Steady State Error Calculator

Analyze position, velocity, and acceleration error constants easily. Compare step, ramp, and parabolic responses visually. Built for quick checks, learning, reporting, and design.

Calculator Inputs

Response Visualization

This chart compares the available steady state error constants used in control system tracking analysis.

Example Data Table

Case System Type Input Gain K Dominant Constant Estimated Error
Case 1 Type 0 Step 10 Kp = 10 0.0909
Case 2 Type 1 Ramp 12 Kv = 12 0.0833
Case 3 Type 2 Parabolic 18 Ka = 18 0.0556
Case 4 Type 1 Step 8 Kp = Infinity 0.0000

Formula Used

Steady state error depends on the input type and the control system type. The classical static error constants are:

Position constant: Kp = lims→0 G(s)H(s)
Velocity constant: Kv = lims→0 sG(s)H(s)
Acceleration constant: Ka = lims→0 s²G(s)H(s)

For common standard inputs:

Step input: ess = A / (1 + Kp)
Ramp input: ess = A / Kv
Parabolic input: ess = A / Ka

In this calculator, the effective gain is estimated using: Keffective = K × H × Plant × Controller × Sensor. Then the selected system type maps that gain into Kp, Kv, or Ka.

Transfer function label entered: G(s)H(s) ≈ (K) / (s(s+2)(s+5))

How to Use This Calculator

  1. Select the system type based on the number of poles at the origin.
  2. Choose the reference input form: step, ramp, or parabolic.
  3. Enter amplitude and loop gain related factors.
  4. Adjust feedback, plant, controller, and sensor multipliers if needed.
  5. Optionally label the transfer function expression for documentation.
  6. Press Calculate Error to show results above the form.
  7. Review Kp, Kv, Ka, steady state error, and plotted values.
  8. Use the CSV or PDF export buttons for reporting.

FAQs

1. What is steady state error?

Steady state error is the remaining difference between the input and output after transient effects fade. It shows long-term tracking accuracy in a control system.

2. Why does system type matter?

System type determines how many pure integrators exist in the open loop path. That directly affects whether step, ramp, or parabolic inputs produce zero, finite, or infinite error.

3. What does Kp represent?

Kp is the position error constant. It is mainly used for step input analysis and helps estimate the final steady state error for position tracking.

4. When is steady state error zero?

It becomes zero when the relevant static error constant is infinite for the selected input type. For example, a Type 1 system has zero step error.

5. Can this calculator handle custom transfer functions?

This version lets you document a transfer function label and estimate results from system type and gain factors. It is useful for engineering checks and learning workflows.

6. What does infinite steady state error mean?

Infinite error means the system cannot track the selected input with bounded final error. This often appears when the needed static error constant is zero.

7. Why include controller and sensor gains?

Those values help form a broader effective loop gain estimate. That makes the calculator more flexible for practical closed loop approximation and comparison.

8. What is the main engineering use?

It helps compare tracking performance during control design, tuning, and reporting. Engineers use it to judge whether the final accuracy meets system requirements.