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Metrics for control objectives

Short answer

Metrics from step response: rise time (10-90% of final), peak time and overshoot percentage, settling time within a 2-5% band, steady-state error, stability/damping, disturbance rejection, and control effort. A good design has small rise time, minimal overshoot, short settling time, and near-zero steady-state error.

Explain the metrics used to measure control objectives.

Control objectives are measured with a set of performance metrics, mostly from the step response of the closed-loop system:

  1. Rise time (tr): time for the output to go from 10 % to 90 % of the final value. Measures speed of response.
  2. Peak time (tp) and overshoot (Mp): tp is the time taken to reach the first (maximum) peak; Mp is the maximum amount, usually in percent, by which the output exceeds the final value: Mp = (peak - final)/final × 100 %.
  3. Settling time (ts): time after which the output stays within a band (usually 2 % or 5 %) of the final value.
  4. Steady-state error (ess): final difference between set-point and output: ess = r - y(∞). Measures accuracy.
  5. Stability / damping: the output must remain bounded and any oscillation must decay (damping ratio, gain and phase margins).
  6. Disturbance rejection: size and duration of the output change caused by a disturbance.
  7. Control effort / robustness: size of the actuator output and sensitivity to parameter change.
 y
 |        _ Mp (overshoot)
 |   ____/ \___ ______ final value (+/-2% band)
 |  /          \/
 | /
 +--tr--------ts------- t

A good design has small tr, small overshoot, short ts and ess close to zero.

✓ Answer checked by Claude Opus 5.5 (high effort)

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