.Buildings.Controls.OBC.Utilities.PIDWithAutotuning.SystemIdentification.FirstOrderTimeDelay.BaseClasses.TimeConstantDelay

Information

This block calculates the time constant and the time delay of a first-order plus time-delay (FOPTD) model.

Main equations

The time constant, T, is calculated by

T = t_on/(ln((δ/|k|-y_hig+exp(τ/(1 - τ))(y_hig + y_low))/(y_hig-δ/|k|))),

where y_hig and y_low are constants related to an asymmetric relay output. ton is the length of the on period of the same asymmetric relay output. δ is the dead band of the same asymmetric relay output. k is the gain of this FOPTD model. τ is the normalized time delay.

The time delay, L, is calculated by

L = T τ/(1 - τ),

References

J. Berner (2017). "Automatic Controller Tuning using Relay-based Model Identification." Department of Automatic Control, Lund University.

Revisions

• March 8, 2024, by Michael Wetter:
  Changed deadband to be consistent within the package.
• June 1, 2022, by Sen Huang:
  First implementation.