Steady-State Error Calculator
G(s) = 10/[s(s + 1)(s + 5)] is type 1 with K_v = 2, so a unit ramp leaves a steady-state error of 0.5.
For G(s) = 10(s + 2) ÷ [s(s + 1)(s + 5)] enter numerator 10, 20.
s(s + 1)(s + 5) = s³ + 6s² + 5s → 1, 6, 5, 0.
0.5
- System type (poles at s = 0)
- 1
- Position constant Kₚ
- ∞
- Velocity constant K_v
- 2
- Acceleration constant Kₐ
- 0
Step-by-step solution
- Type 1: 1 pole at the origin; gain K = 2
- e_ss = A ÷ K_v = 1 ÷ 2
- e_ss = 0.5
Steady-State Error Formula
e_ss = A/(1 + Kₚ), A/K_v, A/Kₐ
Kₚ = lim G(s), K_v = lim sG(s), Kₐ = lim s²G(s) as s → 0
Worked Example
G(s) = 10 / [s(s + 1)(s + 5)] with a unit ramp input:
- Type 1: 1 pole at the origin; gain K = 2
- e_ss = A ÷ K_v = 1 ÷ 2
- e_ss = 0.5
Position constant Kₚ: ∞ · Velocity constant K_v: 2 · Acceleration constant Kₐ: 0
GATE tip
Expand factored forms carefully: s(s + 1)(s + 5) = s³ + 6s² + 5s. The gain in the error constants uses the TIME-CONSTANT form, so K_v = 10/5 = 2 here, not 10.
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Example: The characteristic equation s⁴ + 2s³ + 3s² + 4s + 5 = 0: Result: Unstable: 2 roots in the right half-plane.
Frequently asked questions
What is the system type?
The number of integrators (poles at s = 0) in the open loop. Type 0 has finite step error, type 1 zero step error and finite ramp error, type 2 zero ramp error.
Why check stability?
The final value theorem only holds if the closed loop settles. An unstable loop has no steady state, whatever the formula says.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Steady-State Error Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/steady-state-error-calculator/
IEEE
Scientific Converters, "Steady-State Error Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/steady-state-error-calculator/