control//step response//steady-state error

Steady-state error is the gap left between setpoint and output once a loop has finished responding, and it is the accuracy figure of a control loop: a temperature loop that settles at 176 degrees for a setpoint of 180 has a steady-state error of 4 degrees. Whether a loop has one is decided by its structure rather than by fine tuning, which is why it is checked first.

Steady-state error is the gap left between setpoint and output once a loop has finished responding, and it is the accuracy figure of a control loop: a temperature loop that settles at 176 degrees for a setpoint of 180 has a steady-state error of 4 degrees. Whether a loop has one is decided by its structure rather than by fine tuning, which is why it is checked first.

The rule counts integrators. A loop with no integrator between error and output (a proportional controller on a plant that settles) needs some error to keep its actuator away from zero, so it settles with an offset under a constant setpoint or load; with plant gain KKK and proportional gain KpK_pKp​, a unit step leaves 1/(1+KKp)1/(1+KK_p)1/(1+KKp​). One integrator in the loop, in the controller or in the plant, removes the error to a constant setpoint, and it takes two to remove the error to a ramp. Control texts call the number of integrators the system type.

Where the integrator sits matters for disturbances. An integrator in the plant (a motor driven to a position) removes the error to a setpoint step but not the error caused by a constant load torque, which enters before it; only an integrator in the controller cancels a constant load (integral action).

Droop is the same offset used on purpose. Generators sharing a grid each run a proportional speed controller with a droop of a few percent, so that a change of load is shared among them in proportion to their ratings instead of being fought over by integrators.

?If integral action removes the error, why run a loop without it?

Because some loops gain from the offset. A level in a buffer tank only has to stay between limits, and a proportional controller lets it float, absorbing changes of flow instead of passing them downstream; droop on generators is the same idea. A loop without an integrator is also simpler to tune and cannot wind up.