FAQ: What is steady state error?
From FBSwiki
(Contributed by Richard Murray, 15 November 2008)
Steady state error is a property of the input/output response for a linear system. If the desired value of the output for a system is r (a constant) and the actual output is y(t), the steady state error is defined as
The steady state error for a step response is often reported as a percentage of the input magnitude, similar to the overshoot Mp. Steady state error can also be defined for other types of signals, such as ramps, as long as the error converges to a constant. The steady state error is only defined for a stable system.
For a SISO linear system with state space dynamics
with A a stable matrix (eigenvalues have negative real part), the steady state error for a step input is given by
In the frequency domain, the steady state error for a step input to a unity gain, negative feedback system can be computed from the loop transfer function L(s) and is given by
