steadystatefeil

Steady-state error, also known as steadystatefeil in Danish-language sources, is the difference between the input reference and the actual output of a closed-loop control system as time tends to infinity. It measures how accurately a system can track a reference signal in the steady state and is influenced by the system’s type, feedback configuration, and disturbances.

In standard feedback systems, the steady-state error to common reference inputs depends on the open-loop transfer function G(s) and the resulting system type, defined by the number of integrators in the forward path. Let Kp = lim s→0 G(s), Kv = lim s→0 s G(s), and Ka = lim s→0 s^2 G(s) for a unity feedback loop. For a unit step input, the steady-state error e_ss is 1/(1+Kp) for Type 0 and becomes zero for Type 1 or higher. For a ramp input, e_ss is infinite for Type 0; equals 1/Kv for Type 1; and is zero for Type 2 or higher. For a parabolic input, e_ss is infinite for Type 0 and Type 1; equals 1/Ka for Type 2; and is zero for Type 3 or higher.

Reducing steadystatefeil typically involves adding integral action to the controller (increasing the system type), which yields zero error to a step and improves tracking of ramps. Other approaches include increasing loop gain with caution to avoid instability, using lead or lag compensation, or incorporating feedforward control to counter known disturbances.

Limitations include sensitivity to measurement noise with integral action, model uncertainty, nonlinearities, and actuator saturation. The concept remains a central performance criterion in control design and analysis.