Calculation sequence
Step-by-step method
- Calculate step magnitude and peak overshoot.
- Calculate time from step to peak and settling.
- Compare overshoot and absolute final error with the user-entered screening criteria.
MechanicalAdvancedControls
PID Response Metrics Calculator
Calculate percent overshoot, peak time, settling time, and final error for a documented control response.
Why it matters: Response metrics help distinguish stable control from excessive overshoot, slow settling, or offset.
Calculated result
Engineering evaluation
Percent overshoot (OS)10 %
- Time to peak (tpd)
- 30 s
- Settling time (tsd)
- 120 s
- Final steady-state error (e)
- 1 process units
Engineering interpretation
The documented response has 10% overshoot, 30 s peak time, 120 s settling time, and final error 1 process units. Entered criteria are 10% overshoot and 2 process units final error.
Important limitations
- Trend sampling, filtering, deadband, noise, nonlinear equipment, saturation, disturbances, and the selected settling band affect these metrics.
Engineering knowledge center
Understand the calculation—not just the answer
Governing relationships
OS = (Ppeak−SP)/|SP−P0|×100
tpd = tp−t0
tsd = ts−t0
e = SP−Pfinal
compare |OS| with OStol and |e| with etol
Current substitution
OS = (110−100)/|100−0|×100 = 10%; tpd = 30 s; tsd = 120 s; e = 1; OStol = 10%; etol = 2.
Equation legend
Inputs and calculated quantities
- P0
- Initial process value — process units
- SP
- Final setpoint — process units
- Ppeak
- Peak process value — process units
- Pfinal
- Final settled value — process units
- t0
- Step start time — s
- tp
- Peak time — s
- ts
- Settled time — s
- OStol
- Entered allowable overshoot — %
- etol
- Entered allowable final error — process units
- OS
- Percent overshoot — %
- tpd
- Time to peak — s
- tsd
- Settling time — s
- e
- Final steady-state error — process units
Applications
How this calculation is used
Building design
Define control-response expectations.
Construction
Check trend sampling and tuning implementation.
Commissioning
Quantify a recorded step response against user-entered screening criteria without automatically assigning project acceptance.
Quality controls
Assumptions and limitations
Assumptions
- Entered data describe one stable operating condition and use consistent measurement boundaries.
- Time, energy, and performance values are representative of the stated interval.
Limitations
- This is a preliminary evaluation and commissioning-support tool, not an automatic acceptance determination.
- Project sequences, manufacturer data, tariffs, codes, and professional review remain controlling.
Field use
Verification procedure
- Confirm the operating mode, test boundary, and instrument calibration.
- Collect simultaneous readings or a documented trend interval.
- Compare the result with the approved sequence, submittal, and project criteria.
Common engineering mistakes
- Combining measurements from different operating modes or time intervals.
- Ignoring sensor uncertainty, trend sampling, or the defined equipment boundary.
Technical basis
References and source standards
- International Society of Automation ResourcesControl, instrumentation, alarm, and automation practice context; project sequences and current standards remain controlling.
- ASHRAE Handbook—HVAC Systems and EquipmentHVAC equipment, central-plant, air-system, and control-performance context; verify the licensed current edition during professional review.
- NIST Measurement and Calibration ResourcesFederal measurement, calibration, timing, and unit-system context.
Engineering calculation disclaimer
These engineering tools are provided for educational, preliminary evaluation, field verification, and commissioning support. Results depend on the accuracy of user-entered information and the assumptions stated for each calculation. Every colored status and comparison is a screening indicator only; project criteria, contract requirements, applicable codes, manufacturer instructions, measurement uncertainty, and authorized engineering judgment govern. The tools do not replace project-specific engineering analysis or the judgment of a licensed professional engineer.
Read the full use and limitation statement