blockTimeConstantDelay

Calculate the time constant and the time delay of a first-order plus time-delay model

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 = ton/(ln((δ/|k|-yhig+exp(τ/(1 - τ))(yhig + ylow))/(yhig-δ/|k|))),

where yhig and ylow 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.

Parameters

TypeNameDefaultDescription
RealyHigHigher value for the output (assuming the reference output is 0)
RealyLowLower value for the output (assuming the reference output is 0)
RealdeaBanDeadband for holding the output value

Connectors

TypeNameDefaultDescription
Buildings.Controls.OBC.CDL.Interfaces.RealInputtOnLength for the on period
Buildings.Controls.OBC.CDL.Interfaces.RealInputkGain
Buildings.Controls.OBC.CDL.Interfaces.RealInputratRatio between the time constant and the time delay
Buildings.Controls.OBC.CDL.Interfaces.RealOutputTTime constant
Buildings.Controls.OBC.CDL.Interfaces.RealOutputLTime delay
Buildings.Controls.OBC.CDL.Interfaces.BooleanOutputtriFaiTrue when an error occurs in the autotuning process

Revisions

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