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Rigid-Body Rotational Dynamics (Tank Spin System):

Tank Specs:

  • Material → 304L Stainless Steel
    Length → 15 cm
    Radius → 4 cm
    Thickness → 0.5 cm
    Mass → 1.143 kg

Configuration:

  • Thin-walled cylindrical tank approximation
    Instrumented with internal thermocouples
    Sealed end-cap with wiring feedthrough

Moment of Inertia (Izz):

  • Izz = mR²
    Izz = (1.143 kg)(0.04 m)²
    Izz = 0.001829 kg·m²

Drive Torque:

  • τ = 0.840 N·m

Angular Acceleration:τ = Iα → α = τ / I

  • α ≈ 459.4 rad/s²

Spin Rate Requirement:

  • 2–3 RPM
    ω ≈ 12.57 – 18.85 rad/s

Spin-Up Time:

  • t = ω / α
    t ≈ 27 – 41 ms

Power Estimate:

  • P ≈ 6.5 W

Motor / Servo Notes:

  • Torque–speed curve limits max RPM
    Servo must provide ≥ 0.84 N·m stall torque
    Continuous power ≥ 6.5 W

Design Task:

  • Evaluate 4 candidate servos from electrical spreadsheet →
    Compare torque, speed, power, and mass to select optimal model.


4.2

4.3

5.1

Sensor Inventory

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FDIR = Continuously:

  1. Observe system state

  2. Compare to model/expectations

  3. Flag anomalies

  4. Enter a safe mode

  5. Attempt recovery

  6. Only return to nominal when consistent

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