Velocity Error Constant⚠ unverified

Physics / Controls · Compute the steady-state error from the velocity error constant

Parameters

Input	Symbol	Unit	Default	Description
kv	kv	—	1.0	Velocity error constant (Kv)

Output	Symbol	Unit	Description
result	ess	—	Steady-state velocity error. Returns infinity when kv is zero

$K_v$ — larger $K_v$ → smaller ramp error. Type 1 systems have finite $K_v$; type 0 have $K_v=0$ ($e_{ss}\to\infty$ for a ramp); type ≥2 have infinite $K_v$ (zero ramp error).
$e_{ss}$ — $1/K_v$ for unit ramp; scale linearly with ramp slope.

With $R(s) = 1/s^{2}$ and $E(s) = R/(1+G)$, the final-value theorem gives $e_{ss} = 1/K_v$ when $K_v = \lim_{s\to 0} s G(s)$ is finite and positive.

$K_p$, $K_v$, $K_a$ error constants classify servo accuracy by system type in classical control.

Related Concepts: Acceleration Error Constant, Pid Output, Phase Margin

Notes: Registry calculator velocity-error-constant (unverified). Computes $e_{ss}=1/K_v$, not $K_v$ from $G(s)$.