IntermediateTopic 50 of 101Signals, Control & Comms
Steady-state error
Final error depends on system type and input; integrators remove it.
In depth
For unity feedback, final error depends on system type (number of integrators) and input: type 0: step error 1/(1+K_p); type 1: zero for step, 1/K_v for ramp; type 2: zero for ramp. Final value theorem e_ss=lim sE(s). Integral action eliminates constant error.
Key points
- Position, velocity, acceleration constants
- Disturbance steady-state error
- Type number
ExampleA type-1 positioning system follows a step reference with zero steady-state error.
What is Steady-state error?
Final error depends on system type and input; integrators remove it.
Why is it important to understand steady-state error?
Steady-state error shows whether a control system reaches the target accurately, which matters for setpoint tracking and disturbance rejection.
Why does an integrator remove steady-state error?
It accumulates the error over time, so a constant error keeps increasing the control action until the error is zero.
What depends on the system type?
The number of pure integrators in the open-loop transfer function sets the steady-state error for step, ramp and parabolic inputs.
How is Steady-state error used in practice?
Typical applications include checking that a motor speed controller holds its target under load, choosing an integrator in a loop to remove offset in a temperature control and specifying the tracking error for a ramp input to a machine axis.
What should I learn before Steady-state error?
Study "Time-domain specifications" first (topic 49 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Steady-state error?
Position, velocity, acceleration constants. Disturbance steady-state error. Type number.
Can you give an example of Steady-state error?
A type-1 positioning system follows a step reference with zero steady-state error.
What comes after Steady-state error?
The next topic is "Stability and Routh-Hurwitz", which builds directly on this one.
How difficult is Steady-state error?
It is classed as Intermediate in Signals, Control & Comms (topic 50 of 101). It is an intermediate topic. Work through the beginner topics in Signals, Control & Comms first.