-servo worst case 3 x 2.5 A = 7.5 A; 7.5 A is 15 x a 0.5 A ESP32 5 V pin limit. The brownout warning is a current-limit problem, not a PWM-frequency problem.
Torque margin 3 kg-cm = 3 x 9.81 N x 0.01 m = 0.294 N m; 0.294 / 0.12 = 2.45. The vent example has about 2.45x ideal torque margin before friction, supply sag, and gear wear.
Deadband size 5 microseconds x 0.18 degrees/microsecond = 0.9 degrees. A small no-correction window prevents jitter; making it too wide hides real position error.

Use this as a review record, not a promise. If the servo model, linkage length, travel stops, supply voltage, or move schedule changes, rerun the pulse, current, and torque checks with measured values.

Every number above is taken from the chapter’s own examples and re-derived step by step.

TryRecompute the 45-degree pulse width, duty, and three-servo current demand.
ObserveThe command is 1.25 ms in 20 ms, but three moving servos can demand 7.5 A.
ExplainThe brownout risk is a supply-current problem, not a PWM-frequency problem.
Technical boundaries. The audit assumes a linear pulse-to-angle map and simultaneous stated servo currents. It does not model servo calibration, mechanical load, acceleration, stall duration, cable drop, regulator transients, PWM jitter, deadband variation, or motion feedback.
Audit result

1.25/20 = 6.25% duty, while 7.5 A is 15 times a 0.5 A source capability; separate power is required.