A controller is often judged by how the closed-loop output responds after a reference or disturbance changes.

For a step response, common transient specifications include:

• rise time: how quickly the response moves toward its final value;
• peak overshoot: how far it exceeds the final value;
• settling time: how long it takes to remain within a specified tolerance band;
• steady-state value: the value approached after transients decay.

These quantities summarize different aspects of performance. A faster response is not automatically better if it produces excessive overshoot, actuator demand or sensitivity to noise.

For systems dominated by a pair of second-order poles, damping ratio strongly influences overshoot while natural frequency sets the main time scale. Higher-order systems can often be interpreted through dominant poles when the remaining modes decay much faster.

Performance specifications translate qualitative requirements such as “fast but not oscillatory” into measurable properties that a controller can be designed to satisfy.