`Efficiency`

definition

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module: IndisputableMonolith.Safety.DampeningField
domain: Safety
line: 37 · github
papers citing: none yet

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IndisputableMonolith.Safety.DampeningField on GitHub at line 37.

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formal source

  34
  35/-- Effect of Phase Slip on Efficiency.
  36    Efficiency drops exponentially with phase error. -/
  37def Efficiency (phase_error : ℝ) : ℝ :=
  38  Real.exp (-phase_error ^ 2)
  39
  40/-- Safety Theorem: De-tuning prevents runaway. -/
  41theorem DetuningStopsRunaway (rpm rpm_limit : ℝ) :
  42  let slip := Governor rpm rpm_limit
  43  let eff := Efficiency slip
  44  rpm > rpm_limit → eff < 1 := by
  45  intro slip eff h_over
  46  simp [slip, Governor, h_over]
  47  -- exp(-0.1^2) = exp(-0.01) < 1
  48  exact Real.exp_lt_one_iff.mpr (by norm_num)
  49
  50end DampeningField
  51end Safety
  52end IndisputableMonolith

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