Step Response Metrics (Overshoot / Settling Time / Steady-State Error)

A set of numbers measuring how fast, how stable, and how accurately a system's output reaches a target after a sudden change.

Step response metrics evaluate how well a closed-loop controller is tuned: suddenly change the target value from one level to another (a step input), record how the output changes over time, and read off several numbers. Rise time is how long the output takes to go from 10% to 90% of the total change; overshoot is the percentage by which the output peaks past its final value; settling time is how long until the output stays within roughly 2% (sometimes 5%) of the final value for good; and steady-state error is the remaining gap between output and target after a long time. These trade off against each other: raising Kp speeds up the response but increases overshoot, while raising damping suppresses overshoot but slows the response; pure proportional control tends to leave a steady-state error, which adding an integral term can eliminate. These metrics are used when tuning joint PD gains and when comparing simulated response against real hardware.

ExampleCommanding a joint from 0 rad to 1 rad: the output peaks at 1.13 rad, about 15% above the final settled value of 0.98 rad, i.e., roughly 15% overshoot; after 0.3 seconds it stays within 2% of 0.98 rad, giving a settling time around 0.3 seconds; the final gap from the 1 rad target, 0.02 rad, is the steady-state error.

Also called

Overshoot, Settling Time, Steady-State Error, Rise Time

Related

Proportional-Integral-Derivative Control · Proportional-Derivative Control · Stiffness and Damping Gains · Damping Ratio · Integral Windup / Anti-windup · Control Bandwidth

Sources

MATLAB stepinfo 文档（RiseTime / SettlingTime / Overshoot 定义） (Chinese)
Wikipedia: Settling time
Wikipedia: Steady-state error