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What is Steady-state error?

The difference between the setpoint and the controlled variable that remains after the response of a control system has settled; it is also called offset. In a unity-feedback system it is 1/(1 + Kp) for a step setpoint, where Kp = G(0) is the position error constant, and it does not become zero in a system with no integrator in the forward path (type 0). In a type 1 system, with one integrator, the steady-state error to a step is zero, and an error of 1/Kv (Kv is the velocity error constant) remains for a ramp setpoint. The integral action of PI control is used to remove this error.

Japanese name: 定常偏差

Steady-state error appears in 5 practice questions across 1 topic, including Control Engineering Basics.

Field: Control Engineering Basics

Try it: questions about Steady-state error

In a unity-feedback system the forward transfer function is G(s) = 9/(1 + 2s). Which of the following is the steady-state error for a step setpoint of size 1?

  1. A0
  2. B0.1
  3. CAbout 0.11
Show answer and explanation

Answer: B. 0.1

For a unity-feedback system, the steady-state error to a step is 1/(1 + Kp), where Kp = G(0) is called the position error constant. Here Kp = 9, so the steady-state error is 1/(1 + 9) = 0.1. In a system whose forward path has no integrator (a type 0 system), raising the gain makes the error smaller but not zero. To bring the error to zero, an integrator is added, for example with PI control.

In a unity-feedback system with a stable closed loop, the forward transfer function G(s) contains one integrator 1/s (a type 1 system). Which of the following correctly describes the steady-state error?

  1. AThe steady-state error to a step setpoint is zero, while a constant error remains for a ramp setpoint that increases at a constant rate
  2. BA constant steady-state error remains even for a step setpoint, and for a ramp setpoint the error keeps growing larger and larger with time
  3. CThe steady-state error is zero for all of a step, a ramp and a setpoint increasing with constant acceleration
Show answer and explanation

Answer: A. The steady-state error to a step setpoint is zero, while a constant error remains for a ramp setpoint that increases at a constant rate

The number of integrators in the forward path is called the type of the system. In a type 1 system, any remaining error keeps the integrator changing the manipulated variable, so the steady-state error to a step is zero. To keep following a ramp setpoint, a constant error is needed, of size 1/Kv, where Kv = lim[s→0] sG(s) is the velocity error constant. For example, G(s) = 2/(s(s + 1)) has Kv = 2, and the steady-state error to a unit ramp is 0.5.

Steady-state error in the explanations

Questions that mention Steady-state error (5)

  1. In a unity-feedback system the forward transfer function is G(s) = 9/(1 + 2s). Which of the following is the steady-state error for a step setpoint of size 1?
  2. In a unity-feedback system with a stable closed loop, the forward transfer function G(s) contains one integrator 1/s (a type 1 system). Which of the following correctly describes the steady-state error?
  3. Which of the following correctly describes the Bode plot of an integrator G(s) = 1/s?
  4. A plant that contains no integrator (a type 0 system) is under proportional (P) control. Which of the following correctly describes the general change when the proportional gain Kp is increased?
  5. Which of the following is the correct pair of the main purpose of adding integral (I) action in PI control and its side effect?

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Semiconductor, Electronics and Computing Calculators

PID step response simulatorSee the step response and control effort for a plant and your P, I and D gains

Related terms

Transfer function PID control Phase margin Overshoot Bode plot Block diagram Feedback control Feedforward control First-order system Gain margin

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